tag:blogger.com,1999:blog-57035688076152638512018-05-26T03:47:29.463-07:00How to Prepare for the Gifted And Talented TestGAT tests measure cognitive skills but schools don't teach them. This site helps parents identify the material, teach the skills, and not only gain GAT entry but succeed in the program.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.comBlogger239125tag:blogger.com,1999:blog-5703568807615263851.post-84324892713894073412018-05-19T09:38:00.000-07:002018-05-24T17:58:59.704-07:00100% GAT GuaranteedThere is a 100% guaranteed chance that your child will meet their GAT goals if you just follow the secret formula.<br /><br />Last week, I surveyed the last few years of education and cognitive psych research. Most of this is funded by the NIH and NSF and a few new government acronyms. I did not find a single paper with a research topic that is pertinent to learning, early education, or what it takes to succeed academically. There were a few papers about how to learn cognitive skills by researchers who obviously have never met a child before. An actual parent learns more in 10 minutes of trying to teach their child how to read CAT than any 3 papers on learning.<br /><br />So when I say there's 100% chance your child can become GAT, it's simply due to the depressing situation that the United States is against teaching pre-school kids any useful skills.<br /><br />If you take any paper title, and add 'because we don't teach our 4 year old's to read' you will have an accurate picture of education in the United States. I downloaded the papers from research.gov and found things like 'Comparing a practice based curriculum to an experiential curriculum ... because we don't teach our children to read', or 'Evaluating training methods for teachers...because we don't teach our children how to read.' There quite a few reform minded engineering education papers that should end with '...because we spend too much time spoon feeding math instead of teaching problem solving skills'.<br /><br />When is the United States going to wake up and realize that spending $300 million each year trying to figure out how teachers can make up for lack of reading at home is a waste of money?<br /><br />Jim Trelease, the author of The Read Aloud Handbook and hero to many GAT parents, bemoaned the fact that he went to Washington and was drummed out of town for being an advocate of reading in school.<br /><br />You know that the secret formula for GAT is simply to start acting like a GAT family, make your child read, learning problem solving skills, do some advanced math on a routine basis, and have completely different attitude about the whole endeavor which you can find in my articles. Many parents blow it by confusing lots of work with making progress, when in fact the more classes you go to and the more workbooks you do, the less skills your child will end up with. The irony.<br /><br />I should probably mention this distinction instead of assume it. Non-GAT children score really high on tests and get A's in school because they have memorized and practiced their way to a high level of academic achievement. GAT children score really high on tests and get A's in school because they've learned the skills to figure out things on the spot with no prior work. Think of GAT children as lazy underperformers who know how to cheat without help. I don't know any kids in a GAT program who are simply hard workers, but I know a lot of kids trying to get into GAT programs who spend a lot of time sitting in classes and doing worksheets.<br /><br />This is an important distinction because GAT children, who will invent things and solve unsolved problems need to know where all of the Non-GAT children are so they can hire them to actually do the work.<br /><br />Speaking of GAT, yesterday I found out that my 7th grader is more prepared for college than 63% of high school juniors and seniors in the US. If you've been following my articles recently, you know why I know this and also why I'm reluctant to discuss it. My second thought was 'I need to publish what we did because it was really cool' and my third thought was 'but I can't right now because the little brother wants to go to Stanford'.<br /><br />My first thought was - Oh my gosh, his reading score is higher than his math score. That on it's own is the single biggest determiner of success. I'm really proud. I think I had tears in my eyes. We spent a lot of time working on that over the last 2 years and it's really hard. I wasn't even going to try, but I keep getting emails from someone who is doing EDM Grade 2 with her little one, and it's a constant reminder of why, how, and yeah you can do it. It always pays off. Next year we're going to spend 100% of our time on writing - no math at all.<br /><br />This weekend, we have to fill in some gaps in math, but getting a high score in math is not hard. We have a permanent advantage here, practically cheating. Thanks to Test Prep Math in 2nd, 3rd, and a bit of fourth grade, we spent all of our time at this age on thinking skills and zero time on decimals and long division. There's no question this is behind the reading score as well. This means that I've got a child with the skills to learn 3 or 4 new maths in about 5 days. I know we covered this stuff before, but we don't really practice it. It's more just fun looking at and figuring out confusing things, which is what GAT is all about.<br /><br />We went through each missed question, and here's how the conversation went:<br /><br />What is the answer to this question you missed.<br /><br /><i>It's B.</i><br /><br />Why did you mark A?<br /><br /><i>Because my brain was fried by the half way point.</i><br /><br />Ok, that's fair. Why did you miss this one?<br /><br /><i>Because I don't know what f(0, 3) means.</i><br /><br />I don't either. (If any readers know what this is, please leave a comment. I have no idea. Is it supposed to be a multivariate question? How is a 7th grader taking the SAT supposed to know that?)<br /><br />What about this question?<br /><br /><i>How am I supposed to do that?</i><br /><i><br /></i>We've got 5 days to figure it out.<br /><br />Most of the questions on the math section we're very tricky in a strictly verbal way, as in spending a lot of time reading the question, even for me, and keeping 3 distinct concepts in working memory and coordinated. There was very little in the way of advanced math.<br /><br />Let's back up a little and you can see why I'm not really all that worried about the math section:<br /><br /><ol><li>Son some how gets into GAT program even though his score is 10 points behind cutoff. I'm not kidding. The school was desperate to fill the seat a month after school started. We were dumb enough to accept.</li><li>Parent decides it would be nice if other child could go there to cut down on driving each day. Plus parent frantic about other son surviving his program which turned out to be accelerated by 2 years. What a cataclysmic disaster that could have been.</li><li>Parent reads papers from author of COGAT, notes that working memory and reading are really important.</li><li>Parent reads 5,000 pages of other research on problem solving and determines that heavy doses of confusion also play a role, not to mention core problem solving skills.</li><li>Parent notes that all math books are spoon-feeding and devoid of problem solving skills and working memory.</li><li>Parent writes 4 math books that are all confusion and problem solving. More verbal than math. 4th math book is a phonics book. Now you know.</li><li>Parent's totally unprepared 7th grader does well on college entrance exam, well enough to go to college, just not Harvard.</li><li>Parent looks at test and answers (they do that nowadays) and finds a 100% correlation between early training and current test. I've explained in past articles why this is the case - advanced math is not a good predictor of college success, overcoming trickery is.</li><li>Parent hides good advice on bottom of blog articles and does no marketing at all on books.</li><li>Younger brother who gets all of the benefits of older brother's experiments is going to send his 7th grade test scores to Stanford.</li></ol><div>Then I'll go public.</div><div><br /></div><div>The 7th grader last night asked if he could take AP calculus in high school. </div><div><br /></div><div>He meant freshman year.</div><div><br /></div><div>It broke my heart to tell him 'No, probably not until sophomore or junior year without summer school, but when you take it I don't expect it to be hard.' He's just too darn slow at math to skip high school trig.<br /><br /> </div><br /><br /><div style="text-align: center;"><br /></div><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com1tag:blogger.com,1999:blog-5703568807615263851.post-83424741371651141092018-05-06T13:27:00.001-07:002018-05-11T16:24:10.563-07:00Competitive Parent Magazine Issue #1<div style="background-color: #d49a6a; color: #003333; font-size: 3em; padding: 20px 10px 20px 10px; text-align: center;">Competitive Parent Magazine</div><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; padding: 20px 10px 20px 10px;"><div style="display: inline-block; text-align: center; width: 45%;">Sunday, May 6 2018</div><div style="display: inline-block; text-align: center; width: 45%;">Issue #1</div></div><div style="color: #404040; font-size: 0.9em; margin: 20 10 30 10;"><br />So little time, so many topics. I've referenced Competitive Parent Magazine in the past because it has an annual award called The Pettie that I usually win after careful consideration by the panel of judge, who is me. This year is probably going to be different, because there are parents out there fighting battles that leave me in awe. But we just sat for the SAT. For fun. Anyway, I've taken this week's articles and added them all to the inaugural issue of Competitive Parent Magazine.<br /><br /></div><div style="background-color: #fff8e8; color: #003333; padding: 5 0 5 0;"><div style="text-align: center;"><b>In this issue</b> </div><ul style="list-style-type: square; margin-left: 10%;"><li>Teaching Half Matrices to 4 Year Olds</li><li>Start Your Rigorous Summer GAT Program Now</li><li>Putting the Skittles and the PS4 In The Closet</li><li>Northwestern & Duke Summer Programs</li><li>Trig at Age 9 - A Bookend</li><li>Developing a Writer</li></ul></div><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; margin-bottom: 10px; padding: 20px 10px 20px 10px;"><div style="font-weight: bold; text-align: center;">Teaching Half Matrices to 4 Year Olds </div></div>A Power Mom asked me this question: <i>Are 4 year olds expected to 'get it' with the halving and doubling in Shape Size Color Count? My 4 year old isn't getting it.</i> <br /><br />I've been delaying answering in the hopes that he gets it. I've worked with this boy before and he's extremely bright. The answer is of course no and yes, and it is a very good example of what it takes to develop cognitive skills at any age. <br /><br />For starters, let's jump ahead in Shape Size Color Count to lesson 85. The premise behind half matrices is simple:<br /><br /><ul><li>They're on the COGAT. We needed a score of 99.8 to get into a GAT program.</li><li>My 3.92 year old didn't get it the whole multi-step matrice problem, not even the counting.</li><li>The COGAT loves ambiguity, and a numeric transformation of 2 could in fact be a numeric transformation of double, but you won't know until you check the answer set.</li><li>Doubling is good for 90%. A higher score needs to delve into tripling and quadrupling. Not that quadrupling is on the COGAT, but that level of thinking is.</li></ul>Here's what I'm talking about. I had double up on the quant questions because the color printing costs are so high, and it's worth it.<br /><br /><div style="background-color: #fff8e8; color: #003333; font-size: 1.2em; padding: 20 5 20 5; text-align: center;"><div style="display: inline; max-width: 500px; min-width: 380px; padding: 20 5 20 5; text-align: center;"><a href="http://2.bp.blogspot.com/-r3ObE05Kel8/Wu9L8mviddI/AAAAAAAADBk/iJE0ZUER14U4D0ZmoLWLym6mTXeAWM1TACK4BGAYYCw/s1600/SSCC1.JPG" imageanchor="1" style="max-width: 500px; min-width: 380px;"><img border="0" src="https://2.bp.blogspot.com/-r3ObE05Kel8/Wu9L8mviddI/AAAAAAAADBk/iJE0ZUER14U4D0ZmoLWLym6mTXeAWM1TACK4BGAYYCw/s320/SSCC1.JPG" style="max-width: 500px;" width="100%" /></a> </div><div style="display: inline; max-width: 500px; min-width: 380px; padding: 20 5 20 5; text-align: center;"><a href="http://4.bp.blogspot.com/-uZ0M82Bwum4/Wu9L_lt0tbI/AAAAAAAADBs/UjrbTdiwBdsVH06t2hMNAGaHhYV4sjS_ACK4BGAYYCw/s1600/SSCC2.JPG" imageanchor="1" style="max-width: 500px; min-width: 380px;"><img border="0" src="https://4.bp.blogspot.com/-uZ0M82Bwum4/Wu9L_lt0tbI/AAAAAAAADBs/UjrbTdiwBdsVH06t2hMNAGaHhYV4sjS_ACK4BGAYYCw/s320/SSCC2.JPG" style="max-width: 500px;" width="100%" /></a> </div></div><br />By this time, the child knows what -2 and thirds mean, as well as what a blob fish is. The problem is getting there. Here are some ground rules: <br /><ul><li>A single problem like this for a 4 year old might be a 20 minute affair, but could also take multiple days.</li><li>We practiced halving and doubling in our spare time with pennies, fingers, stuffed animals.</li><li>As soon as a 4 year old really gets it, he will crush you tomorrow by totally forgetting it.</li><li>Something is going on in that brain and none of us know what.</li><li>I've never worked with a child who struggled as much as my child did, but if you want to see the outcome, read the article about Trig below.</li></ul>Cognitive skills don't increase unless the work taxes the skills. Work that taxes cognitive skills results in floundering, forgetting, wrong answers, and multiple attempts.<br /><br />This is hard on most parents. It's much more gratifying to watch your child blow through 20 easy Kumon problems. Most parents won't get their kids past the 98% cuttoff to get into a GAT program because they take the easy route. I think this book took us 2 passes and will take at least 3 months. Maybe 6. It depends on how early you start and how far along your child is counting on her fingers.<br /><br />Like all material, eventually the child gets there, and when he gets there, he has a formidable skill set. In this case, we ended up with a Visual Number sense, which I didn't even know was possible. Ideally, SSCC graduates will do arithmetic on sight. This will create a foundation more more advanced skills that is super powerful. <br /><br />For the first half of the book, we really struggled. After that, we really struggled to get through a single question in 15 minutes. There was lots of discussion and taking breaks to review halving and doubling. If you are looking for an easy repetitive book that magically puts your child above 97% on the COGAT, keep looking. Until then, if your child is in the early months of age 4, this is it:<br /><br /><div style="text-align: center;"><a href="http://2.bp.blogspot.com/-t6JfSBMVkA0/Wu9Ruz2pPkI/AAAAAAAADCA/fSQpzca2d08Ufz9twBikZafX3L1EXQp4QCK4BGAYYCw/s1600/sscc.jpg" imageanchor="1"><img border="0" height="320" src="https://2.bp.blogspot.com/-t6JfSBMVkA0/Wu9Ruz2pPkI/AAAAAAAADCA/fSQpzca2d08Ufz9twBikZafX3L1EXQp4QCK4BGAYYCw/s320/sscc.jpg" width="248" /></a><br /><div text-align:center=""><a href="https://www.amazon.com/dp/154130375X/">Click here to super charge quantitative skills</a></div></div><br /><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; margin-bottom: 10px; padding: 20px 10px 20px 10px;"><div style="font-weight: bold; text-align: center;">Start Your Rigorous Summer GAT Program Now</div></div>Summer is a good time to start your GAT training program.<br /><br />Get a stack of material, including:<br /><br /><ul><li>Rigorous, challenging cognitive skills building thinking material</li><li>Some age-inappropriate math to struggle through, like something your child will see in school in a few years</li><li>Some easier workbooks for backtracking, a bad day, or for doing alone because you're busy.</li></ul><div>Create some ground rules and goals. In this house, the ground rules are 'No math, no computer', where math can be anything. I've added chores to the daily regimen because kids who do chores have a better attitude toward academic work. (Someone explain to me the relationship between vacuuming and problem solving.) My goals are simply 15 to 25 minutes of hard core thinking each day on something.</div><div><br /></div><div>Once you've got that together, you're ready for the next step. Summer is a good time to start your program, but immediately is even better. I'd like to do a study on GAT outcomes for children of parents who start immediately, as in open the box from Amazon assign the first page. The control groups would be parents who start the 1st day of summer school. I already know what the conclusion of this study will look like. </div><div><br /></div><br /><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; margin-bottom: 10px; margin-bottom: 10px; padding: 20px 10px 20px 10px;"><div style="font-weight: bold; text-align: center;">Putting the Skittles and the PS4 In The Closet</div></div>The approach to academic work varies between age 4 and graduate school only in the amount of quality concentration and thinking that the child is capable of. A 4 year old is good for 15 minutes a day, maybe 3 or 4 days a week. A 4 year old has a lot of bad days where thinking is thwarted by hunger, sickness, exhaustion, and the parent accidentally yelling at the child for curling up in a ball under the table. A 3rd grade child is good for daily work, maybe 20 or 25 minutes a day.<br /><br />The approach and methodology for problem solving does not change between age 4 and graduate school. I announced this definitively a few years ago based on working with a 4 year old and a 7 year old. It was a bold assertion.<br /><br />Here is the logic underneath my assertion. My cognitive skills research started with problem solving with IT engineers, graduate school work, and worked backward through high school geometry proofs (thanks Poyla) and down to age 3.9. It was all the same: be baffled, make mistakes, ignore the solutions (it's about thinking, not finding out the answer), trying again.<br /><br />Here I am thousands of hours and hundreds of kids later, with kids covering the age range, and two of my own that are 5 years older, and I can announce with much more confidence that in fact there is no difference at all. Older children are only good for 25 minutes of really hard core top notch thinking. But the material needs 90 minutes of start up time and more routine work. They only appear to work for 2 solid hours, but when they've gotten through the 25 minutes of really challenging problem solving, they are worthlesss.<br /><br />This week, the PS4 went into the closet. I discovered that I have a 13 year old who follows me around - brace yourself for this - talking to me.<br /><br /><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; margin-bottom: 10px; padding: 20px 10px 20px 10px;"><div style="font-weight: bold; text-align: center;">Northwestern and Duke Summer Programs</div></div>I wish I had a picture of the 14 grade school kids who took the SAT last week, but security escorted me out of the building. I think 13 of these were there to qualify for the programs at Duke and Northwestern.<br /><br />Duke has an online program now. If you ask me if you should enroll your child in this program (assuming you pass the rigorous qualification) my answer is definitively yes.<br /><br />The reason we're not personally interested in these programs is because our GAT program is rigorous enough. I think it's the top program in the country. I personally know many graduates who are breezing through one of the top 10 high school programs in the country without really trying. The other reason is that my kids would rather shoot arrows at camp during the summer and I'm more interested in a path to graduate school than advanced chemistry at Northwestern, which we're doing on the side anyway as needed.<br /><br />If you ask me how you get your child past the entrance criteria and into the program, you're asking how do you hone your child's cognitive skills to a very high level.<br /><br /><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; margin-bottom: 10px; padding: 20px 10px 20px 10px;"><div style="text-align: center;"><b>Trig at Age 9 - A Bookend</b></div></div>Let's revisit the very first graduate of <a href="https://www.amazon.com/dp/154130375X" target="_blank">Shape Size Color Count</a> and both <a href="https://www.amazon.com/dp/1530186234" target="_blank">Test Prep Math Level 2</a> and <a href="https://www.amazon.com/dp/1547120010" target="_blank">Test Prep Math Level 3</a> because he's bothering me while I'm trying to type. I hate having to go to amazon to get these links because of that 1 star rating from a plumber (I'm not kidding) on TPM who said that the solutions were wrong. You're not going to get to 99% on the MAP test for the rest of your life with solutions that are obvious in a book that spends 6 pages explaining why each problem is designed for mistakes and repeated attempts. Either he needs to do the problem again or the author does. That's the nature of cognitive skills building<br /><br />In order to keep my 9 year old out of my hair, I drew a few triangles, introduced him (once again) to the sine/cosine unit circle do-it-yourself-with the Pythagorean theorem-calculator, and asked him to tell me everything that is missing. When I say 'calculator' I mean 'without a calculator'.<br /><br />You'd think he'd remember this from 6 weeks ago when we did the exact same thing. It's like age 4 all over again.<br /><br />I like trig. You can teach it in a single 1 hour session.<br /><br />Draw a unit circle on graph paper and draw a line anywhere you want. sin(a) is the y and cos(a) is the x. You can use A<sup>2</sup> + B<sup>2</sup> = C<sup>2</sup> to calculate common values, like 30<sup>o</sup>, 45<sup>o</sup>, 60<sup>o</sup>, 135<sup>o</sup> etc. It helps at this age to always use capitals for line lengths and always use lowercase for angles. A is opposite a, B is opposite B. A calculator could help with 25<sup>o</sup>, but we don't use calculators and just guess on SAT type questions where they deviate from common angle values.<br /><br />Then I ask for the Law of Sines and the Law of Cosines. If you forgot, here they are respectively:<br /><br /><ul><li>A/sin(a) = B/sin(b) = C/sin(c)</li><li>A<sup>2</sup> + B<sup>2</sup> - 2ABcos(c) = C<sup>2</sup></li></ul>For kids in middle school or near middle school, you can find triangle stacks on the web to practice these equations. For age 9, we discuss cos(90) = 0, and stick with the Pythagorean version of the Law of Cosines.<br /><br />Here's the unit circle on the left, and the problem on the right in case you want to try it<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-BpaIzFc2XH0/Wu9f4Pgq5YI/AAAAAAAADCc/pA7SxW4wozsmWiaVqoLg86eT4Z3D6rt5QCLcBGAs/s1600/Triangle.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="282" data-original-width="589" height="153" src="https://3.bp.blogspot.com/-BpaIzFc2XH0/Wu9f4Pgq5YI/AAAAAAAADCc/pA7SxW4wozsmWiaVqoLg86eT4Z3D6rt5QCLcBGAs/s320/Triangle.jpg" width="320" /></a></div><br />Here's the view of the daily math that bought me 60 minutes of free time, minus the 25 minutes I had to backtrack and re-explain the unit circle and help with mistakes (help as in 'Wrong. Do it again')<br /><br /><div style="text-align: center;"><a href="http://2.bp.blogspot.com/-D8oM8zFcDx0/Wu9bAjkeIlI/AAAAAAAADCQ/Z1IAP7MF91YHafTP1Z--VARS3FQmZZQ_wCK4BGAYYCw/s1600/doritos.jpg" imageanchor="1"><img border="0" height="240" src="https://2.bp.blogspot.com/-D8oM8zFcDx0/Wu9bAjkeIlI/AAAAAAAADCQ/Z1IAP7MF91YHafTP1Z--VARS3FQmZZQ_wCK4BGAYYCw/s320/doritos.jpg" width="320" /></a></div><br />You'll note the Dorito bag. At age 4, this was a bag of skittles. I found that snacks are a useful inducement for ridiculously hard age-inappropriate work, especially if your child is crying because you are a mean parent by making them do all of the work. It is important to remember that 20 skittles are no more motivating than 5 skittles, and you can stop giving snacks at any time. Or you can walk 3 miles a day with your child on what I like to call 'Math Talk Walks', but privately I think of these as 'Don't End Up Being A Chubby Videogamer Walks'.<br /><br />We do a trig problem about every 6 weeks. This gives my children 5 weeks to forget what they learned so that trig becomes an exercise in thinking and not an exercise in applying memorized formulas without thinking. That is why I refer to my approach as Anit-Kumon. I don't want a child who get's a 1600 on the SAT because they've trained to get a 1600 on the SAT and then doesn't get into Stanford. Stanford has a method to weed out these kids that I haven't reverse engineered (yet). Instead, I want a child who get's 1600 on the SAT because they can figure out trig on the spot - because they've learned the cognitive tools to do so. Presumably they'll use this toolset for something else during high school and Stanford will notice.<br /><br /><div style="background-color: #ffd1aa; color: #003333; font-size: 1.2em; margin-bottom: 10px; padding: 20px 10px 20px 10px;"><div style="text-align: center;"><b>Developing a Writer</b></div></div>I've been asked often how to develop a writer. I've got a child who will be some kind of a writer, possible a director or advertising media creator who spends his time researching astrophysics websites looking for the galaxy shaped like Yoda. The other one, who we refer to in this house as The Math Guy, also writes a lot, as in songs, books, and posters to sell stuff.<br /><br />The starting point for writing is art, crafts, and projects. The number one skill writers have is that they dream up something that has multiple pieces and which takes a long time to finish. Art is important because it has setbacks. You have to do it a few time to get it right, whatever it is. You want a writer? Sign her up for an art class. Chores are important because they are boring and repetitive. Chores make writing seem like fun.<br /><br />This stage of writing continues from age 7 to 12 while they develop grammar, vocabulary, and articulation skills.<br /><br />At some point around age 11 and 12, you can start (slowly) two activities: The first activity is daily writing, like a journal, and the second activity, at least at the GAT level, is a 4 hour marathon of pain that I like to call 'Crafting Sentences'. We sit down with some school work and take each sentence at a time and fix it. What are you trying to say here? Is 'fix it' good enough, or do you mean 'recraft the dependent clause', 'elaborate on a undescriptive pronoun', 'match the syntax of the sentence to the logic we are trying to convey', or what? During this process, the child says what they are trying to say, and I explain why I'm not clear what they are trying to say and that inadequate sentence that they only spent 2 minutes on sure as heck isn't saying it anyway.<br /><br />I refer back to Test Prep Math, which was as much convoluted logic and vague words as math, and the main reason they do well on the reading comprehension section of the MAP, and think of each sentence as a math problem on its own, as in a 10 to 20 minute exercise of work, mistakes, and trying again.<br /><br />So here we are back to foundational cognitive skills. The little writer slowly realizes that it wasn't about math at all back then. It was about being confused, making mistakes, and trying again. I have mentioned this to both my kids numerous times. Someday they'll leave math in the past; it might be after winning a Fields medal or a millennium prize form the Clay Institute, but some day they'll have to write.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-86556576777313043192018-05-05T12:19:00.000-07:002018-05-05T12:19:00.323-07:00The Little TestToday was a practice test. <br /><br />Practice tests are an important part of a test prep regimen. In the past, we've sat for GAT practice tests, staged GAT practice tests (when none were available), staged standardized tests. <br /><br />Normally, our prep pace is just a few ridiculously hard questions a day. This maximizes learning. But a real test has lots of questions that are easy and a few that are hard (the ones that count if you're trying to meet a cutoff score are the hard ones). A real test is a different dynamic, and one more thing to practice.<br /><br />My favorite practice test was a 2nd grade ITBS where I read the questions and the answer choices to my 4 year old and he pointed.<br /><br />In most cases, the practice test is the real thing, like it was today, with a score that doesn't count.<br /><br />Like always, I grilled my son on the test. What was it like? Who was there? What was on the test? Did the calculator I gave you that only does arithmetic prevent you from getting a trig question correct? How many people were there? This is what I learned:<br /><br /><ul><li><i>I don't remember anything from the test. I only remember one question from my K GAT test. Which rhymes with boon? Moon, spoon, monkey, something else.</i></li><li><i>All the 7th and 8th graders had to sit in a room together. There were only 14 kids in this room and they were all nerds.</i></li><li><i>There were 4 sections, no essay (for kids not in high school) and a mystery section.</i></li><li><i>We had 3 breaks.</i></li></ul><div>He then went on to explain the breaks in detail. I asked what was on the mystery section:</div><div><ul><li><i>It was like a GAT entrance exam, sort of. I don't remember any of the questions.</i></li></ul><div>Now you know everything I know about the taking the SAT in 7th grade. I'm interested in this mystery section. Is it because the SAT is used to qualify kids for the Northwestern and Duke summer programs? I wonder if we'll see our scores on that section.</div></div><div><br /></div><div>I asked one last question. How did you do?</div><div><ul><li><i>I ran out of steam on the last section and didn't finish it, but on the rest I think I did OK.</i></li><li><i>I felt like I was prepared, like I have been preparing for 3 years.</i></li></ul><div>Which he has. Of course, we prepare in a completely different fashion than everyone else, and I expect results from our innovative and rigorous approach.</div></div><div><br /></div><div>The big test, the one that counts, is in a few weeks.</div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-80017171610049814032018-04-29T12:53:00.002-07:002018-04-29T12:53:23.335-07:00The Calm Before the StormNext Saturday is our big day. The rest of Chicago has been getting scores in the mail with test results for K to 4 entry, and it totally stresses me out. Next week I will be a wreck as usual. It's hard enough when one of the kids or parents I coach takes the test. Vicarious test taking is just as challenging to prepare for as actual test taking.<br /><br />A while back, a Power Mom asked for a retrospective what I did wrong. I'm elevating this PM to PMYL, which stands for Power Mom Yoda Level. He questions was some sort of Plato or eastern mind trick to make me reflect. My articles are long enough when I barely have 20 minutes before work to type frantically and check for typos. Brace yourself.<br /><br />The approach I took didn't result in any mistakes of lasting impact. Some of was intentional and most of it was not. The approach can be split into a few categories.<br /><ul><li>I read the papers and presentations of cognitive skills experts and test authors and did exactly what they recommended.</li><li>I read the articles of intelligence researchers, education researchers, and psychologists and did exactly the opposite of what they recommended. From this effort, I can explain exactly what's wrong with education in the US, but I didn't gain any actionable strategies for my own children.</li><li>I bought all books in print and tried them out. Only a handful were useful as busy work.</li><li>I wrote my own test questions, attempting every permutation possible in a desperate attempt to pass the test by brute force. Somewhere at about the 60% mark, the light bulb went off and I realized it wasn't about shapes. It was about thinking.</li></ul><div>Except vocabulary. Vocabulary is about vocabulary. My favorite researcher of all time pointed out that when a child is learning to read, all cognitive skills - math, whatever, all of them - are actively deployed by the child's brain. He also stated that each vocabulary word doesn't just increase a child's knowledge by a single word, it spurs cognitive growth. Red is not just the name of a color, it is a member of various classifications, has a hue and brightness and other qualities, is used to represent concepts like stop and danger, works in some situations and not in others, looks good on some people but not others and comes out of your finger when you cut yourself. The magic happens with the cognition left over after the word red is worked, cognition that is then applied to other things, like math.</div><div><br /></div><div>So I discarded phonics books from the last decade that look more marketing and fun than learning and thinking, and listed out every word 5 letters or less that would appear in a scrabble championship. After a few years, the result was a Pre-K Phonics Conceptual Vocabulary and Thinking which I sometimes right as Pre-K Phonics Conceptual Thinking because that's how most people google it.</div><ul><li style="display: inline-block; list-style-type: none; width: 45%;"><a href="http://3.bp.blogspot.com/-JubWfNBcK-Q/WuYVhJq-hiI/AAAAAAAAC-M/cLY2uFZ1BBYLSH4-t2lghyyse4BwUGinwCK4BGAYYCw/s1600/Thinking.jpg" imageanchor="1"><img border="0" height="320" src="https://3.bp.blogspot.com/-JubWfNBcK-Q/WuYVhJq-hiI/AAAAAAAAC-M/cLY2uFZ1BBYLSH4-t2lghyyse4BwUGinwCK4BGAYYCw/s320/Thinking.jpg" width="247" /></a></li><li style="display: inline-block; list-style-type: none; vertical-align: top; width: 45%;"><h2>What's inside</h2><ul><li>Phonics through 2nd grade</li><li>Instructions for a solid reading program at the 99% level</li><li>Math vocabulary through 2nd grade, just in case</li><li>The reason my 13 year old is sitting for the SAT on Saturday</li><li>The reason why I use terms like incredulous, inculcate, and fallacious with my kids and they don't roll their eyes</li></ul></li></ul><a href="https://www.amazon.com/dp/154045620X" style="display: block; text-align: center;">Click here for fabulous phonics</a><br /><br />While Math House is called Math House because I have many wasted years studying graduate math and trying to solve the Riemann hypothesis, the phonics book is the gem of the collection. Guaranteed high math scores on advanced material is not enough to crush the reading section. I think my kids spend 2 or 3 hours a day reading - on a good day, and we don't have nearly enough good days. Last week was mainly band concerts, baseball games, the school play, and me working way too much.<br /><br />Speaking of last week, here is a question from the SAT from last week's article.<br /><br /><div style="margin-left: 20px;">The author uses an extended quote in lines 61-69 as part of a larger attempt to </div><div style="margin-left: 30px;">a) convey the impact of an unexpected discovery<br />b) illustrate the suddenness of a decision<br />c) simulate a child's misconceptions<br />d) criticize the artificiality of the "young adult" classification<br />e) describe a young reader's sense of history<br /><br /></div>As I mentioned in the prior article, after a few years of research, we reduced all reading comp exercises to a simple mathematical proof. It's almost long division now. But there is a prerequisite that I didn't mention. These questions are packed with vocabulary. I should have chosen one of the harder questions but even in the question above you can see convey, misconception, artificial, sense, and not the 2nd grade definition of sense.<br /><br />Somewhere in the Pre-K Phonics introduction, I might mention that opposites are not very useful, but synonyms are extremely valuable for the COGAT. This applies to the SAT as well.<br /><br />One Power Mom did Pre-K Phonics with her 4 year old and asked me <i>do you really expect kids to know 'due' and 'dew'?</i> Ha. No I don't. I expect them to figure out that there are things like dew and due lurking out their, which is a cognitive gold mind, but mainly I expect parents to read these two words in a phonics book, freak out, and raise the bar in their house. Some words strike the imagination of one child, some strike the imagination of the other child. You never know. Some times we would just burst out laughing and move on. Sometimes the word went on the Word Board for the 112 days it took to get it because I thought it was important for the COGAT.<br /><br />From then on, it was 3 years of the Word Board and vocab workshop. By 2nd grade, words just became the fabric of Math House.<br /><br />By the way, I owe this Power Mom an article on how to get a four year old to internalize halving and doubling, tripling and cutting into thirds and make it part of their visual-spatial cognition. Maybe next week.<br /><br />In the mean time, for the last week, we've done zero to prepare for the SAT on May 5. I first came up with this idea 8 years ago, when a Mentor Mom told me that her 7th grade daughter got a 700 on the SAT and Stanford sent her a letter asking her to apply in 4 years. Since then, I've been asking the question, what if we could crush the verbal section? Our incremental preparation could fill about 30 pages if I included all of the setbacks, 3 pages with just recounting the how to.<br /><br />Well, we probably can't crush the SAT because we go so very slow on our work, both math and verbal. It's tempting to change gears and shoot for speed, but the MAP test is in June and we need 99% to get into high school. The MAP and the SAT are not the same thing, and I don't want to negatively impact the MAP. So the SAT has been relegated to MAP practice. Still, it's the SAT.<br /><br />Last night I was out with Power Dads on a biking brewery research tour and we were discussing how preparation is going for the MAP. All of their kids are genuinely smarter than my kids. Officially, it was just a biking brewery tour, but I don't drink much, I ask a lot of questions, and dads talk a lot when they drink. So putting that altogether it was prime research. One dad said his daughter was in a prep course and she recently had a grueling 4 hour MAP test prep session. The SAT is our prep, but it's only 3 1/2 hours so I kept my mouth shut. We might have the edge, however, in the grueling department.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-27513427936637081372018-04-21T06:17:00.000-07:002018-04-21T06:19:03.289-07:00Tiger Mom RevisitedSome of my readers complained that when they google Test Prep Math they get GMAT results. This is totally offensive to me. If a result came up with the GRE math, chemistry or physics subject, that would be OK. After all, 99% on the MAP tests year after year in grade school is going to be a waste of time if Stanford turns down my children's graduate applications. At the risk of looking like every other test prep website:<br /><br /><div style="text-align: center;"><ul><li style="display: inline-block; list-style-type: none;"><a href="http://1.bp.blogspot.com/-VimShjs5fUg/WtsnG-OsC8I/AAAAAAAACzA/_HYPbpB-CF4tVO_beSZn5nb-oLjLas5oACK4BGAYYCw/s1600/Test%2BPrep%2BMath%2BLevel%2B2.JPG" imageanchor="1"><img border="0" height="320" src="https://1.bp.blogspot.com/-VimShjs5fUg/WtsnG-OsC8I/AAAAAAAACzA/_HYPbpB-CF4tVO_beSZn5nb-oLjLas5oACK4BGAYYCw/s320/Test%2BPrep%2BMath%2BLevel%2B2.JPG" width="200" /></a><a href="https://www.amazon.com/Test-Prep-Math-Level-2/dp/1530186234" style="display: block;">Click here for 2nd Grade</a></li><li dp="" est-prep-math-level-3="" event.stoppropagation="" https:="" onclick="" style="display: inline-block; list-style-type: none; margin-right: 20px;" window.open="" www.amazon.com=""><a href="http://3.bp.blogspot.com/-HimEyQYFHW0/WtsnIWZEJNI/AAAAAAAACzI/-QJKuBkzfUIiOyj4j3CM4ay2Zw_0nc6lwCK4BGAYYCw/s1600/TestPrepMath3.JPG" imageanchor="1"><img border="0" height="320" src="https://3.bp.blogspot.com/-HimEyQYFHW0/WtsnIWZEJNI/AAAAAAAACzI/-QJKuBkzfUIiOyj4j3CM4ay2Zw_0nc6lwCK4BGAYYCw/s320/TestPrepMath3.JPG" width="200" /></a><a href="https://www.amazon.com/Test-Prep-Math-Level-3/dp/1547120010" style="display: block;">Click here for 3rd Grade</a></li></ul></div><br /><b>On To Tiger Mom</b><br />In the famous seen in her book, Amy Chua recounts a 4 hour ordeal of screaming and crying while she forces her daughter to rehearse an impossible piece for an upcoming piano recital. Chua is presented as an overbearing evil mom with unrealistic expectations for her child and no concern for her child's long term mental health.<br /><br />This scene replays itself over and over in Math House, usually on simmer instead of full boil. There are two important difference between the Evil Overlord of Math House and Tiger Mom. These differences are why I am not a Tiger Dad, and beyond criticism, and Chua took a lot of flack for her book, even though Chua and I think and act in nearly same way.<br /><br />The first difference is that I have assumptions, not expectations. My expectations for my kids are abysmally low. I strive for zero expectations. I expect that a 7 or 8 year old would rather play video games and watch TV instead of worry about his future. I expect that a young child will cry when presented with a problem that exercises grit and cognitive skills. Maybe he'll just complain at first, but as soon as it's clear I'm not doing his work for him (because then he won't get the benefits), he might try crying. I expect him to not know what he's doing, to make lots of mistakes, to do far less than I've assigned, and to end up with wrong answers. That's where the skill set is born, and that's why he's doing this work. If I gave him something he could do, like 30 easy math fact problems, he'd look good but fall far short of the goals I have for him.<br /><br />On the other hand, I have assumptions. I assume my kids will get the work done one way or another because I'm withholding all fun activities until it is done. I assume that I can't withhold food because his performance will suffer (tried that, it doesn't work). I assume that he'll learn key skills that other kids don't learn and that a year from now, he'll be scoring in the top 1% on everything for the rest of his life and be 6 years ahead of other kids in key subjects, even subjects we don't do at home, all because I stayed focused on grit and cognitive skills during 2nd and 3rd grade.<br /><br />I like to say 'Of course you don't want to do this. You're 8 years old. I'm an expert at being an 8 year old. I was an 8 year old for an entire year'. Seems like a good thing for a dad to say.<br /><br />I expect the first 6 weeks are going to be really tough because school just spoon feeds easy work and the parent is used to helping and answering questions when the child falls short. Scaffolding is great when you want your child to memorize and master a bunch of new concepts in a short period of time, but the child never learns the thinking and learning skills tackle learn pre-algebra on his own.<br /><br />4th grade was a blur of algebra. You can't do algebra without pre-algebra, and that means you either have to learn it on the spot or get assigned backtracking material by The Overlord before you can move on. I threw in some functions, a little geometry (prove everything starting with a line is an angle of 180 degrees), a little trig (everything you need to know in 30 minutes or less), and it's on to SAT test prep books.<br /><br /><b>Test Prep Math Level 4</b><br />SAT test prep is surprisingly easy compared to the real thing. I generally assign 5 problems at a time, from the math section, with no time limit. A few years later, we've not only completed all the math problems but learned high school math on the way, with the exception of advanced trig topics and calculus. Again, my expectations are really low for this exercise. I expect almost nothing. I assume we'll get through it and come out on top.<br /><br />In a few weeks, my 7th grader is sitting for the real deal, all 3 1/2 hours of it. I gave him a few timed versions of certain sections, but our real goal is the 6 hour MAP test ( 3 hours of math on one day, and 3 hours of reading comp on another day). I figure 3 1/2 hours of SAT brutality should be good practice for the 7th grade MAP.<br /><br />After we licked math, we had a book full of reading comp questions. The reading comp was really hard. It didn't go well.<br /><br />I traveled to the planet Dagoba to be trained by the Jedi Master Yoda of reading comp. A high school English teacher, he coaches SAT on the side. He told me things like "When the question asks 'which answer reflects the tone of the passage', count words in the passage, you will". He also told us to 'figure out an answer wrong, why you got'. His advice got us past Baffled; it gave us things to do instead of crying and yelling at each other, but ultimately it's not for 99% and its not for an 11 year old.<br /><br />Once again, I'm stuck with an area of cognitive research that is unexplored and undocumented, so as the Foremost Expert in the Field of Real Cognitive Skills, The Kind That Actual Children Have, Not The Useless Made Up Crap That Fill Education Journals, I took on the challenge.<br /><br />So I applied the learning framework outlined in Test Prep Math. After all, the math word problems in TPM target reading comp. This isn't obvious how a math problem prepares a child for reading comp until you see the SAT. Here's why reading comp = math and math = reading comp.<br /><br /><div style="margin-left: 10px;">The author uses an extended quote in lines 61-69 as part of a larger attempt to<br /><div style="margin-left: 10px;">a) convey the impact of an unexpected discovery<br />b) illustrate the suddenness of a decision<br />c) simulate a child's misconceptions<br />d) criticize the artificiality of the "young adult" classification<br />e) describe a young reader's sense of history</div></div><br />Step 1 - look at lines 55-60 and 70-75 for the answer. This is more of a geometry thing that I'll cover later.<br /><br />Step 2 - Notice each answer has 3 concepts. You simply take each concept (like convey), and if the author complains, states, recounts, but does not <i>convey</i>, cross out the answer. Test Prep Math hammers away at the 3 bucket limit of working memory, and here it is in action on every single question in the SAT reading section. The iterative permutations of solving these questions are identical to Section 3 of TPM, which is why figure matrices are such good predictors of academic success.<br /><br />That's it. There are no other question types. It is really helpful if the child can tell you about the author and the type of passage (propaganda, argument, description, memoir, what ever) because the first 2 questions are going to require this knowledge. But all questions require the same mathematical approach. If a question looks like its a different type, it's just disguise.<br /><br />Once we got this, I went from assuming that reading comp questions are impossible to assuming that I'm going to be disappointed if my kids miss any. 'Convey' went on the Word Board.<br /><br />I think somewhere in the intro to Test Prep Math I might fess up to targeting reading comp. I should have said targeting 99% on reading comp.<br /><br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-64558095462156734312018-04-13T22:51:00.002-07:002018-04-13T22:51:11.774-07:00Now Is The TimeOver the next few months I'm going to be unleashing some really powerful test crushing material that I've been working on diligently for the past few years. All of this fits under the head of 'well, we did that stuff, let's see if it will work elsewhere'. It does work elsewhere.<br /><br />I've noticed that interest in GAT material drops off after the test scores are released in the spring. I suppose this is normal. Normal as in not the top 1%. When I was in eighth grade, I read the biography of the world's greatest athlete. He used to have really intense workouts after the year-end tournament was over. Like right after. That night.<br /><br />Giftedness is going to be born in the next few months.<br /><br />Have you ever heard the expression 'Fake it until you make it'? There is a great Ted Talk on this subject from Amy Cuddy. My idea of giftedness is similar. My idea of giftedness is to take the skills of the gifted and use them. It's not profoundly gifted, but with a little practice and change it's enough to get into a gifted program. <br /><br />An odd thing happened on the way to giftedness.<br /><br />The difference between a gifted child and a profoundly gifted child is that the profoundly gifted child has so much practice exercising gifted skills that she does it quickly, so quickly, in fact, that neither she nor her parents can explain how she actually does it. It's like magic.<br /><br />It's not magic if you look closely.<br /><br />Last week I doled out more SAT test prep to my 9 year old. I've been working a lot and it's good for a few minutes without distraction. Here's one of the questions I gave him. Take a minute to solve it.<br /><br /><div style="text-align: center;"><a href="http://1.bp.blogspot.com/-wMXzq9E3pU8/WtGOnI9lnHI/AAAAAAAACd0/k7iXCZF5h-0VPQApd1rpnaLoRHddHWMewCK4BGAYYCw/s1600/MVIMG_20180414_000855.jpg" imageanchor="1"><img border="0" height="320" src="https://1.bp.blogspot.com/-wMXzq9E3pU8/WtGOnI9lnHI/AAAAAAAACd0/k7iXCZF5h-0VPQApd1rpnaLoRHddHWMewCK4BGAYYCw/s320/MVIMG_20180414_000855.jpg" width="240" /></a></div><br />He asked me what the area of a circle was. I thought kids learned that by this age, but whatever. Before I could leave the room, in the space of about 15 seconds, he solved it. That was freaky. I asked him how he solved it, and he showed how he subtracted one half circle from the other, etc., and nailed it.<br /><br />We spent 18 months learning the skills from the ground up with Test Prep Math. There were 2 types of questions. The first type required a long discussion and argument. The second type required 4 or 5 attempts. A year of weekly math later and the discussions have dissipated.<br /><br />I maintain a slow pace of a few problems here and there. I've been worrying a lot about how our slow pace in Math House is going to thwart the SAT. The MAP test requires a slow pace, and we need a perfect score this year, so I don't want to add risk by practicing timed tests. Last week, I wondered if we should just switch to Kumon and drill boring useless math facts. I know that slow, careful, and lots of mistakes produces award winning mathematicians so I'm going to stick with principles. But I gave a 55 minute practice test to older brother and he only finished 30 questions out of 38. In 70 minutes. He'll be lucky to break 1200. I'm beginning to feel the same way I felt watching them being led away to the COGAT at ages 4 and 5. It was excruciating. How am I going to survive 3 1/2 hours of waiting while my baby takes a college entrance exam? Older brother is only 13 and is the subject in one of my diabolical experiments yet again.<br /><br />The younger feakazoid learned his visual spatial skills from Shape Size Color Count. He does an adequate showing on reading comp within the official time limit as well. That skill set started with Pre K Phonics and Conceptual Vocabulary & Thinking and was fully developed by the Test Prep Math Series. Those 4 books (there are 2 Test Prep Math books) stand out for two reasons. There is a 2 foot high stack of test prep material for K and 1st grade. I have a four foot stack, but only recommend about 2 feet of it. There is almost nothing for children who aren't in K or 1st grade. Secondly, these 4 books are the only books on the market that present material at the 99%, at least by the end of the books. What is the secret to doing work at the 99% if you're not actually there yet? It's slightly different than fake it until you make it, but in the same spirit. Go slow, do less, and make more mistakes. Until you make it.<br /><br />If you want a permanent showing at 99%, step out of the crowd. Work diligently when the rest are taking a break. Work differently (think Anti-Kumon instead of Kumon). K and 1st are extremely competitive years but scores drop off after that because the interest drops off. If your child hasn't reached the magic age of 4 yet, think about SSCC and phonics. If K and 1st grade were a struggle, double the effort in 2nd and 3rd grade. It's worth it in the long run.<br /><br />In my next article, I'm going to describe how Math House crushes reading comp questions. It's going to be a let down for my readers. Math House built math from the ground up with foundational skills and ignoring routine practice and memoriation. We didn't get around to worrying about reading comp until all the math parts of the practice tests in the SAT book were finished and we were looking for the next challenge. By this point, foundational skills were used and not discussed. We ended up with a simple reading comp formula that works. No wisdom, cleverness, counter cultural pedagogy wars. Just a simple formula.<br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-80845695605421530042018-04-07T17:57:00.001-07:002018-04-08T09:02:40.114-07:00My Latest Insane PlanBefore I announce my new plan, and freak everyone out, I'm going to issue disclaimers.<br /><br />Math House is very low pressure. Our bar is pretty low. I think a day is successful that has no video games. I have zero expectations. I never know if the next paper I grade will be all wrong or all lucky.<br /><br />Let's go through plans of the past and how they generally turned out.<br /><br /><ul><li>I spent 2 years carefully crafting a phonics book that includes phonics through 2nd grade. Every word that could possibly be relevant to a cognitive skills test and can be sounded out. The last shred of expectation were crushed out when it took 3 weeks to get past CAT.</li><li>We jumped into 2nd grade math midway through K. 3 weeks again to get through the first page.</li><li>I've got 6 or 7 other plans that I presented on this website in the last 7 years.</li></ul><div>Of course, a little here and a little there paid off. Within 4 or 5 months, the little ones were zooming along adequately. The bar raised itself.</div><div><br /></div><div>The new plan is to take the SAT in 7th grade. This is where you feel bad as a parent and panic because things are so competitive and you're falling behind. </div><div><br /></div><div>We'll, it's not about the SAT. I read an article this week that explains why 1600 on the SAT won't help you get into Stanford. Stanford only accepts 4% of applicants. I couldn't help but think a) 1600 on the SAT won't help and b) 4% is a easier to achieve than the 2/10th % that we faced for 1st grade.</div><div><br /></div><div>The SAT plan began in 2nd grade with TPM. If you've ever seen it, and you think 'this isn't school math' your right. It's the base of the mountain. School math is more of a detour through the foothills. This doesn't mean TPM is super hard (some of it is), it's just super different. Different will get you into Stanford, according to the article. I started experimenting with SAT books with older kids when TPM was written.</div><div><br /></div><div>My last insane idea was to start assigning work from an SAT test prep book after 4th grade. Here's your SAT question: How long will it take to get through a 600 page book if you only do 4 or 5 problems a week? The work accelerates on it's own, by magic, just like my other insane ideas.</div><div><br /></div><div>Back to the new new bar. On May 7, my 13 year old will spend the morning in a high school taking a 3 1/2 college entrance exam. What fun. I'm not sure how he's going to do, but here's what's going to follow:</div><div><ul><li>First, we get to see the whole test and his answers. This is a new service by the college board. I can't wait. I'll be able to compare our practice to the real thing and prepare little brother appropriately.</li><li>Then in a few years, he'll be sitting for the PSAT, the shorter easier version of the SAT. Will he be stressed taking a test that is easier than the one he took in 7th grade? I don't think so.</li><li>But even more importantly, a few weeks later he'll sit for the Test That Won't Be Named for entrance into high school. How can you expect a child to do well without practice? I don't consider a test prep course practice. You don't practice sky diving jumping off the stairs onto a mattress. You practice sky diving jumping behind enemy lines in the dark while the plane is buffeted by flak.</li></ul><div>I gave him his first timed test today - one 55 minute math section. I think it was section 7. He did awful, as usual. I let him go 90 minutes and I think he quit after 75 minutes on his own. (He's on to my trickery.) Awful is a normal performance going into the test, as I have pointed out to many, many parents worried about COGAT prep.<br /><br />Adendum<br /><br />This morning - a day after the timed math test, and the day after I published the article above - I'm assessing our situation. I don't like timed tests and he needs to get every single answer correct no matter how long it takes for that other test. So I'm going to do only one timed reading test and then we're going back to our normal program for that other test. The SAT is going to an endurance exercise of concentration. I had this idea that we will 'prepare for the test' if you know what I mean, but this doesn't really work for our plan, so instead we're just going to sit for the test and I'll find out how ready my 13 year old is for college. In other words, he's not going to get an extra 150 points because we made a concerted effort to get an additional 150 points. <br /><br />I know kids at this age who are ready to sit for an SAT type test. They've had the right training. They are nearly at the peak of the mountain. Math house is working toward a much much higher mountain and we're only at about the 40% mark right now. It's really hard for me to be competitive and patiently hold back at the same time.</div></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-72569392941606718802018-04-01T05:06:00.000-07:002018-04-08T08:47:42.362-07:00The Word Board<br />At a young age (like 4 to 6 or 5 to 7), each of my kids made trips to the Word Board a few times a week to see if any of the words from Vocab Workshop or phonics were mastered. Of course, if 'organize' appeared, I couldn't help but throw in 'organization', 'organic', 'origami' or anything else I could think of, so it was hard for them to keep up. The best part of this exercise was that it made up for a lack of discussion in the house, because we were usually reading or doing math or cleaning or eating. It turned me into a vocabulary parent. Our nightly reading time became more question and vocabulary oriented.<br /><br />The Word Board started simply to track which words from the Vocab Workshop book were mastered. If I got a slow response and some thinking, the word stayed. If it was a really important word, the bar was raised and I wanted synonyms as well. There are two reasons for delay. First, if you zoom through Vocab Workshop, you get to a level that's too hard, or you have to use Wordly Wise, Vocab Workshop's more boring cousin. Oppositely, some words are really hard, and you can leave the word on the board and move to the next section.<br /><br />Recently, a Power Mom suggested that I advertise. While I'm not interested in monetizing my blog, I will gladly include an ad for my favorite toothbrush, even if I don't get paid and their graphics leave little to work with. Also, currently only available on eBay. But they are soft, grippable, and counter cultural. Here is my ad.<br /><br /><a href="http://compostableplates.com/product/panda-smiles-adult-bamboo-toothbrush-soft/" target="_blank">Click to buy.</a><br /><div style="text-align: center;"><a href="http://3.bp.blogspot.com/-loEvVqpK6DE/Wr_Jtld_yqI/AAAAAAAACEg/H29UwBHBzoI_s-khlaes5dUhsijzkHd8ACK4BGAYYCw/s1600/Ad.jpg" imageanchor="1"><img border="0" height="136" src="https://3.bp.blogspot.com/-loEvVqpK6DE/Wr_Jtld_yqI/AAAAAAAACEg/H29UwBHBzoI_s-khlaes5dUhsijzkHd8ACK4BGAYYCw/s320/Ad.jpg" width="320" /></a></div><div style="text-align: center;"></div>The Word Board saved us in phonics. Phonics at a young age go really slow. At one point, we had 100 words on the board, including 'CAT', the very first word, which was never read adequately. I know from experience in any subject that a child may take 3 weeks on the first page and 2 weeks on the next, but if you stick with it and wait for their brain, suddenly they get it and zoom through everything. You just have to be patient and keep reminding yourself that you are reading the blog of an insane person. But once it happens in reading, math, COGAT test prep, you see the process and can relax. Until that delay happens in science, writing, pre-algebra, and everything else advanced you do, then it's just annoying.<br /><br />I think that the Word Board was mainly about me learning to be a parent in an educated household. It raises the level of expectation and it raises the level of the discussion. More importantly, it trains a parent to let the child do the work with no help. It trains the parent to wait for a correct answer, even if it takes 4 weeks. It trains the child that mommy won't help. The child realizes that he actually has to do the work. But there is no penalty, no time limit.<br /><br />By no help, I mean this:<br /><ol><li>"What's this word mean?" (Let's say ambidextrous is the vocab word.)</li><li>10 minutes of silence later, <i>Live on water and land</i>?</li><li>"No, that's amphibian. Last time, I said an amphibian is an animal that lives on water and land. 'Ambi' means both. Phibian probably means tell a small lie or something to do with habitat. It's greek from about 2500 years ago. Or latin. Small break for daddy to wiki phibian. Ambitdexterous means that you can write with both hands because you either have brain damage or you practice writing with both hands. Let's take a break to write our names with both hands at the same time.</li><li><i>I know what habitat and amphibian mean.</i></li><li><i>"</i>Those words aren't coming down until you get ambidextrous"</li></ol>Then mommy will come by and ask why I'm subjecting our 5 year old to ambidextrous. By 4th grade, he will have forgotten what this word means.<br /><br />Once we both got past the training, I could raise the bar as high as 'Stand and Deliver' while I challenged them on word meanings. Since I didn't care whether the word came down this week or next month, it was all them. Nor do I give a fig about their self esteem. They can earn it if they want it. Which they did. The hard way. I've got 2 kids with enough self esteem to fill a class room.<br /><br />We retired the Word Board after about 3 years. The Word Board only came back sporadically. Three years defending at the Word Board produces a child who will acquire and retain word definitions on sight, and this makes the Word Board less useful except for advanced math and science.<br /><br />I speculate that bilingual children are going to get a permanent advantage for the same reason. The first few years of their lives are a big Word Board to sort through.<br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-15403501598999533142018-03-31T01:29:00.000-07:002018-03-31T04:43:09.065-07:00Step OneI see a strong correlation between what we're doing now at the end of grade school to make gains on the TTWBN and what we did years before simply to gain entry into a special program.<br /><br />In the this series of articles I'm going to rehash the groundwork and put a bookend on it. I think reading is the foundation, so I'm starting with reading.<br /><br />In the last article, I stated that success in education is highly correlated to the level of discussion that takes place in the home. There are only 3 areas of research that have identified a cause of intelligence (roughly defined as permanent academic skills that manifest themselves in a strong, accelerated academic performance).<br /><br />The first is summarized in Welcome to Your Child's Brain and concludes that if you maintain an ongoing one way discussion with your infant, your infant will reach age 4 reading at a 6th grade level. I've see parents do this and it's breathtaking. <br /><br />The second area of research is more important because most of us are too busy being a parent to talk. This line of research concludes the level of vocabulary used in the house will determine you're child'd education potential. I like this line of research better because it allows for a late start.<br /><br />The third area of research is presented in The Read Aloud Handbook and states that reading to your child will put them permanently ahead of the crowd. I like this approach even better because I was never good at having an ongoing discussion with my child because he was always knocking something over, and 'Please refrain from disassembling you're brother's block tower until he has indicates disinterest' didn't seem as appropriate as shouting 'Stop it right NOW!'. During nightly reading, however, we could have some fairly productive Q & A. Nightly Read To is good parent training.<br /><br />What I like best about reading, however, and the reason I put it number one is that many kids get into special programs simply because they do nothing but read. They struggle mightily with figure matrices, and it takes them extra years to finally get past the test. But once they do, they generally end up permanently at the top of the academic heap. Whereas my approach is simply to cheat with lots of logic and problem solving. Why spend 6 years reading when you can just spend 3 months in thinking and working memory boot camp? Being the underdog and trouncing readers is quite satisfying. Then I stepped back and wondered 'What if a child did both?' Light bulb.<br /><br />In the introduction to Pre-K Phonics and Conceptual Vocabulary I lay out a reading program that goes way beyond over the top. It was the most fund* I had with my kids. I probably only need a few changes to my advice:<br /><br /><ul><li>'Pre-K' is somewhat misleading because it goes straight through 2nd grade material.</li><li>No child will ever grasp the difference between 'dew' and 'due', but presenting a fairly advanced and confusing concept at such a young age pays dividends for test prep. (I should write a whole article on this bullet, but in short a child who knows there is a concept lurking out there that is extraordinarily complicated and thought consuming is on the verge of some serious thinking when faced with cognitive skills workbooks.)</li><li>You will definitely want science and nonfiction represented in your reading list, but do not show any enthusiasm or push this in any way. As soon as you hand your child the Magic School Bus and indicated that it is really important to know science, science will become uncool automatically and you may discourage a future scientist. Same with history. Try to look at science books nonchalantly. </li></ul><div>*Fund is a typo. It was supposed to be 'fun'. But I'm going to leave it as is because I think fund is just as appropriate. However, reading was a lot of fun.</div><div><br /></div><div>When we read, I'm more than happy to short circuit the learning process and define words, share background and history, point out logic. The child will get enough time testing their skills in silent reading and picture books. As a bonus, eventually you will lack all credibility and merely stating the obvious becomes an exercise in your child pointing out why you are wrong. But that comes later. In the meantime, this is the best of all times to make up for the fact that you didn't carry on a lively discussion at ages 2 and 3.</div><div><br /></div><div>The classical approach to education reserves this time in your child's life, maybe up to 4th grade, for packing their brain with as much information as possible. Pack it in. Then jam some more in there. Reading together will help you do it. This is a low pressure exercise. Throw spaghetti at the wall and see what sticks. You can do this a little at a time or use a spaghetti cannon like I did. It's not really about gaining anything but just having fun.</div><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com2tag:blogger.com,1999:blog-5703568807615263851.post-25137315327603233902018-03-28T22:43:00.000-07:002018-03-28T22:43:12.808-07:00The Covert BlogI'm trying to minimize the SEO on my blog. SEO stands for search engine optimization, and it means that you put key words in your articles so that it shows up on search engines. If my editor finds out, then I'm in trouble.<br /><br />In this article, I'll answer a common question that I get. Where is this heading?<br /><br />From the beginning, I've found summarizing my research for the public allows me to scrutinize my evidence and edit out failed experiments so that what's left is reliable advice that you can bank on. In the first year, when I was competing for a spot in a "special school program" (you know what I mean) I nailed that test for that program. As I was writing, and reviewing past articles a month or so later, I would see things I missed, obvious things, and the door was opened.<br /><br />I feel like this special test (you know what I mean) is 100% crushable way beyond the required cutoff score. The pedagogy to get there is counter cultural and counter intuitive. I don't see evidence that it can be replicated in a school setting except in a few standout programs led by visionaries. Most parents will never meet success because they can't let go of 'learning something'. 'Something' always interferes with 'learning'.<br /><br />I'm turning my attention to that other test that 40,000,000 kids take every year in school. My research is sneaking into my blog whether I like it or not. Our target is this year and then again in 3 years. It is much more competitive than the first test mentioned above, and the approach is almost identical with the exception of shapes being replaced by advanced math and the pictures replaced by unknown vocabulary words. I refer to this test as the TTWBN (the Test That Won't Be Named test).<br /><br />Most parents face both the special test and the TTWBN test for entry into a special program. Before 2nd grade, the best way to prepare for the TTWBN is just to be 2 years ahead in school. Somewhere around 2nd grade, other bright kids catch up, and it's not enough to be ahead. A child has to master academic skills at a very high level. I'm going to write more about this test without giving away the most critical competitive element - its name.<br /><br />The common view of special programs is that that the children of wealthy parents will always have a competitive advantage. The skill set behind this test is almost always attributed to inherited or genetic intelligence, a myth which has been dispelled. The genetic link only makes sense to researchers oblivious to the scientific method and who have never met an actual child. 'Intelligence' is not definable let alone measurable, and you can't correlate an unmesaruable variable to anything else no matter how much wishful thinking is passed off as results. If you sit in a wealthy household, you'll observe educated parents maintain an environment rich in vocabulary, discussion, and reading. Education is highly correlated to wealth. Vocabulary is the foundation of the whole enterprise. Thus wealthier households are much more likely to produce gifted children. The research on vocabulary as the predictor is strong, compelling, and generally ignored. If you sit in the house of a poor science teacher, you'll see the same dynamic in action and the results are the same. If you don't have a stack of data on household discussion and test scores you'll miss the dependent variables.<br /><br />So my first long term goal is to put vocabulary and reading into the poorest households at the level that my children experienced. It's unlikely I'll do this, but one of the children who went through my program (thanks to a parent who found out it's possible) will decide on a career in education.<br /><br />The other long term goals, in order of priority, are for bright thinkers of the next generation to tackle poverty, violence, and the propensity of governments to spend the money of the next generation and bankrupt their educational and social systems. This makes me a liberal and a hard core conservative at the same time, so I'm throwing in a forth goal that one of our future leaders will get democrats and republicans to work together, something along the lines of 'let's spend money on poverty by doing something effective' subject to 'we can't steal money from the next generation to do it'. Sounds like a republicrat program to me.<br /><br />I've been watching young people step up in two areas recently; both areas have been in the news. They are beginning to touch on the core arguments but are not tackling the lies and fallacy and mislogic and ingrained misthinking that need to be overcome . They're close and they're hearts are in the right place, but we really need a few young John Locke's to step up and transform the world in these areas. <br /><br />I'm too busy to do it myself. I have too much education research to do.<br /><br /><br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com4tag:blogger.com,1999:blog-5703568807615263851.post-23046390086372947412018-03-24T11:53:00.002-07:002018-03-24T11:53:35.085-07:00Really Bad AdviceMy google news feed has delivered articles from the SAT experts. I've been reading how to solve the hardest math problems on the SAT to see if I can improve my super secret strategy for the TTWBN test. I'm learning that the experts don't know anything useful.<br /><br />The goal of an expert is to dissect the problem down to steps that lead to the solution. This teaches nothing, of course, except for a memorized list of steps for a problem that will never be seen again. The solution advice has an element of time management, as in narrow down the problem to the work that has to be done in the shortest time possible. This approach will backfire, because once you short circuit the analysis with time pressure, it's much harder to find the right path. Dead ends will be stress inducing. Unless you are an expert and already at the 1600 level, in which case it's easy. <br /><br />The TTWBN test has no time limit, and we're going to take full advantage of that fact, like 4 hours per topic. The difference between preparing for the TTWBN test now and the SAT in high school is that we'll spend one or two sessions under time pressure before the SAT . The prep process is going to be identical, including spending 10 minutes per question.<br /><br />I've rarely mentioned one of George Poyla's strategies for solving geometry problems. Rarely mentioned it, but we do it all of the time and it's behind 'Read The Question' for little people preparing for the COGAT. He warns readers that geometry proofs will need to use prior results, maybe from the last proof or from last week, to solve the current problem.<br /><br />The version that I use for grade school is that if you see a geometry, solve everything before you read the question. I want every line labelled with a length and every angle with degrees. If it's an algebra problem, be prepared to rearrange and transform. I've written before about this in the context of verbal analogies. Here's what inevitably follows:<br /><br /><ul><li>We get stuck because someone forgot that a + b + c = 180 or adjacent angles sum to 180 or something else that we didn't cover yet. So we cover it.</li><li>During this process, the characteristics of the problem at hand become clear.</li><li>The solution strategy presents itself and the answer usually becomes known before the pick list is surveyed.</li></ul><div>This is a much better approach than "What I am supposed to do?" followed by me explaining solution steps. I might as well talk to the wall.</div><div><br /></div><div>Before 4th grade, this skill is called 'Read The Question' and involves me asking lots of what if questions about a figure matrix or verbal analogy for 20 minutes before we actually pick an answer. I originally did this because really challenging COGAT test prep questions take me a long time to create and aren't found on practice tests so I wanted to get the most out of each question.</div><div><br /></div><div>I'm currently experimenting with similar approaches to Reading Comp. When I get to the end of a boring passage, I remember very little about the passage, maybe 2 nouns like bridge and engineer. Then I get a list of questions that ask who the author is, what type of writing is this, how are they feeling, how many arguments are in the passage. Then I go back and reread the passage to find out. 3 years into this, it dawned on me that I'm going to be asked this stuff anyway, so I might as well look for it.</div><div><br /></div><div>A parent might be fooled by the engaging quality of most reading comp passages. Don't be fooled. You're an adult now. Everything is interesting to you. Your child is totally bored beyond comprehension. So I announced that after the passage is read, and before we begin work on the questions, I want be told a lot about the passage, like who's writing it, what type of writing is it, what's the point of each paragraph, when did it happen? I'm inching our way toward not having to read the passage a second time thoroughly (thinking ahead to a timed test). I'm the same way about the questions. Was line 32 about eclectic dissension? Exuberant facilitation? Ascetic abnormalism? If we're luck, the answers will have about 20 words that need definitions analysis in the context of the narrative. Unless it isn't a narrative.</div><div><br /></div><div>Will the child take the hint and adopt this approach to reading or math? Certainly not in my presence, out of spite, but probably in the classroom and when it counts on the test. I've caught them both doing things properly when they thought I wasn't looking.</div><div><br /></div><div>So here's my bad advice. If you follow my approach properly, your child will get through very little material, probably do it wrong 5 times, forget the next day what was learned, and not have any academic knowledge to show for it. All the while, the important skills will be forming. Then one day they will magically know everything and things will be really easy. The first few months are a struggle.</div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-14247862306411663862018-03-17T09:57:00.000-07:002018-03-17T10:35:38.320-07:00The Test That Won't Be NamedIn this article, I'm going to jam 7 articles into one because I'm really pressed for time on the weekends.<br /><br /><b>Review of Home Schooling Literature</b><br />I've been reviewing home schooling guides lately to see if there's anything that I can add to my At Home School curriculum. "At Home Schooling" means doing a little extra work weeknights and weekends to make up for the slow pace of learning at school.<br /><br />Home school curriculum guides are pretty disappointing. If I were full time home schooling my child, I would be planning to send the child to Stanford at age 14 because home schooling is so easy. The curriculum guides shoot for something more average.<br /><br />As most curriculum guides point out, trying to teach anything to your child is really hard. What they don't point out is that your child will learn at an accelerated pace once you stop teaching. The impossible becomes the easy. The secret is in the approach, which I will describe in the next article (below).<br /><br /><b>The Secret to Learning</b><br />Almost every week, I have to remind my kids that they have to slow down. I had to tell the younger one this story again.<br /><br /><i>There were two equally bright, equally capable children. One was dumb and one was a genius. The dumb one looked at a hard problem, became frustrated because he didn't know it, and started guessing. He got the wrong answer. The genius looked at the same problem, became frustrated because he didn't know it, and started to work on it slowly one step at a time. He tried 3 times to do it, and finally chose the answer, which was also wrong.</i><br /><i><br /></i><i>A third child who was equally bright and capable also struggled with this problem. He was smart. He also took a long time to work through this frustrating problem, and after his fifth try, he bothered to check his answer, found a mistake, and fixed it. The smart child got the correct answer. </i><br /><i><br /></i>The smart child is getting 99% on the Test That Won't Be Named, but the genius is stuck between 85% and 95%. Both are learning about the same amount. Maybe the smart child is getting a bit more out of the learning process because he's checking his work. What's the problem here? The problem is that the smart child is fixated on the goal of a solution, especially the correct solution, and the genius is more interested in the learning process. Eventually, the smart child is going to be in an advanced accelerated course (or maybe pre Algebra) and the work is going to be really hard. Both the genius and the smart kid will make lots of mistakes, and this will bother the smart kid so much that he drops out. But the genius, who doesn't care about the answer in the first place, will just plod on as usual until he has a PhD in a joint Law Medicine Chemical Engineering Medieval Slovakian Literature.<br /><br />I've warned the genius that he better start checking answers because if he doesn't get a perfect score on the TTWBN test he can forget about AP courses because he won't get into a good school.<br /><br /><b>The Secret For Parents</b><br />Among equally capable parents, we find dumb, smart, and genius parents. The problem that parents need to solve is that you have a child doing a problem - whether it's a cognitive skills exam, or one of the 2 main sections on the TTWBN test - and your child is totally not getting it. Dumb parents expect their child to get it, smart parents expect their child to get it after a long struggle, and genius parents really don't care.<br /><br />Once you see a child go through this process, you get it as a parent, and work and frustration is replaced by work and learning. For this reason, the 2nd child should always end up twice as smart as the oldest sibling, given a fraction of the learning time.<br /><br />When I was a dumb parent, I came up with the parent skill set in order to survive the first few rounds of my ridiculous At Home School curriculum goals. The very first goal was to skip first grade math and do 2nd grade math starting on winter break in Kindergarten. This was the worst and best idea I ever came up with. (Tip - if you do hard core COGAT test prep at age 4, 2nd grade math at age 5 isn't all that challenging).<br /><br />As a reminder, my survival steps include start every problem by acknowledging that you are totally baffled, take a long, long time reading the question, going so far as to do a workbook on the topic before you get to the answer, make a lot of mistakes and go out for ice cream any time the child gets 100% wrong, and if a test is coming up, check the #%$!!!! answer. The parent will encourage these steps. For the parent, I'd like to add 1) set your expectations at zero, 2) I really mean zero, not .0001 but zero, and 3) stop looking at the solutions.<br /><br />You can't practice learning skills (see prior paragraph) if your child is doing a 30 question timed worksheet or knows the material or doesn't make mistakes. That's why we have a pace of 1 to 5 super hard problems in Math House.<br /><br /><b>Reading</b><br />I always considered reading to be a filler activity. I'm beginning to think differently. Competition for GAT seats is between kids who read 6 hours a day, and those of us who will just become really good problem solvers (aka shapes, math and logic) and cheat our way into the program. Cheating is much more satisfying and is the basis for higher order math.<br /><br />To be on the safe side, we did lots of vocab (vocabularyworkshop.com) and 2nd grade phonics starting on day 1 (Pre-K Phonics Conceptual Vocabulary and Thinking). But it was always primarily silly and fun. Why discourage a life of reading by putting pressure on the first year?<br /><br />I think my casual approach to reading is the reason language arts thrived in Math House.<br /><br />Yes, I grilled the kids at the Word Board (<i>How would a commander on the battle field use the word 'dispersion' in a sentence?</i>), but they didn't actually have give me a proper response and I didn't want to take the words down because I was going to quiz them on the synonyms in a few days anyway.<br /><br />But mainly we went slowly and had fun. When I say slowly, I mean when you try to slow down to nothing the child learns at a highly accelerated rate. That doesn't make sense until you see it happen, but it always does.<br /><br /><b>The Magic of Slow</b><br />I've decided that I'm no longer teaching math in Math House. Once again, I want to teach How To Figure Out A Problem. We lost that last summer trying to tackle high school math. Figuring out a concept is a much more useful skill than getting a correct answer on known material. That was the whole point of TPM. If your child masters Figuring Out A Concept, then At Home Schooling is more productive.<br /><br />In order to prepare for TTWBN, we've been working with an SAT test prep book. This doesn't mean that we're tackling high school material at a high school level. The SAT is more like grade school material for an advanced child in really convoluted problems. This characterization of the SAT motivated Test Prep Math and it's been paying dividends ever since, until we started doing high school math last summer and started to focus on knowing match concepts.<br /><br />Here's a problem that demonstrates the full range of skills, those listed above, and the skill of Seeing (aka take time to look at every element of the problem and see the things that other kids miss for lack of vocabulary or patience). No matter how old your child is or how long he's received this training, he still forgets to practice the basic skills because he's in a hurry to finish math and get on to something more enjoyable, like going to the dentist.<br /><br /><div style="text-align: center;"><a href="http://3.bp.blogspot.com/-zGTNqFB1cNs/Wq04dffOShI/AAAAAAAABvs/ubA0SSJcPswof4SaRcfoo7wN5WQZwQJaQCK4BGAYYCw/s1600/Untitled%2Bdrawing%2B%25288%2529.jpg" imageanchor="1"><img border="0" height="188" src="https://3.bp.blogspot.com/-zGTNqFB1cNs/Wq04dffOShI/AAAAAAAABvs/ubA0SSJcPswof4SaRcfoo7wN5WQZwQJaQCK4BGAYYCw/s200/Untitled%2Bdrawing%2B%25288%2529.jpg" width="200" /></a></div><br />The triangle above is isosceles and AB > AC. Which of the following is false?<br /><br />I'm going to omit the answers because of an important technique Poyla's How To Solve it (1945). When I translated Poyla for 5 year old's preparing for a gifted exam, it becomes 'Read the Question'. The translation applicable to preparing for the TTWBN is 'if you see a geometry problem, solve everything before you look at the actual question.' (If this were age appropriate SAT test prep, then I'd take Poyla at face value because the topic of the book is geometry proofs for high school students and we'd be working under time limits.) The version for algebra is 'you're going to transform the equation so stop trying to solve it in your brain' and for trig, 'get out the basic formulas and be prepared to do geometry or algebra on top of that'.<br /><br />Anyway, we reviewed the definition of an isosceles triangle (totally forgotten since age 5 training), the sum of the angles in a triangle, and a hint where the base of the triangle is. There are the 3 steps that require Working Memory. Love this problem. Don't care about the solution.<br /><br />Initially, this problem resulted in guessing so I had to jump in and 'help' by asking questions. When I work with other people's children, they are more than happy to work thoroughly and patiently, but when I work with my own children they get frustrated and guess. Am I exaggerating? No. This is why it's so much work for a parent. Other kids just assume that I'm a teacher and therefore this will be a doable problem or else I wouldn't teach it, and things go well, but my own kids assume I'm an Insane Tyrannical Cruel Math Despot and am torturing them. You will face the same problem with your own children, which is why the survival skills above are so important.<br /><br />We've been working consistently at a pace of about 5 problems per day, and over time the child might do 3 problems on his own (incorrectly) and only need help on 2, and before you know it, he's back to needing help on all 5 problems because I had to switched to much harder material.<br /><br />Anyway, it was this problem where we ran into guessing and I decided I would much rather have him just work the question than try to solve it until he substitutes his subpar approach with '15 minutes of reading the question and 1 minute of getting it right'.<br /><br /><b>Reading</b><br />I've been happy to ignore reading until now, just doing the minimum lots of vocab and a couple hours of reading a day, an approach that paid dividends, but this year the older one has to take TTWBN for real and the younger one would rather do the verbal sections than the math sections to spite me. So it's time to get serious.<br /><br />When I bought the SAT books a few years ago (2nd dumbest and smartest idea ever), we had a lot of success but my 5th grader and I failed at the reading comp. We never made it past baffled.<br /><br />I knew a high school English teacher named Yoda who taught SAT test prep classes and begged the little green guy for advice. He said, 'Ask why you got the question wrong, you must'. I'm not kidding, aside from the Yodese accent; this is the only thing he said because we were sitting in a Boy Scout meeting whispering and then got shushed, and I haven't seen him since. For a year, we kept coming up with the answer 'Because neither of us know what the heck we're doing trying to do with SAT reading comp questions in 5th grade' and then gave up.<br /><br />Now I've got a 4th grader and a 7th grader with identical books (each have a copy) and I'm starting to get it. If you've got a 99.6% GRE level in vocabulary (because on the pre-test you got a 50% so you did some serious test prep back in the day) or a good dictionary, the reading comp section boils down to...but first I should point out that given the age difference, it's a totally different experience with each and the 4th grader finds those small passages that ask about sentence structure - saving the long passages for 6th or 7th grade.<br /><br />By the way, to overcome the vocab deficit, I've found that about half the time if you just add a 'y' to a word it's good enough. Decisive becomes Decisiony and we can move on. The rest of the time its a longer discussion.<br /><br />Anyway, it once again boils down to Math. It boils down to math. It's all just logic, one word at a time, counting sentences, iterating. If Math is 100% language based (I've said that before) it's only fair that reading becomes 100% math based. The left-brain-right-brain theory turned out to be totally wrong.<br /><br />Or, if you don't like that answer, it boils down to math in the sense of be baffled, spend a lot of time on the question (including the pick list), go slow, make mistakes and try again, and check your work.<br /><br />It's also patterns. By the time we're done, I'll know every technique, aspect, variation, and trick of the SAT. For example, when an answer choice is 'the author reluctantly agrees partially', you need to find concrete evidence in lines 30-33 of reluctant, agreement, and partial not whole. Applying Poyla to this material, you better be able to tell me the author's life story after you read the passage and before you start answering questions. It took me a year to figure that out, but now it seems obvious.<br /><br /><b>The Danger of Test Prep Classes</b><br />The problem of a classroom of any type is that to serve all 20 or 30 students, you have to TELL them the material. All kids are paying the same amount, and they'll all come out KNOWING the material and performing well on a test if you just tell them. This will work on a standardized test or even some gifted tests for some kids with specific learning styles. I worry about the longer term impact (jury is deliberating).<br /><br />The problem of TTWBN is that there isn't enough time to teach all of the material that the test covers at the level we need to be each year, and this is the big year. So I'm back to focusing on figuring things out.<br /><br />How important is At Home Schooling? Is it important enough for me to set aside a few hours a week, maybe a few more for research and preparation? Is it important enough for me to go through the frustration and headaches?<br /><br />What will the child think if I say 'This is not important at all to me to spend any time on it, but I'm going to make you go to this totally unimportant class'. The child cannot visualize money and he doesn't visualize you sitting in traffic. If you are not physically there going through the same pain, a bright child will conclude you do not value this activity at all that you are making him do. You won't see an impact with little kids, but you will see it later.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-79926587295775160362018-03-11T09:21:00.003-07:002018-03-11T09:21:36.094-07:00The Kindergarten ChallengeHere's a challenge I received from a reader. <br /><br />The 1st grade child scores 99% on the NNAT one year than falls to 80% the next. Reading and math scores also fall. All scores have to be near the 100% mark in three months for GAT entry.<br /><br />The child is going to be home schooled. I'm very excited about this. It only takes a few hours a day to give the child 8 hours of education, and the child can sleep in every day which is critical for intense instruction. This leaves about 50 minutes for test prep and 2 hours for art, crafts and projects every day and 3 hours of reading. I consider science to fall under crafts and projects at this age. Think sorting rocks, vinegar and baking soda. First grade will take about 4 months under these conditions, and second grade another 4 months.<br /><br />The parent needs to find out the times of day when math works. Is math first thing in the morning, or is it morning painting and Read To? Test prep needs 2 times, one in early, late or mid morning, and one sometime in the afternoon.<br /><br />There are a few reasons why the scores fell year-over-year. I could write a whole article just on that topic. For now, the things I care about are a) anything score 50% is not a bad starting point, b) three months of prep is better than eight weeks, and c) we need to slow down the pace of learning, probably by about 90% and ramp up the complexity of the material. If the child did not do well on the test because the parent teaching methods and attitude are a total disaster (been there) then we need to fix this, which will be a separate article.<br /><br />Yes, I said slow down the pace of learning. This is probably the biggest factor in GAT preparation. My pace when I coach is 1 problem in 20 to 30 minutes (depending on the child's age) and 5 or 6 problems when the child works alone. We're just as slow in math, and I've managed to get two kids into high school math at age 9 or 10 on 5 problems a day. Not that they're especially talented in math.<br /><br />The premise of "slow" is slightly counter intuitive under a deadline. Here's the explanation. When you build an academic culture where a little work goes a long way, you're using the skills measured by the GAT tests, skills that are also critical to standardized tests like the MAP. Unless it's a timed test, but we can account for that after the learning takes place. When you have a culture where problems are easy, correct answers are expected, and worksheets are long and fast, the child is going to totally bomb on a test like the COGAT and NNAT.<br /><br />I would make time for Vocabulary Workshop because it's so much fun and children learn how to eliminate answer choices as they quickly progress toward harder material. I would have a Word Board for something because it's where adult discussions take place and where the child has to stand up and deliver. Or fail. There's always the next day.<br /><br />For math and test prep, let's teach this child so that he or she gets to 99%. I've been going back through my articles thinking about my teaching methods. I don't think articles are clear on my preferred approach:<br />1. Give the child super advanced material and let them flounder. Eventually they will pick up the skills to work with super hard advanced material.<br />2. Give them advanced material and let them do all the work before you don't grade it. (No typo, read that again.)<br />3. Walk through the super hard material together, one question at a time after they do it.<br />4. Do it with them, one question at a time, mostly just asking questions.<br />5. Give them simple material on a super advanced topic so that they can learn one step at a time on their own.<br />6. Give them last year's workbook (last year may actually be next year depending on the circumstances) so that they can catch up on material they need to know in order to keep up with 1 to 3 above. They can do this on their own, or with some starter help.<br />7. Lay 5 skittles on the table, one of each color, and provide a skittle each time your child gets a correct answer.<br />8. Give them a skittle just for making an attempt.<br />9. Do the problems yourself while they watch.<br /><br />Lately I've been doing 4b, which is to break down a problem entirely and a class or rules, but I didn't do this in first grade. I did say Shape Size Color Count over and over when they were stuck to remind them not to look at a problem for 15 seconds and announce that they were stuck, because that's called 'The Beginning of the Work'. <br /><br />Which approach do you use? I used them all.<br /><br />I used a variety of material, not because of the Spaghetti approach, but because sampling is the best way to find out what works, a child needs to learn from all materials, and a child needs to learn all learning styles and accommodate all teaching styles. It's not a matter of what the child likes best (aka the easiest), but what works best on which day to meet our goals.<br /><br />Finally, both cognitive kills tests and the upper levels of standardized tests in math and reading require deep, careful thinking over an extended period of time, mistrust of answers, tackling something unknown, surprising, new, with subtle, hidden complexity. How to you train a child to have these skills? #1 through #5 on the list above. It works the best with 1 super hard long 25 minute mind numbing problem, but in practice, this is a total disaster with crying and yelling, so I've settled on 5 medium really hard problems in 25 minutes. After that, brain exhausted.<br /><br />I almost forgot. We also did music starting in Kindergarten. I gave my child an electric piano and the Piano Adventure series, and no help what so ever except for tempo. <br /><br />Remind yourself that the child will be sitting in some advanced class someday without your help. The child will be taking a test without your help. This is what you are preparing them for. So many people get hung up on them having to know math because they have to get above 95% on the math section. It's so much easier to train them to think and then math comes really easily after that.<br /><br />What would this take? I think a few reading comp books, about 10 to 15 each, maybe 3 math workbooks, judicious use of the web, 2 vocab workshop books (current followed by current + 1 for starters), maybe one reading comp book, but lots of reading of all kinds. I would go to Michaels and buy lots of cheap crafts and things like that bead thing, concentrating and creativity activities, painting, and then whatever test prep books you want. <br /><br />Origami. Almost forgot. Origami is really good for visual spacial and fun, and the test we're challenged with in this case is the NNAT after all. You can create all sorts of animals. Do not let you're child do an activity that requires you to do it. It's kind of the opposite of test prep and how I do math. <br /><br />Totally excited about this. The thing I got out of this time period is a) I learned how not to be impatient or expect anything or care about correct answers and b) I ended up with a much closer relationship with my children and some credibility with them. a) led to b). a) also leads to a boatload of learning in a short period of time.<br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com3tag:blogger.com,1999:blog-5703568807615263851.post-42592442784695003442018-03-03T12:09:00.001-08:002018-03-03T12:09:20.341-08:00Putting Skills To The TestI've been working with a few hypotheses since about 2011 based on my research into the COGAT. Six years later, it's time to see how these hypotheses faired over time.<br /><br />Since I am the only person in the universe who a) believes skills exist, b) believes that skills are learnable and c) isn't making you buy a product or service to learn about skills, this website is pretty much your only resource. It would be nice if it were accurate as well.<br /><br />Here are my hypotheses.<br /><ol><li>The COGAT measures the skills that predict academic success.</li></ol><div>This hypothesis is based on the simple observation that school districts pay a lot of money for the COGAT in order to populate their gifted and talented programs. I read the research of the current test author and determined that he stands apart form cognitive skills researchers - all skills and no genetic intelligence.</div><div><br /></div><div>Any parent who forgoes COGAT test prep (or a similar cognitive abilities test) has no interest in a child with cognitive abilities. </div><div><br /></div><div>Unfortunately, future academic success is dependent on a child who has continued interest in academic pursuits. If the child lives in a house that devalues academics or goes to a school that devalues learning (aka most schools governed by No Child Left Behind) then hypothesis #1 may be undone. What started as an assumption is now ongoing research. So far, so good.</div><div><ol start="2"><li>The skills are age independent.</li></ol><div>Another way of stating this hypothesis is that once the skills are learned, the child has them forever. A child could pick these skills up at age 3, or age 15. Everything I've seen in the last 6 years supports this hypothesis. A corollary to this hypothesis is that the probability that the child will pick up these skills decreases every year after 1st grade, probably because of NCWLB, with the exception of age 15 (which I haven't personally researched yet.)<br /><br /></div></div><div>I first came up with this hypothesis while reading a description of the classical education in the Well Trained Mind. The classical education has a breakpoint every 4 years and is based on the development of the child, brain or otherwise.<br /><br /></div><div>I've noticed leap in skills around 5th/6th grade academic material, certainly by middle school, which I've had some fun with recently and describe below.</div><div><ol start="3"><li>The list of skills is boring and unremarkable.</li></ol></div><div>I'm not going to restate my skill inventory here, but if you read the list in prior articles, it's not really earth shattering. I think I would have more readership if I could come up with clever sounding names for the skills or write articles like '10 Things You Didn't Know About Skills', but there are only 4 or 5 things you didn't know, and those are the skills. </div><div><br /></div><div>What I find more interesting is watching a child go through the transition from not using the skills to overcoming very difficult material by applying the skills. Take Mistakes, for example. A child doesn't need this skill, and is not incented to use it because it requires some effort and controlling emotions. The reason the child doesn't need this skill is because parents and teachers are willing to explain the mistake, show the solution, explain the solution. There is a high price on making mistakes in the first place. Once the support structure and penalties are removed, the child has to go through the process of proving to himself the value of mistakes, as in make one, learn something, try again and again, and achieve the solution with no help. It's like military boot camp. Not fun when you're there, but it pays off.</div><div><br /></div><div>In practice, I observe the emergence or application of about a dozen sub-skills during this process. The sub-skills are germane to the subject and child specific. I've never seen a reason to discuss most of these (except the big 5) because we'd end up just replacing spoon-feeding-training subject matter with spoon-feeding-training sub-skills and be back to a helpless child who's not getting it. Right now I'm tackling middle school reading comprehension with a vengeance and we are heads down on the sub-skills, but that article will wait until we get past the high school entrance requirements.</div><div><br /></div><div>Recently, a 4th grade buddy came over to play Minecraft. In Math House, the rule is no math, no computer. In this case, 'math' meant learning algebra from scratch in 25 minutes or less. This child is solidly at the top of the gifted spectrum. I don't know why his parents didn't bother to teach their 9 year old algebra yet - probably because they are not insane - but it qualified him for my research.<br /><br />During this experiment, I noted that there is a leap in skills required of algebra. I'm not talking about- abstract thinking or a new language in the form of different syntax or seeing pre-algebra for the first time. Because of this leap, the child went from 99% in skills to 0% in skills before working his way back. Also, note that parentheses alone work a magic spell on children that makes them forget everything they've ever learned. <br /><br />Here's a transcript of the experiment.<br /><br />Me: Solve this equation: 3 + 5 = ? (He responded 8, then looked at me like I was a moron.)<br /><br />Me: Solve this equation: 3 + 5 = ___ Does it matter that I changed the question mark with a blank? (He responded no.)<br /><br />Me: Now solve this equation: 3 + ___ = 8. Is it totally confusing that the blank has moved? (He answered no.)<br /><br />Me: Not solve this equation: 3 + x = 8. I am replacing the blank with an x. Instead of telling me what goes in the blank, tell me what x is. Is this to confusing for you? (He answered no.)<br /><br />Me: Now I want you to use algebra. Instead of just solving for x, you have to transform the equation one step at a time. You can either add a number to both sides, subtract a number from both sides, multiply both sides by a number, or divide each side by a number. (There are a few more transformations, and I didn't mention expressions, but we're keeping it simple because we only have 25 minutes for this experiment.)<br /><br />Me: Here is everything you need to know about algebra. Look at these 2 equations and tell me what is wrong with the second one:<br /><div><ul><li>x = 2</li><li>3 + x = 8 - 5x</li></ul><div>Me (after a brief discussion): The first one is perfect. I know the answer immediately. The second one is broken because it doesn't have a letter on the left side and a number on the right side. Fix it. You can only use 1 of the four transformations, and you can only do one transformation at a time.</div></div><br />Rules: a) apply one of the 4 transformations to both sides, b) only apply one transformation at a time.<br /><br />We took a break at this point to remember the scale problems from 2nd or 3rd grade math (which he forgot) and assure ourselves that the 2 sides stay equal when these transformations take place. Then he had to tackle these 2 problems:<br /><br /><ul><li>3 + x = 8 - 5x</li><li>7x - 15x = x(x + 5)</li></ul><div>It's really fun to watch what happens next. First of all, rules a) and b) from above are both violated repeatedly. "Both sides" is forgotten. Gifted kids are gifted in part because they can solve complicated expressions in one shot. In practice, they combine steps. Doing only one step and writing it out is like eating broccoli. When I teach algebra to young kids, I'm always battling them trying to figure out the answer in their head, which they can do. I'm asking them to stop doing things in the way that they are good at, and start doing things in a way that they are not good at and will likely lead to an incorrect answer. It's more than Baffling for this reason. </div><div><br /></div><div>Next, they forget how to add and subtract single digit numbers.</div><div><br /></div><div>Any pre-algebra kids learned up to this point is also forgotten. This includes parenthesis and not adding x to 5, because you can't and x to 5 and get 5x or 6.</div><div><br /></div><div>I made some really cool observations during this experiment. The subject wondered what 5x means, and then realized why dot means multiplication - because writing 7 x x to mean 7 times x doesn't make sense. His skills of analyzing the question were strong. Analyzing the question in algebra, at least initially, means learning quite a bit on the spot that was not previously known (which I minimized in the problem above). It's a leap in this skill. Once we get beyond simple one variable equations, the question analysis takes a leap.</div><div><br /></div><div>It's hard to make the leap to 5x + x. What does this mean? It means that you have 5 x's, and I give you another x, how many x's do you have now? It's like working with a 3 year old on addition. Did you forget to add? Do you want to do it on your fingers, butter bean? Do I need to invite the 3 year old down the street here to teach you how to count on your fingers? I really need a control group where I don't antagonize the subject.</div><div><br /></div><div>The most remarkable observation for this experiment is that the child typically (100% of the cases) get's stuck on what to do even though according the rules, the only thing to do is apply one of the four transformations to the equation. Maybe they can clean up the expression by making 7x - 15x equal -8x, but that's not what they are stuck on. Without doing enough of these problems, it is not clear which arithmetic operation to apply to each side. Addition? Multiplication? Subtraction? Division? These kids break the transformation down to a simple question & answer, and they don't know the answer. The correct approach is to try all 4 and see if the resulting equation is getting fixed (aka easier) or more broken. Algebra has the skill of Mistakes build right into the process.</div><div><br /></div><div>That is the biggest leap in skills.</div><div><br /></div><div>At age 5, a gifted child will make a mistake, not be bothered, and try again until the solution is correct. Really gifted children (on standardized tests, anyway), check their answers to verify that they didn't make a mistake.</div><div><br /></div><div>With algebra, initially, on each step there is a 75% chance that you will make a mistake, and you may have to try all 4 to see where the equation is going. That is a 25% error rate built in to each and every step. Sometimes you might even have to do 2 or 3 steps, trying a series of transformations, before you know you are on track, and you've ended up with a score in the single digits before you get past the first problem.</div><div><br /></div><div>I've occasionally mentioned that I think drawing is a valid way to teach a child to be gifted in math. Hand your child a 2 inch stack of paper and a dozen pencils, and ask them to draw a realistic looking horse. All of the cognitive skills are used to their extreme in this exercise. Children who draw for a living should become math powerhouses*. </div><div><br /></div><div>*It depends on what they draw. Horses aren't good enough. Needs something with lines and circles in it.</div><div><br /></div><div>I prefer crafts for math training to prepare for algebra.</div><div><br /></div><div>Anyway, the subject passed the 25 minute algebra lesson and his parents didn't complain yet about any signs of psychological damage.</div></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com3tag:blogger.com,1999:blog-5703568807615263851.post-8603296718896808752018-02-28T21:11:00.000-08:002018-02-28T21:11:02.230-08:00Skills In PerspectiveIn the last article, I went a little overboard on the technical detail with some middle school competitive math. I tried my best to lay out problem solving so that you can see it is consistent with little children and consistent with the high school, college, graduate school and post doc experience.<br /><br /><hr />Let me explain this bluntly.<br /><br />You want your child to have problem solving skills. This is much better than having to help with math or hire a tutor to spoon feed your child steps from question to answer.<br /><br />But if you try to teach your child problem solving skills in the hopes that these spur cognitive growth, you will fail. It's as bad as having your child memorize formulas and rote practice applying them.<br /><br /><hr /><br />Here's a brief history of skills. In 1945, a researcher at Stanford named George Poyla took 3,000 years of research into how mathematicians solve problems from philosophers, ancient Greeks, and mathematicians themselves, and wrote a book called How To Solve it to help high school teachers mentor their students on solving geometry proofs. The emphasis of How To Solve it is 'mentoring', not doing any work for the student or teaching problem solving algorithms or heuristics.<br /><br />By the 1970's problem solving was turned into a pre-packaged, spoon feeding program to help students apply problem solving methods to pre-algebra and more advanced maths without the need to understand anything that they are doing, let alone math.<br /><br />The #1 problem in problem solving is that the defective learning approach that emphasizes a speedy, correct answer that has been memorized and practiced has evolved into a defective learning approach that emphasizes a speedy, correct answer using a problem solving technique that has been memorized and practiced.<br /><br />When I finished translating How To Solve it into a method suitable for parents of 4 year olds, I was stunned to find a solid approach that also works for graduate school. I added a step that researchers at Berkeley identified as the #1 success factor for surviving their first year calculus courses. The first experimentee of the program is now 9 year's old, and needs about 10 minutes to get a score of 50% on SAT reading comprehension tests. Obviously, we have a way to go, but the method is so general that if pretty much works everywhere, including assembling Ikea furniture and fixing plumbing issues. I would recommend it simply for the benefit of not having to call a plumber.<br /><br />Here is the short version of the problem solving method:<br /><ol><li>Be Baffled (thanks Berkeley math department)</li><li>Spend a lot of time thinking about and exploring the problem</li><li>Make mistakes and try again</li><li>Check your work (I added this because it raises test scores)</li></ol><div>In between #2 and #3 sit the process of problem solving. In the last article, I demonstrated the most powerful problem solving techniques from the standpoint of a baffled parent trying to help their child learn some new material that is way beyond the child's skill level. Think figure matrices, multiplication, fractions, exponents, algebra, trig or whatever. I'm going to continue the numbering from the above list and explain why shortly.</div><div><ol start="5"><li>Start with a much, much easier version of the problem, like 1 x 2 = 2 and just keep adding to it and iterating until you are back to the original problem. This can take weeks if you're trying to teach multiplication to a 5 year old. In some cases, the child is missing something fundamental from material we skipped, so we just backtrack to an easier math book to practice the prior material and then come back to the problem. Backtracking happens a lot in Math House. Ironically, I can teach basic Trig in about 30 minutes, but it takes months to teach basic alegra.</li><li>Translate the hard problem into 2 easier problems and solve the easier problems instead. This approach usually involves decomposition or regrouping in the early years, and gets trickier in high school math.</li></ol><div>There are other good approaches for more advanced topics outlined in Poyla, like solving the problem backwards, applying some theorem or proof that you just learned in the prior problem (which works for both Geometry and the COGAT), filling in the missing word or shape. If you give the child enough space to explore the problem and make mistakes, the child will learn these methods on their own, or even better, make up their own methods however inefficient.<br /><br />When I combine the two lists, which is why they are numbered contiguously, I end up with 90% of my teaching method for math until we get to Algebra and Geometry.<br /><br />There is a great deal of contemporary discussion on the topic of why students are struggling in Physics. The consensus of physics teachers is that students are more interested in getting to the solution (using the internet to find the method) and less interested in learning physics. You can find many, many books written to demonstrate the step-by-step approach to solving every class, subclass, and subsubclass of algebra problem if you wish to be an algebra expert without knowing what you are doing. If a parent would just take a step back from Teach To The Test, you'd find that it takes a fraction of the time to get a 99.9% based on thinking and learning than a 90% based on practice and memorization. To emphasize this point, we tend to do 2 to 5 problems a day and make much more progress more quickly than children who do 30 or 40 easy problems a day.<br /><br />Learning happens from the start of the first problem until the student realizes that there is a formula or method that can be used to solve problems of this type. When the child struggles with 2/3+ 5/7, lots of learning is happening. But once the child realizes that each fraction has to be transformed to share common denominators, we're done with learning. Learning also stops when the solution is checked as well, right or wrong.<br /><br />The biggest complaint I receive from parents who start down the path that I recommend is that it doesn't work. By 'doesn't work', it means that their child is frustrated, lost, and getting nowhere. To me, this is a description of the initial stages of the process a not a defect or shortcoming in the approach. Some stubborn kids need about 6 weeks to undo the programming from school, programming that you must know what you are doing, do it quickly, and obtain the correct answer without effort or challenge. It takes a while for the child to realize that expectations have changed. <br /><br />Sometimes it takes 2 or 3 weeks on a half dozen problems to teach the child that we are going to go slow, think a lot, be confused, hit dead ends, have to backtrack, and get things wrong a lot. To accelerate this process (meaning show the student that the rules have changed), I'm usually confused, get the wrong answer, and don't check the solutions. Once the child gets past this hurdle, the pace begins to go very quickly, and if you stick with this approach, the child will in a few years teach themselves entire subjects very quickly, or if you insist on teaching your 9 year old algebra, not very quickly but adequately.</div></div><div><br /></div><div><br /></div><div><br /></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-414815082458240142018-02-24T16:14:00.002-08:002018-02-24T16:14:31.860-08:00Skills in ActionA reader challenged me to explain how to do competitive math. I'm excited about these problems because they demonstrate a fundamental skill set that is developed during learning to read at age 4. It's very similar to the skills that cognitive skill sets like the COGAT teaches. It's 100% learnable.<br /><br />What I like about this problem set is that a parent can work through these and have the exact same experience that your child goes through. I'm hoping that parents who take the time to work through this material will have better training when your child shows you a figure matrix that is baffling. It's also a good opportunity for the parent who discovers this website 6 or 7 years too late so that I can show that it's never too late.<br /><br />I've gotten numerous questions about what follows Test Prep Math 3. I like competitive math as a warm up for SAT test prep. We dabble with pre-algebra, but usually only in a Algebra 1 setting. Sounds hard, but this is the skill set.<br /><br />Here we go. Picture a competitive math worksheet with 40 problems on it, that has a 45 minute time limit. I suppose if we were serious about competition, we'd train for learned strategies to address the time limit, but we're not serious about competition, just doing a bit of daily math. I think 5 problems is asking a lot of an 11 year old.<br /><br /><b>Question 1:</b> F - T - L - T - ? - ? Find the last 2 letters in this series.<br /><ol><li>I have no clue how to do this. Anyone you has seen this question type probably doesn't have any clue because it has unlimited subjects. But I have the most important skill of all, which is the proper way to be Baffled, which is to not care that I'm clueless.</li><li>I think for a minute about adult IQ tests. Friday, Tuesday, Something That Begins with L, Thursday. Fail.</li><li>F = 6, T = 20, a difference of 14. L = 12, T = 20, - 8 + 8? Fail. Skill 2 - don't care how many incorrect answers I get.</li><li>I stop and think about the question a bit. Kids only know arithmetic, language, geometry, and a tiny bit of algebra. Pre-Algebra is fair game. In the real world, I should have used Skill #3 which is to spend more time thinking about the question and less time getting incorrect answers, but in competitive math with no time limit, lots of learning can happen in dead ends.</li><li>Going the geometry route, all the letters have a single vertical line. F has 2 vertical lines and T has 1. That's 3. L has 1 vertical line and T has 1. That's 2. I forgot to look at the answer set. My skills are rusty because the answer set is part of the question.</li><li>The answer set is:</li><ol type="A"><li>L - T</li><li>L - B ( I think this B has no vertical lines.)</li><li>L - M</li><li>T - P</li></ol><li>If B is the answer, using counting horizontal lines in the series, we get 2 - 1 - 1 - 1 - 0, but if we take pairs of vertical lines, we get 3 - 2 -1. B is the answer, I accidentally stumbled on it, and I have no clue why I am correct. But it was the best of a bunch of confusing bad answers.</li></ol><div>This problem took me about 15 minutes. It's very similar to the type of work I do on a daily basis. I wonder if competitive math tests are structured so that super duper problem solving kids prioritize the questions and their time before answering and just skip this one. Probably. </div><div><br /></div><div>When you work with your child and do a problem that is really hard for their age and skill set, just like the one above, here's the benefit you both gain:</div><div><ol><li>You get used to working with baffling things and don't get put off.</li><li>You make a lot of mistakes and don't get put off. In fact, in my failed attempts (attempts not include above), I learned a lot of interesting things and picked up a few mini-skills on the way to dead ends.</li><li>The solver is forced to think creatively and view the problem from different angels. It will take a lot more problems to learn creativity, but since I am making a habit of baffled and mistakes as skills by force feeding my child these problems over and over again, we'll get their eventually.</li><li>I never looked at the clock or the solutions. This problem is kind of tricky and fun. The solution will end the learning process and reinforce the Rule #1 that it's not about learning or getting better at something, it's about being right or wrong. Rule #1 will destroy your child's ability to learn. Rule #1 is an anti-skill.</li></ol><div>When I work with kids, a team will really help, and I'm the only one available for the other team member, so in practice I ask a lot of questions (as needed) and make suggestions for the next attempt (as needed). I'm always baffled. In practice, I'm suggesting skills and approaches from my toolset of exactly 5 approaches to any math problems. </div><div><br /></div><div>Why is it that when your child comes to you and asks what 'dispersed' means, you're more than happy to tell him, in fact you're so happy your bright little child has an interested in vocabulary and is not skipping over unknown words when reading, but when your child gets a math problem wrong, you're disappointed? What a horrible destructive way to teach children to hate math. Adding a time limit makes it even worse, because then a teacher can mark of a series of unanswered questions. This is why schools can completely eliminate tests through Junior year in high school and produce kids who blow away college entrance exams.</div></div><div><br /></div><div>OK, let's see what we get out of more baffling problems.</div><div><br /></div><div>What is the remainder when the 15-digit number 444444444444444 is divided by 9?</div><div><ol><li>Are you kidding - this is too big to fit in the calculator. Curse you competitive math test author. The answer pick list is irrelevant. Again, I have no clue.</li><li>Too hard of a problem. So I fall back to how we tackled any math - starting at age 4, when it's too hard. We start with the easiest version of the problem and work our way back to the harder problem:</li><ol><li>4/9 ~ r 4</li><li>44/9 ~ r 8</li><li>444/9 ~ r 3</li><li>4444/9 ~ r 7 this is good practice for division but a fail in solving the problem.</li></ol><li>Then I remembered that when I teach division, I always make the student turn 36 ÷ 9 into 3*3*2*2/3*3. Now were trying to turn this problem into a more solvable, easier version of this problem. Here's goes:</li><ol><li>4*111111111111111/9 = ? Still hard. Fortunately, I can look back on the first fail and continue.</li><li>1/9 ~ r 1</li><li>11/9 ~ r 2</li><li>111/9 ~ r 3. Get it? Light bulb. </li><li>Continuing, I get to r 0 at 1111111111 which puts 111111111111111 (15 digits) at r 5.</li></ol><li>Unfortunately, I'm stuck having to multiply the whole thing by the remainder. This stinks, I stink, and your child stinks, so we're going to have to take baby steps.</li><ol><li>Since 1/9 = 0 + 1/9, 4*(0 + 1/9) = (0 + 4/9) ~ r 4, which is what I got in the first fail. Notice I'm checking the answer, which is skill #4 at the base of the cognitive skills pyramid. I suppose this requires some pre-algebra.</li><li>11/9 = (1 + 2/9), so 4*(1 + 2/9) ~ r 8, again, just like above.</li><li>111/9 = (12 + 3/9) but 4(12 + 3/9) is going to give us 48 + 12/9, slightly confusing, and I have to go read the question yet again. Oh yea, we're dividing by 9, and trying to find the remainder, so I can write 48 + 1 + 3/9 ~ r 3 just like expected.</li><li>At some point, the lightbulb goes off, and I can just jump to 15 ones's/9 = (something big + 5/9), and I multiply by 4 and get 4*something big + 20/9 ~ r 2, which is not even on the answer list. The choices are 4, 5, 6, and 7. </li><li>So starting over, which I'm totally used to because we do it all the time, I note that the 9 digit number 111,111,111/9 = 12,345,679 r 0, duh, should have thought this though. This makes 111,111,111,111,111/9 = something big 6/9 (since 15 digits is 6 more than 9 digits), and 4*(something big + 6/9) = 4*big + 24/9 = 4*big + 2 + 6/9, giving me the correct answer of 6.</li></ol></ol><div>We've got 3 big solutions approaches that we start using when the child is about 3 years old. </div><div><br /></div><div>At some point, your child is looking at * * * * * * of something and you ask her to count. She answers 12 or 5 or gives up, so you start small, like *, then * *, then * * *. I teach addition, fractions, and multiplication this way. It works in graduate school and it was by experimenting that I found it works really well at the youngest ages. It works on pre-algebra. It works on all forms of high school math. It's required for competitive math. Math books do this from chapter 1 through chapter 15, but we do it in 5 minute increments and don't really need a math book.</div></div><div><br /></div><div>Next, when a problem is too hard, turn it into an easier problem. This is the foundation of algebra. You might as well start now.</div><div><br /></div><div>Finally, notice that there are 3 steps to this problem. If you've seen TPM, you know why I think 3 is so important. It builds working memory. For the age group for the problem above, we're probably beyond working memory, and if not, doing these problems will bring it back. But the working part in 3 steps is where the little brain turns itself into a big brain by defining relationships and patterns and working abstractions into algorithms from one part of the problem to the second to the third. You see all three in the solution above. A genius can do it in one step only under one condition: the genius worked through enough of these problems to get really good at devising and applying algorithms. Don't be fooled into thinking it's genetic. The rest of us are happy doing the 3 steps one step at a time. One step at a time is good for 99%.</div><div><br /></div><div>Moving on, how about this problem. What is the value of 1 - 2 + 3 - 4 + 5 - 6 + ... + 81 - 82?</div><div><br /></div><div>This problem not only demonstrates the value of spending way more time exploring the question than trying to answer the question, it also demonstrates the value of what I call "Seeing". I learned it from the COGAT. It involves looking at the problem from different perspectives. </div><div><br /></div><div>I checked to see that there were an even number of elements to this equation, all equaling negative one when paired, and came up with -41. Eight minutes of thinking about the equation and 4 seconds deriving the answer. With 40 questions and a 45 minute time limit, I would have come in last on the competitive math exam. Can you picture me sitting with a bunch of 6th and 7th graders? </div><div><br /></div><div>This next question is my favorite and a really great exercise on it's own to teach exponents. I love this question. This differs in an important way from the math I would give a younger child but is identical in nature to the non-verbal section in TPM. It involves doing a lot of work, organizing and thinking about it, and then answering. </div><div><br /></div><div>If a and b can take on the values in [0,9] (meaning that they can each be 0, 1, 2, ... 9), then the expression a<sup>b</sup> can take on how many different odd number values?<br /><ol><li>To start, I just created a grid with 0-9 on the rows and 0-9 in the columns and started calculating the expression based on inputs. In a competitive math situation, this is a waste of time and requires thinking, but with most kids (and 9 year olds), I make them use the brute force approach because they usually have never seen a<sup>b </sup>outside of 4<sup>2</sup>. I've got a whole exponent crash course (including negative and fraction exponents), but this seems to be a good starter exercise. </li><li>The rows are a and the columns are b. I didn't calculate the *'s but I could have. <table><tbody><tr><td>*</td><td><b>0</b></td><td><b>1</b></td><td><b>2</b></td><td><b>3</b></td><td><b>4</b></td><td><b>5</b></td><td><b>6</b></td><td><b>7</b></td><td><b>8</b></td><td><b>9</b></td></tr><tr><td><b>0</b></td><td>?</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td><b>1</b></td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td><b>2</b></td><td>1</td><td>2</td><td>4</td><td>8</td><td>16</td><td>32</td><td>64</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>3</b></td><td>1</td><td>3</td><td>9</td><td>81</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>4</b></td><td>1</td><td>4</td><td>16</td><td>64</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>5</b></td><td>1</td><td>5</td><td>25</td><td>125</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>6</b></td><td>1</td><td>6</td><td>36</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>7</b></td><td>1</td><td>7</td><td>49</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>8</b></td><td>1</td><td>8</td><td>64</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr><tr><td><b>9</b></td><td>1</td><td>9</td><td>81</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td><td>*</td></tr></tbody></table></li><li>This seems to be a fail. Too hard. I did notice that only one zero in the top row and one from row 2 and column 2 are going to be included. What is zero raised to zero? It's either one, zero, or undefined, but if you read the question again (and you should because it's a skill), it doesn't matter to the answer.</li><li>After rereading the question yet again, I noticed that I only have to deal with ODD numbers. With the exception of '1', the rows with 5, 7, and 9 qualify, and since 3*3*3*3 = 9*9, the row of threes where the exponent is odd also qualifies but not when the exponent is even. And we can add 1 only once and ignore zero. And that gives the correct answer of 27 (the whole row of 5,7,9) + 1 (from the one) + 5 (from 3 row where it doesn't repeat a value from the 9 row) = 33.</li><li>It's possible to jump to step 4 as a competitive math coach, but not a regular bright kid doing competitive math coach.</li></ol><div>I'm guessing the question needs about 5 readings before this work can begin. I've watched little mathematicians create charts to answer questions and it's very gratifying.</div></div><div><br />Finally, the last question is this. If x and y are integers and 360x = y<sup>3</sup>, what is the minimum possible value for x + y? At this point, we left all kids under 4th grade behind and we're just looking at algebra. Or are we? Yes, I'm running out of steam and have already covered all the really great problem solving techniques. <br /><br /><ol><li>After 30 minutes with the question, I decided that x is just a function of y, so forget about x. Just find the smallest possible value of y. Or do algebra. It's late, I've exceeded the maximum good thinking time of a grade school child of 25 minutes, and the Olympics are on.</li><li>But I don't like 360, so I wrote 2*2*3*3*2*5x = y<sup>3</sup>. Then I rewrote it to be 2*2*2*3*3*5x = y<sup>3</sup>. You can see that if y is an integer, x has to be 3*5*5, making y = 2*3*5. So x = 75, y = 30, and the answer is 105. </li></ol>I got the entire solution correct by following these steps:<br /><br /><ol><li>I had no clue what to do.</li><li>I went off in the wrong direction by trying to use algebra, which I can, but doesn't solve the problem for a kid who doesn't know algebra. Fail.</li><li>I tried again.</li><li>I spent more time looking at the question and eventually started to rearrange it in the hopes of finding an easier problem. (I.e., I used one of the big five 5 math problem solving techniques.)</li><li>I looked at it, specifically looking at the root primes against the exponent on the other side of the equation. I used my power of seeing things differently.</li><li>The answer emerged with no effort.</li></ol>This is why studying for the COGAT is so critically important. It's the easiest way to get the skills. If you missed this opportunity, there are other opportunities including competitive math. It seems harder and more complicated because your child is older and the math more obscure, but it's about the same. If you did this when your child was younger, you would have blocked out all of the tears and frustration by now and just remember how it all worked out. Same with bed wetting in the middle of the night. Remember that? Of course not.<br /><br />Is there anything different between a child who does this problem successfully and one who gives up? Not mathematically. It's all in these base skills which are 100% learnable and needed for high school math. If you want a strong competitor in a math contest, you'll need interest and a lot more practice, but if you just want a five on the BC Calculus without having to nag your child or hire a tutor, do a few problems and focus on the skills.<br /><br /></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-24285755285232039592018-02-17T08:14:00.003-08:002018-02-17T08:22:46.174-08:00Totally Doable If Done RightIn the last few weeks, I've stumbled across a whole new group of people who are suddenly concerned about their child's education either because they decided it would be nice to have an actual child in the next few years, or they have an actual child and just found out about the COGAT, or they are getting COGAT scores back and deciding that it's time to get serious.<br /><div><br /></div><div>My Power Mom's Group, or PMG, from last year is officially demoted to Last Year's Power Mom's Group because your kids all met their ridiculously high cutoff goals (and are solidly on their way to additional goals). There's one more item on the todo list for the next few months and then I'll declare a 100% success rate based on selection criteria that includes a) great parents and b) capable kids. The new members of LYPMG are going to get heavy doses of my super secret program to crush the MAP test in the coming years. How similar are the COGAT and the MAP? COGAT skills are a prerequisite of the MAP, but the COGAT type math isn't what people generally consider to be math and the MAP has way more math than anyone realizes. If you are not in LYPMG, then you'll read about my super secret MAP program but you won't realize that you're reading about it until I can get everyone in the house past the 7th grade MAP.</div><div><br /></div><div>For newbies, I've been working on a less insane sounding description of my math approach, with a nice sounding title like Easy Fun Math*. (*Also known as Ridiculously Hard Insane Math until you get it, and then it's just Ridiculously Hard Math.)</div><div><br /></div><div>Here goes.</div><div><br /></div><div>First, read read read read. If your child only has 60 minutes per day of at home schooling, devote 40 minutes to reading. If your child has 6 hours a day because it's Saturday, devote 5 hours and 40 minutes a day to reading.</div><div><br /></div><div>Secondly, do not, under any conditions, every teach math. The skills your child needs to excel in math are organizing, seeing patterns, trying again, iterating, comparing, trying out different options, defining, extending, explaining, rethinking, simplifying (ie organizing), decomposing (ie organizing), and not being put off by mistakes, lack of information and clarity, and total confusion because if your child isn't working in on a math problem that starts with mistakes, lack of information and clarity, and total confusion then they are not working on a math problem that will develop the skillset. The super advanced skill set for math includes good executive skills and a lot of Grit. If your child develops these skills under your guidance, your child will excel in math. If you teach math, your child won't need any of these skills, won't develop them, and then someday will fail at math.</div><div><br /></div><div>Look at 'First' and 'Second' again. Higher order math skills are developed by reading. This really matters when your child is 2 and 3. By 4th grade, it will be assumed but not a major factor in the program.</div><div><br /></div><div>Third, at the 99.8% level, which is totally doable if done right (Totally Doable If Done Right, my new motto, and this just replaced the original title for this article which was Advice for Newby Math Parents), there are a lot of parent skills involved. While the child is learning each new skill, you will be learning a new skill. Your child will see math in a different way, and you will see coaching math in a different way.</div><div><br /></div><div>Forth, your child's math score is going to be constrained by working memory. I can't stress this enough. School math needs one or zero working memory buckets in the brain. Think 'Ann has 2 apples and Bob has 5 apples. How many apples do they have together.' Test Prep Math starts with 2 and ends up with 3 working memory buckets - or more - on every problem. I've settled on 3 since it appears after 3 a pencil is needed. </div><div><br /></div><div>Test Prep Math emphasizes messy, sometimes unanswerable problems (in clumps of 3, all mixed up and interspersed with vague words and ridiculous plots). Now you know why.</div><div><br /></div><div>There is an ongoing debate on whether or not children should memorize their math facts. Teachers who need to get all 30 kids in the class past arithmetic errors in 2nd or 3rd grade are generally stuck with memorization exercises - even in GAT classes. Researchers who are figuring out how to get kids to the upper levels of math excellence can explain why memorization is counter productive. </div><div>If you search 'Boaler Memorize Math Facts' you should find a few really good articles explanating why memorization is a bad idea by the leading researcher in this field. You may also come across an <a href="https://gregashman.wordpress.com/2015/09/19/jo-boaler-is-wrong-about-multiplication-tables/" target="_blank">counter argument from Greg Ashman</a> that totally misses the point, but get's so close with this diagram that he's one sentence away from solving his own problem. Look at this diagram:</div><div><br /></div><div style="text-align: center;"><a href="http://2.bp.blogspot.com/-4er-FaL1jsk/WohLlqGxh_I/AAAAAAAABP0/GiT1FVB1xIY6Xru5RRFHo-IhQMnFdhxVACK4BGAYYCw/s1600/Ashman.jpg" imageanchor="1"><img border="0" height="234" src="https://2.bp.blogspot.com/-4er-FaL1jsk/WohLlqGxh_I/AAAAAAAABP0/GiT1FVB1xIY6Xru5RRFHo-IhQMnFdhxVACK4BGAYYCw/s320/Ashman.jpg" width="320" /></a></div><div>Note to Ashman, the goal here is not to use long term memory to help with the math facts but to triple working memory. Also note that this diagram makes me want to sneeze.</div><div><br /></div><div>Boaler attributes number sense to strong math skills. Number sense and math fact memorization are two exclusive roads to math, and memorization falls short. In my ground breaking research I found that use of working memory isn't just a tool for math, it's a math skills generation factory. The child learns the next level of math skills while working arithmetic in working memory. When people see the term 'Working Memory', they see 'working MEMORY'. It's more accurate to view this as 'WORKING memory AND MATH SKILLS GENERATION FACTORY'. Please note that Boaler's research concerns making math accessible to everyone, but my research concerns a child who just blew away the COGAT and is looking for the next big leap in skills. </div><div><br /></div><div>Maybe groundbreaking doesn't cover it. Here's what we got out of the workings of working memory in action: an 8 year old who is solving problems off of middle school competitive math tests.</div><div><br /></div><div>When I wrote, and rewrote, and refactored and added to Test Prep Math, I met my goals to tackle working memory, base skills, and no math if it can be helped. I failed on the no math part because I couldn't help sneaking in math. A little geometry, a little algebra, and if you look closely, you'll see the makings of other maths, but I generally avoided division, and avoided decimals and anything else that is on a Common Core list. This approach doesn't work for everyone. Some people are short sighted and think of math as topics from a math book. Others already taught their kids math and the horse already left the barn.</div><div><br /></div><div>One of my favorite exercises is to do Every Day Math Grade 2 in K. For those that missed the opportunity in K, it's simply known as Current+2. I think of this as an exercise in Grit and not math, kind of a warm up to the challenge that will follow. Last week, a reader shared her child's current math situation which sounds so dire, what with mistakes, frustration, and not getting it. Once again, my children are even worse in comparison, but we manage to score consistently in the high 90's (like 99, which is what I expect) and do almost no work at all. One year ahead in math for us and maybe 40 to 60 minutes during the week. That leaves plenty of time for reading, crafts, and projects. My secret isn't smarter kids but kids who don't quit. And we do things totally different, like work smarter and not harder.</div><div><br /></div><div>After successfully avoiding the memorization of math facts, I've extended the counter cultural approach with not really ever learning math or being remotely competent in any one math topic. Focusing on underlying skills for years at the expense of math has really paid off in a big way.</div><div><br /></div><div>You'd think the next step after Test Prep Math would be learning actual math, maybe tackling Pre Algebra. Instead, we took a detour into competitive math, not really like school math at all, and then I've opened up 7th through 12th grade math topics for any given weekend. I think we have about 3 20 to 30 minute sessions each week, and the topic could be a first look at derivatives, exponents, polynomial zeros, 'What is sine and why am I making you go through this pain?' or anything else. One week it was exponents, and the next week my older kid saw logs for the first time and had to invent and derive formulas for logs that corresponded to the exponential formulas that we worked in the prior week. When this child sees logs again in a month, he will have remember exactly zero of it, but he's got the tools to make short work of it.</div><div><br /></div><div>After 4th grade, the little one will spend the next year or two working through SAT books. Other parents will try this and find that it's a disaster. Our experience will be even worse, but we'll plod on come out with 2 completed books, about 18 practice tests in all, and then move on to the reading comp sections. I've recently summarize the parent coaching skills needed to get through this approach successfully. When the 9 year old gets through the first page, 3 problems attempted, 3 wrong answers, and a lot of complaining and tears, I'll wonder why the heck I'm doing this. Then I'll remember that I've done this type of thing many times before, and it will magically work out in the end.</div><div><br /></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com4tag:blogger.com,1999:blog-5703568807615263851.post-73186882225368901442018-02-10T19:47:00.000-08:002018-02-10T19:47:31.197-08:00Visual Math Et CeteraFor years, I have been asked for a recommendation for 4th grade math. I now have one, and one for 5th grade as well. It's called <a href="https://www.amazon.com/Mindset-Mathematics-Visualizing-Investigating-Ideas/dp/111935871X/ref=sr_1_1?ie=UTF8&qid=1517965885&sr=8-1&keywords=mindset+mathematics+grade+5&utm_source=Youcubed+Updates&utm_campaign=dffbcc2fb8-EMAIL_CAMPAIGN_2018_02_04&utm_medium=email&utm_term=0_230e567c40-dffbcc2fb8-133942873" target="_blank">Visual Math</a>. These are not expensive books. The authors are from a ground breaking group of researchers that I've been following since the beginning of getyourchildintogat.com. Back in January, I wrote an article where I said that our current math curriculum needs to be flushed as an artifact of the Industrial Revolution. There is equally challenging, more engaging, more pertinent math to the information age. Visual Math.<br /><br />Except that I'm stuck on fractions, polynomials, mononomials, exponents, algebra, trig and calculous because darn it, they show up everywhere in math and all fields whether you're doing machine learning, number theory, or Hollywood CGI. I guess I'm always one rebellion ahead of the next trend.<br /><br />I don't face the same broad classroom education challenges that the authors of Visual Math face. I face the challenge of a single kid. My idea of visual math starts with COGAT test prep, Building Thinking Skills, and the rest starting ASAP, like age 4. See my curriculum page. In a house enriched with crafts followed by Minecraft, visual skills are overdeveloped.<br /><br />But the genius of Visual Math isn't just a much better more appropriate visual (and thus more timely) curriculum, it's the approach outlined by Jo Boaler years ago that is question heavy and solution light. In other words, spending time understanding and defining the problem, whatever that may be, in the process really learning math, and as an after thought deriving a solution. You've heard it before from me, and this is where I got it. There is much more to the approach beyond this.<br /><br />I'm a big fan of a single problem that is hard, multi-step (working memory intense) and requires a lot of time to solve, preferably something goofy or non-sensical, if that's what it takes to turn a predictable answer into an argument. I don't want a child to come out of this having mastered 3 x 5, which is useless, but having mastered getting there from the unknown, or better yet, an unknown mess.<br /><br />And that brings us to 1/2 and 2/3. A few months ago, a reader asked what to do about struggling with fractions. I offered to get on Skype, but since I'm insane, and can turn any 30 second problem into a 30 minute challenge, the reader declined. Too bad.<br /><br />There are 2 parts to a good fraction problem. <br /><br />The first part is 1/2 takes about 3 brain clicks to understand. I think 98% of the problem with fractions is that kids expect 1 click, they don't get it on one click, and they are frustrated or worse. I watch this with the brightest children trying to tackle fractions at a totally inappropriate age. The second part is the fraction in a more complicated setting of a pre-algebra problem. Too hard for younger kids, but doable at a pace 10 times slower than a 5th or 6th grader. Solving a fraction problem is multi-step. When I work with fractions and children, or algebra, or exponents, I expect a few weeks to get them to admit that they have to work the problem step by step. They are determined to do one single step, because it's one problem after all, and if they have to do 3 steps, then it becomes three times the work.<br /><br />Kids who are trained in math hit a wall with fractions. Kids where are 99.9% wizzes hit a wall for the opposite reason. Both groups underestimate the problem.<br /><br />Lately I've been working on the next challenge. How quickly can I get kids to be adept with pre-algebra, exponents/logs, functions, geometry proofs, algebra, trig and calculus? By quickly, I mean a small number of problems and weeks per topic. My group is 4th to 7th.<br /><br />In each case, a few problems can be used to explore the basics. During this time, there is wonder involved with the new syntax and the concepts that it articulates. Like the first time a child stumbles on negative numbers or square roots. A few problems get the job done. To take the next step requires a special problem solving approach for each field. We avoid the complicated applications that fill 90% of a decent text book and just stick with the basics. <br /><br />I've come up with a one session introduction to trig that addresses many of the questions (about 25%) on a good trig final. One session for a 9 year old. I remember struggling with this exact same material for about a month in high school, trying to remember formulas. I'm really disappointed about how bad the course was and how unprepared I was (not having studied math between 1st grade and trig). But I'm mainly disappointed with the approach to math from the 1920's which I used in high school. <br /><br />The last thing I'm going to do is explore the other 75% or so of each of these topics. I think this will be an 8th grade exercise. Is it possible to send a child to high school prepared to be bored with A/B calculus or chemistry? Can this be done with almost no work whatsoever? I'm starting to think so. <br /><br />I enjoy getting articles from readers that include an age and a topic and a description of how much they are struggling. I think, wow, we struggled much worse. I can tell them that and actually solve a problem. I can also state, if needed, 2 or 3 ways to get past it and how long it will take (longer than you think.) In some ways, this is just like potty training. Some parents wring their hands over every trip to the potty, and others let their kids poop all over the place until the problem takes care of itself. The only thing I did differently was discuss plumbing while cleaning the poop off so that I'd have someone I could count on someday to clear clogs.<br /><br />Someday is almost here in math. In plumbing, my 13 year old routed the pipes right before his birthday.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-87379727663213174052018-02-03T09:45:00.001-08:002018-04-21T05:27:06.532-07:00Innovations in Math EducationI promise as soon as I complete this article I'm going to start populating the reading list in the prior article on reading. But first...<br /><br />My 8 year math program is about to come to fruition. In April, math Experimentee #1 (a newly minted teenager who started K with a bunch of my newby missteps) is going to take the MAP test, and after a long interval of not caring, this score counts and it has to be a 99%. In this article, I'm going to summarize where we are, demonstrate the leap in math skills that happens in 4th grade, demonstrate how my math program is dramatically different than regular programs, and present it in such a way that I lose most readers before I get to the end because that 99% is competing against about 10,000 other kids in Chicago who's parents are all googling 'How To Get 99% on the MAP So My Child Gets Into A Decent High School'. Also, I'm going to discuss my approach in purely in 4th grade terms to help parents of younger children plan ahead, and explain why Test Prep Math is the way it is. <br /><br />Let's start at the beginning. My first goal back in K was to conquer Every Day Math. We didn't have to pick everything up at once, just a lot of hard work to show 'You Can Do This'. My goal was simple. For Experimentee #1, the goals focused on entering a GAT program in 1st grade, given that we were totally behind because we did nothing to prepare for it, not even phonics or learning to read, but at least the math would be familiar (it would be EDM Grade 2 - a complete repeat) and he would have some confidence.<br /><br />After crying, forgetting, getting them all wrong, spending a week or two on a single 6 question worksheet page, having to find 1st grade books to practice concepts and skills we never saw before, I transformed the following survival skills into Academic Coaching Skills that we would use for the rest of our lives and pass down many generations (hopefully) of bright descendants until one actually wants to study math in graduate school. Here they are:<br /><br /><ol><li>Set Your Expectations To Zero. Don't expect your child to get anything correct, understand it, remember it, work on their own, or anything. Even if you do the same problem every day for a week and it's 7 + 6 = ? This is the parent skill. The child-parent team skill is to enjoy 'Being Baffled' on totally hard work that has never been encountered before that will take a lot of time to sort out.</li><li>Make Mistakes. Mistakes are the key. After a while I stopped looking at solutions because I expected mistakes. </li><li>Take A Long Time. When we slowed down to 30 minutes per problem, we started making progress. This is also known as 'Read The Question' where we spent more time thinking about 7 + 6 and what it could mean and how to work it before solving it. </li><li>Other tips I put in the blog over the years, but the top 3 were the key.</li></ol><div>So here's what we got. At one point, we sat down and looked at Student Journal #1, with every single problem answered. Every single problem. No child anywhere does every single problem in a math book, or every page or even every chapter. This is a rare and invaluable life lesson. Experimentee #1 has an extremely high tolerance for work, chores, painful work, hard chores, ridiculously hard chores. Even better, Experimentee #1 is not put off in the slightest by being totally confused on material that is way beyond his abilities.</div><div><br /></div><div>Somewhere during this process, the speed of learning and work accelerated to match the challenge, and by about 1/2 through Student Math Journal #2, we quit because the challenge was gone.</div><div><br /></div><div>Experimentee #2 experienced hard core phonics (Pre K Phonics Conceptual Vocabulary and Thinking age 4.0) and hard core math (Shape Size Color Count age 3.9) because I wanted to address any gaps I found in GAT preparation and more importantly COGAT prep, and did it with a sledge hammer the size of an SUV. Experimentee #2 has math skills that Experimentee #1 will never have, like a child who learns to play the violin from birth will always outplay a child who picks it up at age 6, but Experimentee #2 has a completely different work ethic. Experimentee #2 will sit down with something quietly for hours and master it, but not without a lot of complaining about the fact that he can't pick it up immediately. Experimentee #1 never complains.</div><div><br /></div><div>There is a completely different path for K and 1st grade that will produce almost identical short term results. Many parents enroll their children in an after school math program. In a good program, the child learns problem solving skills and solution strategies as well as practices math daily. This is not a bad approach, but it is not consistent with the goals I mentioned above and a few I am going to add shortly.</div><div><br /></div><div>After 1st grade, we stopped learning math and went more hard core into Test Prep Math. This series is not about becoming adept at advanced math topics, but becoming adept at navigating convoluted questions, staying in the 'math game' because the questions are somewhat on the goofy side and don't include boring, manufactured math book type questions, and building working memory. This book is not designed for children already at the 99% level for math, it's designed to get them there shortly thereafter. I've had a few parents who's kids finish 2 years of after school math (and are at 99% already) complain that the beginning of the book is too easy. Kind of a 'duh' moment for me, but one I need to mention for those kids, Test Prep Math Level 3 in 2nd grade is preferred. The purpose of this book is to lay the groundwork for 99% thereafter, not to put a 99% kid at 99.9%, except by accident (which is what we experienced, by the way). </div><div><br /></div><div>Instead of more math, we went directly from Test Prep Math into reading comp questions. This should be obvious from the problems in Section 1. Section 2 takes us directly into competitive math questions (because I need something to fill the gaps before ramping up real math in 4th grade). But the MAP score is only half math; the rest is reading comp.</div><div><br /></div>For those of you who get SAT books when searching for Test Prep Math, here they are: <div><ul><li style="display: inline-block; list-style-type: none; margin-right: 20px;" onclick"event.stopPropagation();window.open('https://www.amazon.com/Test-Prep-Math-Level-3/dp/1547120010');"><a href="http://3.bp.blogspot.com/-HimEyQYFHW0/WtsnIWZEJNI/AAAAAAAACzI/-QJKuBkzfUIiOyj4j3CM4ay2Zw_0nc6lwCK4BGAYYCw/s1600/TestPrepMath3.JPG" imageanchor="1"><img border="0" height="320" src="https://3.bp.blogspot.com/-HimEyQYFHW0/WtsnIWZEJNI/AAAAAAAACzI/-QJKuBkzfUIiOyj4j3CM4ay2Zw_0nc6lwCK4BGAYYCw/s320/TestPrepMath3.JPG" width="200" /></a><a href="https://www.amazon.com/Test-Prep-Math-Level-2/dp/1530186234" style="display: block;">Click here for 2rd Grade</a></li><li style="display: inline-block; list-style-type: none;"><a href="http://1.bp.blogspot.com/-VimShjs5fUg/WtsnG-OsC8I/AAAAAAAACzA/_HYPbpB-CF4tVO_beSZn5nb-oLjLas5oACK4BGAYYCw/s1600/Test%2BPrep%2BMath%2BLevel%2B2.JPG" imageanchor="1"><img border="0" height="320" src="https://1.bp.blogspot.com/-VimShjs5fUg/WtsnG-OsC8I/AAAAAAAACzA/_HYPbpB-CF4tVO_beSZn5nb-oLjLas5oACK4BGAYYCw/s320/Test%2BPrep%2BMath%2BLevel%2B2.JPG" width="200" /></a><a href="https://www.amazon.com/Test-Prep-Math-Level-3/dp/1547120010'" style="display: block;">Click here for 3rd Grade</a></li></ul></div> <div>From 1st through 4th grade, we only stayed a year ahead in math while I put together the basic skill set that we need. This basic skill set is very similar to the skill set that kids would use to survive an advanced engineering or abstract math course in college but it's missing formal solution strategies. College is the other goal, and I'm thinking ahead as usual.</div><div><br /></div><div>At inappropriately young ages, while we were biding our time putzing around with current + 1, I started introducing advanced topics, just for fun, just to exercise thinking and start to explore the wonder of math. It was enormously enjoyable to surprise a kid with these types of questions:</div><div><ol><li>What is 5 minus 3?</li><li>What is the square root of 4? 9?</li><li>What is 1 divided by 2?</li><li>If 1/3 of my donuts are chocolate, what percent of these are not chocolate?</li></ol><div>If your child sees any of these questions for the first time in school, I guarantee the wonder, fun, learning and enjoyment of math will be totally crushed out of the experience because your child will be presented with definitions, comprehensive examples, and a long list of routine problems that have nothing to do with anything. It then just becomes a pattern matching and lookup referencing exercise. The child will 'learn' math, but not know how to learn.</div></div><div><br /></div><div>Sometimes we would resort to backtracking, which is finding a workbook or online resource to practice the material during the learning process. If we got '1/4' kind of but not really, a worksheet might fill in the gaps. If a concept (fractions in this case) requires an understanding of division that is not there, we would certainly backtrack to a division worksheet and then come back to fractions.</div><div><br /></div><div>Over time, however, I discovered the power of bucketing, which I subsequently labeled 'Power Bucketing'. This is very similar to what I witnessed with Experimentee #1 going into 1st grade and being handed the same EDM Grade 2 workbooks that were completed the previous year. Math is much easier to understand the 2nd or 3rd time than the first time, and quick mastery is the likely result.</div><div><br /></div><div>With '3 - 5', I would just leave the question out there and not answer it. Or maybe I would answer it, but then a month later I would ask it again and watch the same process starting over again from the start, but going a bit faster and progressing a bit farther. When this come up again out of nowhere the third month, we might end up with mastery with almost no work and exactly zero practice. Even better if the child sees negative numbers on his own in a book, he dives right in and the result is not only self-mastery, but he owns it.</div><div><br /></div><div>SQRT(4) and also 5x - 13 = 2 will demonstrate the leap in skills that takes place around 4th grade. Kids coming off work like Section 2 of TPM can calculate both of these without understanding how they do it. Good little mathematicians iterate through possible solution values until they arrive at the answer, and great little mathematicians add weighing with high-low bands that narrow to the solution strategy to arrive at the answer more efficiently.</div><div><br /></div><div>After 4th grade, when the brain is capable of higher order thinking, these two exercises gain new meaning. The definition of SQRT(4) is the number when squared that equals 4. In other words x^(1/2) is solved backwards. Square roots present the opposite syntax of squares, and the solution is to back into the answer. This is critical for topics that are going to come later. 5x - 13 = 3 is a simple introduction of y = mx + b, which is an important framework for characterizing more complicated problems, and the elements of y = mx + b have additional meaning besides finding a number.</div><div><br /></div><div>There are also new skills that come with these math concepts. A 3rd grader will jump in and solve either problem to get a number. It's all one step. A 4th or 5th grader will decompose the problem, spend more time analyzing the question, and learn more during the problem. I've introduced younger children to the next level of math skills, like problem decomposition and making a hard problem easier; this exercise can take 20 minutes and is really good for thinking. It requires a lot of working memory which is why in 2nd and 3rd grade working memory is most of the focus. But older children do this intentionally, quickly, and know why they are doing it.</div><div><br /></div><div>Let's look at some pre-algebra concepts that have been a real struggle for me to teach. </div><div><br /></div><div>First, x^2x^3 versus (x^2)^3. Per formula, the first is x^(2+3) and the second is x^(2*3). But we're not interested in formula's, because formula's produce math dummies. </div><div><br /></div><div>The way to do these problems is to work the question and not solve the problem. x^2x^3 is simply (xx)(xxx) = x^5, and (x^2)^3 is (xx)^3 is (xx)(xx)(xx) = x^6. Eventually, the child will memorize the formulas in the same way they used to count on their fingers for 5 + 3 and eventually knew that 5 + 3 is just 8. Before 4th grade, the best I can do is lay the ground work for decomposition, restating the problem, multi-step solution operations, but they still jump into more advanced problems trying to get to a number in one (hard) thinking step. I've noticed that after school program kids are drilled in multi-step solution strategies, but I don't want a child trained in math solving. I want a thinker.</div><div><br /></div><div>This is the biggest difference in my goals and methods. I don't want a child who is trained in math, a a child good in math, a child who knows (advanced) math topics or a child who is 99% because of this training. I want a child who does really well in math he has never seen before or mastered because he is a thinker and a learner and can apply thinking and learning to math. I've always said if you need a 99% because it is required for GAT entry, do what ever it takes this year and forget your principals. In 7th grade, I can't say this; it is not possible to short cut your way into a 99% without a solid learner-thinker. Also, we've never actually deviated from principals or practiced rote math and we have always either been at 99% or been within striking range (in a bad year). I will say that it's never too late to start. There are advantages to starting early, but starting late does not preclude achieving the ceiling on a test.</div><div><br /></div><div>The most challenging topic using my approach on pre-10 and post-10 children is parenthesis. I will illustrate with this problem: (6^2 + 18 + 2 + 4^2)) - 2^2. This is not a complicated problem, but it is not possible to do a page of these problems with a child still learning exponents and parenthesis without writing down at least 3 or 4 steps in order to check steps for errors. In other words, it's faster and easier to let the pencil do the work than the brain. Before 4th grade, I'm happy to endure 4 or 5 wrong answers from mental calculations because the impact to working memory (not to mention arithmetic practice) is useful. But with the problem above, working memory gets a work out and the child still has to write down each step to survive the problem.</div><div><br /></div><div>In our 1 year ahead math program, it is common for kids to fall to 85% by about 6th grade. The program administrators - geniuses way ahead of their time - are focused on the final result and this interim dip is a researched based way to achieve the final product. The extra 14 points are achievable with a bit of extra work. If you review this article from the beginning, you'll see 3 or 4 math education concepts that all work together to produce 99% without a lot of extra effort. I don't think this approach would work very well in a classroom situation without modification, but it certainly can at home. Once any topic above is presented above, the next step depends on the child's response in the context of the child's individual skill set. A parent who gets to know their child and experiments a little with backtracking, repetition, exploring the question will stumble toward success.</div><div><br /></div><div>Now back to the 7th grade challenge that introduced the article. We have a very ambitious goal but not a lot of time to achieve it given homework and nonschool activities. The topics, approach, learning environment, and general mess of our preparation is in my opinion an exact mirror of the test.</div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com5tag:blogger.com,1999:blog-5703568807615263851.post-91501415172945658112018-01-21T18:31:00.000-08:002018-02-03T10:18:35.649-08:00A Decent Reading ListI’ve been asked to recommend good books to read for 2nd to 3rd or 4th grade. I’ve search for a decent source so that I wouldn’t have to do this, but there is no decent source. There are many recommended reading lists, including grade schools, libraries, and sites that bill themselves as good sources, and none of them provide even a tiny fraction of the good books that are out there.<br /><br />In the book Pre-K Phonics Conceputal Vocabulary and Thinking I provided a comprehensive recipe for strong reading. It was inspired by the very inspiring introduction to Susan Wise’s seminal work The Well Trained Mind. She said that she would take a laundry basket to the library. I did this for 3 years. It’s enough to put your child squarely into ‘Chapter Books’. In Pre-K Phonics, I took this to the next level, and maybe the level after that.<br /><br />By 4th or 5th grade, your child will be reading books of their own choosing, books that take a week or two to read and have 10 more in the series or genre, and your recommendations will likely be ignored for the next 15 years.<br /><br />That leaves a very important 2 year gap where the child needs help finding good books. This is also the last time that Read To (super important) will be easy to do.<br /><br />In this article, I’m going to lay out the approach, and then over the next few months, I’m going to fill in the blanks. The math work that I provided for the early years is now coming to fruition in 4-7th grade weekend math (because of homework it’s no longer daily). We simply need a 99% on both sections of the MAP test in order to get into high school. That’s not asking much. Some day I’ll tell this story, and it will sound a lot like age 4, only with much more advanced topics. In the mean time, it’s time for reading.<br /><br />Here are the buckets.<br /><br /><b>Mandatory Books</b><br />I’m convinced that the Hobbit and Roald Dahl’s complete works (including autobiography) should be mandatory reading during this age. The list is much longer and needs work. If your child reads the Magic Tree House somewhere between late K and early 2nd, you are where you should be. The mandatory books will get you to the next level. (When I say ‘reading’, I mean Read To as needed, especially with the Hobbit.)<br /><br /><b>Top Notch Books</b><br />Gifted programs have a formidable reading list that includes classics like Kira Kira. These books are easy to spot because if you query the book in Amazon, you will see teachers guides in the search results. I suppose that’s not easy if you don’t start with the list. This is probably the most important list for my readers and the one I’ll work on first.<br /><br />To put this list together, I’ll simply steal it from a dozen programs I’ve watched over the years. Feel free to add to this list in the comments. At some point, I’ll just move this to the permanent pages.<br /><br />[Feb 3 - I've been trolling through material and it's so bad I'm going to have to go through all of the publisher's websites.]<br /><br />2nd Grade<br /><br /><ul><li>Dear Mr. Henshaw</li><li>The Miraculous Journey of Edward Tulane</li><li>Bunnicula</li><li>Sarah, Plain and Tall </li><li>Charlotte's Web</li><li>A Long Way from Chicago</li><li>Harry Potter (not in school; I recommend the whole series spread out over the next 5 years)</li><li>Boxcar Children</li><li>The Story of Pilgrims Progress (not sure about the age yet)</li></ul><br /><br />3rd Grade<br /><br /><ul><li>Fair Weather</li><li>Mr. Tucket</li><li>The One and Only Ivan</li><li>A Wrinkle in Time</li><li>Bud Not Buddy (pair with historical context and there is a play on this as well that's pretty good.)</li></ul><br /><br />4th Grade:<br /><br /><ul><li>Chasing Vermeer</li><li>Because of Winn Dixie</li><li>Love That Dog (poetry)</li><li>Kira Kira</li><li>The Mixed Up Files of Mrs. Frankweiler</li><li>Call of the Wild (boring)</li><li>Amulet (graphic novel series - not taught but all kids read it)</li><li>The Hitchhikers Guide Guide to the Galaxy (I don't know why this is here)</li><li>The Watsons go to Birmingham (pair with historical context)</li></ul><div>This <a href="https://www.mensaforkids.org/achieve/excellence-in-reading/excellence-in-reading-4-6-list/" target="_blank">link from Mensa</a> for 4-6 grade is not bad, but dated.</div><br /><br /><b>New Books That Are Classics In The Making</b><br />We have two libraries near us that are the 2nd and 3rd largest in Chicago. Because of this, we get to see all the books worth reading somewhere in the shelves. We tried them all.<br /><br />Most of these are for girls and have a girl theme. We really enjoyed these, but being boys, ignored the girl themes and simply enjoyed the creativity and good story. I’m sure there are good boy themed books, and I’ll list these, but mostboy themes seem formulaic. These books are 3-5th grade.<br /><br /><ul></ul><br /><ul><li>Keepers Trilogy (2nd or 3rd grade advanced) </li><li>Savvy (my favorite, definitely a girl book)</li><li>Tale of Desperoux </li><li>Percy Jackson and The Olympians (my 4th grader also recommends the Magnus Chase series)</li><li>I have to wait for a few kids to get back from Boy Scouts to complete this list, including one boy (not mine) who read the Lord of the Rings trilogy in 1st grade and got a 100% when I grilled him on it.</li></ul><br /><b>Books You Didn’t Think About</b><br />I am a big fan of picture books and winners of foreign book awards. The ones we choose tend to be small in words and big in mind blowing concepts. I had to do inter library loans to get many of these.<br /><br />Shel Silverstien is on this list. We bought his books and read them daily. Jack Prelutsky is on this list. David Weisner (Flotsam) and Brian Selznick (all his picture books).<br /><br />One day my child was writing a few poems for school. They were really, really good. It wasn’t a fluke.<br /><br /><b>Books To Enjoy Reading</b><br />If you search for lists for a 2nd grader (or a 4th grader because your child is an advanced reader) you’ll see a list that includes mainly junk. It might as well be comic books or romance novels. But we read all of these because it guarantees that your child will have one or more books in hand at all times. The child is not gaining anything out of these books (think Diary of a Wimpy Kid and Middle School) other than the habit of reading all of the time. So we read all of these. But not at night, when it was reading time, and a quality book should be in hand.<br /><br />James Patterson (top selling author) started writing books for reluctant middle school readers because his son was one. This list includes some really great works for advance 2nd and 3rd graders, especially boys, such as Treasure Hunters. You can’t put one of these books down. There isn’t much cognitive value to his books. That’s not the point. It’s about becoming addicted to reading.<br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com11tag:blogger.com,1999:blog-5703568807615263851.post-18310837512869252132018-01-14T14:36:00.002-08:002018-01-14T14:36:17.359-08:00Struggling in MathI have gotten a lot of questions in the last 2 months that I will summarize and then answer:<br /><br /><ul><li>My child is struggling with their At Home Schooling math, which consists (usually) of me making them do a math work book that is 2 years beyond their grade level.</li><li>My child started school at 99% and is now at 85%.</li></ul><br />I tend to stay focused on preparing for a strong high school math experience; neither of these two issues ever bothered me and your children are smarter and better than mine. We did have a dip in test scores and I went into RED ALERT mode until it was corrected. Both of these topics have been covered over the years, but it's pretty hard to dig through my blog to find answers. In addition, I already deleted the 300 articles that had a play-by-play of my struggles.<br /><br />Both of these are linked, because in order to get to 99%, your child either has to go to expensive after school math programs that will gradually make them hate math, or your child will work ahead at home.<br /><br /><b>Struggling In Math</b><br />The answer to all of your struggling questions is called 'Backtracking'. We do it all the time. I can't imagine doing any math above grade level without a lot of it. Here are some examples that I've written about while we were doing it:<br /><br /><ol><li>If we were doing EDM Grade 2 in Kindergarten 3 days a week, at least one day a week we did a first grade math workbook that was just adding and subtraction. Some times this is a nice break, sometimes it's catch up, some times it's practice.</li><li>Sometimes I take 2 or 3 weeks off to cover a concept that we never had or a concept that we just plane stink at.</li><li>Sometimes an entire section in the workbook is almost all wrong. Sometimes it's just a page or an important problem. The kid just doesn't get it. I circle the pages and we move on. A month or 2 later, we'll come back to the circled pages and do them again.</li><li>When the child is younger, there are some bad days because of hunger/sleep/sickness issues and we just do flash cards or arithmetic worksheets. Bad days happen rarely at older ages (always the day after a sleep-over), but when they do, we do nothing at all that day.</li><li>Sometimes we take time off from math and do projects like a puzzle or sewing something or a craft or a writing project or art, a comic book, whatever. In each case, the child just starts doing it and I will not interfere. I am convinced that these activities will produce a stronger mathematician than actual math.</li><li>We like to do things backwards. So if the book does it one way, we redo the whole thing backwards.</li><li>We like to do things step-by-step. Identifying the mini-steps helps you find backtracking material. Here's a really simple example. 23 x 15. This has 4 separate multiplication operations and 3 addition operations. Maybe your child should just practice multiplying 3 x 4 and 30 x 40, 9 x 2 and 90 x 20 etc for a while before coming back, or 20 x 15 and 3 x 15.</li></ol><br />There are two difference between you and me. First, as previously mentioned, your children are smarter than mine. Secondly, we back track a lot. Why continue to struggle with the same material? Do something else, practice something, come back to it later. It will all get done in the end because we are both picky and uptight parents about math.<br /><br /><b>Test Scores</b><br /><br />Lately I've been getting a lot of feedback from many parents that test scores are falling. I get this from almost all parents (like 85% of the ones I talk to) at some point during grade school, usually right around the midpoint. Here are the reasons:<br /><br /><ol><li>Your school program teaches and practices math at about the 85% level. Over time 99% children will end up working at the 85% level.</li><li>Your child is sick of doing math and needs a year off.</li><li>You are not doing daily math at home at a suitable level and 15% of the country is.</li></ol><div>None of this is a bad thing. I think our program starts pushing math at the appropriate time and produces graduates who are really strong in math. This will not make a parent happy in the following 2 circumstances: #1 Your child needs a 99% right now on an annual standardized math test this year. #2 You have some other objectives in mind that requires a 99%.</div><br /><br />Here is my 3 part recipe:<br /><br /><ol><li>Get math at a suitable level.</li><li>Do it. Backtrack a lot.</li><li>Focus on problem solving techniques and not math. Math will take care of itself.</li></ol><div>I can now see that I need another article because the leap between 3rd and 5th grade and it's called problem solving skills. My particular approach can be summarized as focusing on nothing but problem solving skills during 2nd and 3rd grade and it works. Not just any set of problem solving skills, but the core skills that are the foundation of all others. That, in a nutshell, is 95% of the motivation behind Test Prep Math. The other 5% is making math less boring than it normally is. </div><div><br /></div><div>But I'm hearing from parents of 3rd and 4th grade children that didn't go this route. I've got some thinking to do. It's solvable. Anyone can catch up to any level you want to get to.</div><div><br /></div><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com3tag:blogger.com,1999:blog-5703568807615263851.post-78808336400197275182018-01-12T09:18:00.000-08:002018-01-12T09:18:00.327-08:00The Language of MathThere is a strong and important connection between math and language.<br /><br />Think about a child learning language before the age of 2. You point to a blue ball and say 'blue'. The child sees round, blue, rubbery, your finger, you making some weird noise, you're looking at him or the ball or both, and you're probably smiling. What is blue? Then you point to a blue wall and say 'blue' and the kid is more confused than ever. <br /><br />In order to figure out blue, ball, yellow, green, box, toy, your child has a lot of confusion to sort through, is going to make 5,462,298 mistakes, and you're going to be smiling the whole time, and on top of that the child is going to have to identify patterns, sort through permutations and eliminate candidates until he comes down to blue is an attribute of color. The child may not see round or plastic or squishy yet, maybe he can sense it, but when there is a word tossed out there for 'round', his ability to think logically will be substantially improved.<br /><br />By 1915 or 1911, I'm still debating, cognitive psychologists determined that the process of reading uses 100% of all cognitive skills. 100%. This will never happen again.<br /><br />If you want to know why I'm so over the top obsessed with reading and vocabulary during age 4, so much so that I created Pre-K Phonics Conceptual Vocabulary and Thinking to jam as much 2nd grade material into the brain of a child who can't pronounce C-A-T, you now know why.<br /><br /><b>Don't Lose The Magic</b><br />Learning to talk and learning to read, not to mention learning to walk, are much harder by a factor of a gazillion than anything a child will learn thereafter, including Pre-Algebra. But somewhere after learning to read, maybe around addition, the parent loses the Magic Learning Environment that allowed your child to overcome insurmountable learning objectives. You used to sit there smiling dumbly mistake after mistake totally happy every time your child rose an inch off the ground and then fell. Now you're yelling at your child for forgetting what 8 + 4 is or struggling with x<sup>-1</sup>. At least I am. We ALREADY discussed the exponent graph 3 times. Would you just pay attention once?<br /><br />The magic was that you were willing to try to teach your child what words mean, despite not having the slightest clue how this works, through mistakes and trying over and over and over again, usually smiling the whole time, and learning just exploded.<br /><br />This is the first connection between language and math and it's pretty lame compared to what follows.<br /><br /><b>Reconnect the Two Dots</b><br />If math uses a certain sub set of cognitive skills, but learning to read (definitely) or learning word definitions (probably) used 100% of cognitive skills, wouldn't it be great if you could bring the missing cognitive skills back to the math learning process?<br /><br />I think this is theoretically possible and in practice I just ask them to explain verbally to me how to what the question is asking, what do they know, is there anything they have learned before that can help, can you articulate your solution strategy? I also throw in anything I can think of related to a problem, like 'Polyhedron' or some other word to get that verbal section of the brain working.<br /><br />But mostly I like to talk through problems and concepts.<br /><br />Recently, we came across this question: What is 42% of 66? This is an advanced post TPM problem. I got it off a high school Algebra I final that has 190 questions and would be very hard for high school We're doing about 5 problems per session and learning a lot. This is an opportunity for a long discussion involving fractions, decimals, and %, as well as problem decomposition and lining up multiple steps, followed by cheating with algebra. In other words, in addition to math, it's going to be about 25 minutes of talking.<br /><br />Here's some fun verbal math discussions for a younger age. In these cases, I did very little talking and just left key questions out there for 3 or 4 weeks while the math sank in. Then we discussed, and I asked why? or prove it to me.<br /><br /><ul><li>The definition of 'square root' is this. 2 is the 'square root' of 4 because 2 x 2 = 4. What is the square root of 9? Does 10 have a square root? (Not yet, but it will later).</li><li>What is the square root of negative one? It's call 'i'. What is i * i? Why is this important (because the Fundamental Theorem of Algebra does not hold true without i in case you're wondering). What is the square root of - 4? </li><li>What is 2 - 5? I love this discussion. It goes like this: "Three". If 2 - 5 is 3, what is 5 - 2 and why are they both 3? This can't be right. If you have 2 and you give away 5, what do you have left? "You can't do it". Oh yes you can my friend, yes you can. </li></ul><div>If I can't find something to discuss in math work, I'll start looking for more math. y = mx + b and f(x) = mx + b are great topics for discussion and not writing. That's why we end up covering advanced math at a young age, simply to have something to <i>talk</i> about. How's this going? About as well as learning how to talk in the first place.</div><div><br /></div><br /><b>Is Any of This Going To Help?</b><br />I'm not 100% sure yet, but it might help with math learning. It's definitely helping with writing. Trying to compose an explanation for a complicated mathy topic just learned is really hard. It is a foundation leadership skill. It's similar to a reading comp skill, but only vaguely. It's easier than any classroom speaking task. I'm certainly not going to end up with a wall flower, what with me demanding a thorough explanation to a complicated explanation.<br /><br /><b>Product Recommendation</b><br />I highly recommend IQ Twist or IQ Puzzler Pro. We've had these sitting around for the last few years and my kid and his class are now obsessed with them. His 4th grade teacher is buying them for the classroom.<br /><br />It wasn't until I solved a problem myself that required turning and flipping multiple shapes when I realized that it's NNAT and somewhat COGAT training. We started talking through the solution to one tough problem and how one shape could only go in one certain place before I realized that this is all logic, visualization and math. If you run out and buy these for a 1st grader like I did, feel free to reach out for help because it took me a few years to figure out how to use these with a younger child.<br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com7tag:blogger.com,1999:blog-5703568807615263851.post-25662792469561710372018-01-08T10:58:00.000-08:002018-01-08T10:58:03.775-08:00Real MathMy son complained about his daily math. It was some problems from two Pre-Algebra topics.<br /><br />If we do pre-algebra every day it's going to get boring. I refuse to do either decimals or long division or math facts or anything between kindergarten math (totally engrossing) and pre-algebra (marginally useful) because it's all boring and useless. <br /><br />I need a fall back plan. He's been playing IQ Twist lately (highly recommend this game even though I don't get paid for any of my recommendations) and that got me thinking. There is this great math book called Mathematics 1001 that has 1000 math topics in addition to 2 pages on trig that allowed us to cheat our way through it. One of the topics in this book called 'Net's looked like the shapes in twist, and a little reading later uncovered this idea.<br /><br />Here are two <b>Nets</b> for a triangular pyramid. If you cut out either Net, you can fold it into the triangular pyramid. <br /><br /><div style="text-align: center;"><a href="http://2.bp.blogspot.com/-vADMGurqR30/WkKWHHS5UuI/AAAAAAAAAr8/uiRmA0v50BYJvMpbRNftaj-K5uCzFyFBACK4BGAYYCw/s1600/net%2Bof%2Bpyramid.jpg" imageanchor="1"><img border="0" height="128" src="https://2.bp.blogspot.com/-vADMGurqR30/WkKWHHS5UuI/AAAAAAAAAr8/uiRmA0v50BYJvMpbRNftaj-K5uCzFyFBACK4BGAYYCw/s320/net%2Bof%2Bpyramid.jpg" width="320" /></a></div><br />There are 11 nets for a cube. Draw them.<br /><br />I watched two sets of skills in action. First, there was geometric visualization, including rotating, flipping, and 3 dimensional manipulation of shapes which trumps the two dimensional manipulation on a cognitive skills test. If we were facing a test this year, I would have only shown the diagram on the left above and asked for 2 more nets for the triangular prism (even through there is only one because cognitive skills tests test your ability to come to terms with incorrect questions).<br /><br />Secondly, there were budding permutation skills at work, which is an extremely important math skill. Since no kid is going to get to 11, this gives me the opportunity to suggest permutations. "What's a permutation?" Well, take the letters a, b and c. I can write them as abc, acb, bac, bab, cab, and cac. There are 6 permutations of the letters a, b and c. Please give me the permutations of 1,2 and 3. This should be pretty simple. Then look at the basic T shaped Net for a cube, and start permuting the squares, one square at a time.<br /><br />We got to 7, which is pretty good for my 25 minute time limit. I need to stop at 25 minutes to save room for follow up questions, like telling me the rules for building a Net while staring at the 11.<br /><br /><b>Real Math</b><br />I expect this child to go far in math. He's not going to go anywhere without some intervention. Here is my intervention.<br /><br />I showed him a web diagram of the 11 nets for a cube. I stated that some guy (Albrecht Durer) asked how many ways you can create a folding diagram for a cube, and he came up with 11.<br /><br />Then I showed my kid the pre-algebra worksheet of about 20 equations. <br /><br />I asked this question. If there is a mathematics professor and researcher at some university asking questions and writing papers and going to conferences and helping his colleges in the Physics and Information departments apply abstract math to their work, which math is this professor doing right now? (And by way of association, which math are the physicists and computer sciences clamoring for?) Does it look like this (pointing to pre-algebra) or does it look like this (point to the 11 nets for a cube.) <br /><br /><b>The Answer</b><br />The answer is the net stuff. And why is it that your school curriculum looks like pre-algebra, the type of math that mathematicians don't do?<br /><b><br /></b>Here is my (mostly inaccurate but totally) true history of math curriculum in the United States. In 1930, a vice president at Ford Motor company created a list of skills needed by factory workers and accountants and dealers to create and sell cars. This skill set was widely applicable to industrial work of all types. A curriculum was created to teach it and used throughout the United States. Lots of cars were produced and everyone was happy. This curriculum is still used in 2017 in the midst of the Information Age.<br /><br />Of the 96 maths out there, school is going to consist of the 5 that would help you build cars by hand or build a bridge, which you are never going to do. The maths that you actually need to get through your life - starting now - are not taught at all.<br /><br />What I find most interesting is that the 5 maths taught in US curriculum are almost devoid of skills compared to the maths that could be taught. <br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-91083294334007340452018-01-02T09:17:00.000-08:002018-01-02T09:17:02.708-08:00The Train Wreck RevisitedThe 'Train Wreck' is one of the 5 things that should keep a parent awake at night worrying. Three of these are reserved for children over the age of 12, and that only leaves 'Lacking Motivation to Read' as the two things you need to worry about right now.<br /><br />The term 'Train Wreck' is used in situations where a child who previously got all A's in math is now getting a C. This most commonly occurs between 4th and 8th grade. It can also occur in Algebra or Geometry. This term also applies to a child's test scores falling from 99% to anything below 90% and is somewhat related to regression to the mean.<br /><br />None of this is very shocking. You want shock? Let me define this term formally.<br /><br />Train Wreck: At one point, your child held a formidable skill set and did well in math. A few years later, when your child faces a new math, the child doesn't do well because the child does not possess the skill set required to do well. You are left wondering what happened and either correctly blame yourself or incorrectly blame the teacher.<br /><br />The most common cause of the 4th grade Train Wreck is a child who is overly endowed with skills entering 1st grade and spends the next 3 years at school not thinking. By 4th grade (depending on the school district and curriculum), there is a jump in complexity, and the child has no tools in the tool shed. The train wreck in middle school or freshman year is usually caused by a catastrophic failure of curriculum, but can also be the result of a bright child languishing in an average curriculum.<br /><br />Regression to the mean is an empirical consequence of the level of instruction in school. Kids who score below the mean usually catch up test-score-wise while experiencing instruction at the mean, and kids who do much better than the mean usually slow down while experience instruction at the mean. I'm waiting for the field of cognitive psychology to have a 'duh' moment and figure this out, but tat the time of this writing, they are still baffled. Anyway, Regression to the Mean is a less dramatic version of the Train Wreck but is caused by the same factors.<br /><br />There are at least 2 leaps in cognitive requirements that take place in grade school math, and at least two in language arts. In high school, a really great curriculum will have at least one leap every year (most don't). Are you happy with your child scoring well this year, or are you really concerned about their score in 2 or 3 years? Thanks to No Child Left Behind, teachers are mandated by law to be concerned only about this year at the expense of next year. Thanks to having 30 kids with a variety of skill sets, the teacher can only do so much. You're going to have to pick up the slack. <br /><br />Happily, I've found that being only concerned with 2 years from now tends to take care of this year and next year for no additional effort. By when we work ahead 2 years, I stay focused on the skills, not the math.<br /><br />There's a really great book by a psychologist to deal with the Train Wreck. There's a lot of great 'Yoda' in this book, but it's downfall is that the author doesn't address the skills issue. He has a valid excuse because he has a PhD in Psychology, a field who thinks IQ magically happens. I've done a little work in this area, but not enough to write a book. My market is shooting for 99% (if you're reading this, this is now your official goal if it wasn't before) and we're going to need the whole bag of skills to get from X% to 99%.<br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com4tag:blogger.com,1999:blog-5703568807615263851.post-16240347444335764862017-12-29T18:00:00.000-08:002017-12-29T19:01:40.859-08:00Fractions in 2nd GradeLast month, a reader asked me how to teach fractions to a 2nd grader. I'm assuming that the reader is asking me to provide the magic formula for a child of a specific skill set (which I haven't measured) paired with a parent who has a specific skill set (which I haven't measured). This is a tough problem that requires the Force. I retreated to the island of Skellig Michael off the coast of Ireland so I could meditate.<br /><br />This article is going to describe how to teach a math topic (in this case fractions). The approach for fractions shares a lot with other topics. Fractions is especially important in math because it is slightly abstract and always multi-step, follows 3 straight years of spoon-feeding one step problems in school, and therefore befuddles students and parents alike for want of cognitive skills.<br /><br /><div style="text-align: center;"><b>The Parent</b></div><br />Before we launch into this topic as a parent/coach/Jedi Master, we need to take a step back to appreciate the importance of this math topic. It is fascinating, alluring, captivating. Without this appreciation, it's hard to pass our love of math to our children. If your child is ready to take on fractions at a young age, you will convince no one by saying "Fractions are totally boring and pointless to me but I'm going to make you do them anyway".<br /><br />What are our goals for fractions? We want the child to know fractions so that they can look at a super hard problem and see the answer right away. We want the child to emerge from these fraction studies with a formidable skill set that can be applied to other quantitative areas. We want to present this child with something like exponents or algebra someday and the child will say "Leave me alone. I can do this all by myself".<br /><br />There are some years from K to 8 where you want your child to do 45 minutes of math a day and be really, really good at it. In our case, there were 3 of these years. I wouldn't do it every year because the child will learn to hate math, and it's not necessary anyway. If this happens to be one of these years for your child, in addition to what I describe in this article, get them a decent workbook that includes fractions and make them do every single problem in the book no matter how long it takes. Otherwise, just do what I recommend here.<br /><br /><b>Fraction Foundation</b><br />The first thing we need is a high level definition of fractions. When you divide 20 by 4, you end up with 5. This means splitting 20 into 4 groups gives us 5 in each group. If you have 20 skittles, but I'm only going to let you eat 1/4 of them, you're only going to get 5. These are two different concepts, but the exact same mathematical operation, namely 20 ÷ 4 = 5.<br /><br />What does it mean to divide 7 by 2? What does it mean to divide 1 by 3?<br /><br />There are two times when we have these discussions. The first time is when I think we're going to be studying fractions in a few months or next year. I call this Power Bucketing. This discussion will create a brand new bucket in the child's brain called 'Fractions', and when the child sees fractions in school, while the other kids are trying to come to terms with fractions, my child will already have an empty filing cabinet in their brain for fractions and will have a permanent head start in this area.<br /><br />When I teach fractions, we spend the first week just asking what fractions are. I will give the child 10 to 20 minutes for them to think through these simple problems, like 7 ÷ 2 = 3 1/2. After we've exhausted the mental capacities of the child, I'll ask for a picture or show them how to diagram fractions.<br /><br />If you look through 2nd, 3rd, and 4th grade math curriculum on the topic of fractions, fractions are introduced slowly. I'm not going to speed through this process. <a href="https://www.ted.com/talks/j_j_abrams_mystery_box" target="_blank">Please view this Ted Talk on J.J. Abrams from 2007</a>. Look at that box with a question mark (in the video). As long as the box is sealed, your child's imagination is in play. As soon as you open it and describe its contents, you've ruined your child. Let the child figure out what is in the box on their own.<br /><br /><b>Fraction Lifestyle</b><br />At this point, you can introduce fractions into your conversation. Think about a really smart parent with multiple PhD's who just talks their child into Stanford. We want to be like this parent, only not as nerdy. The two most obvious uses of fractions are time and baking. Get your child a brownie mix and make them do all of the work. Put post it notes on the refrigerator reminding yourself to talk about time only in fractions, as in 'it's 1/3 past 5, what time is it?' By the way, my older child has been in charge of making desert for years thanks to fractions.<br /><br /><b>Fraction Overdrive</b><br /><a href="https://www.ixl.com/math/grade-4" target="_blank">This page from IXL</a> describes the basic fraction related skills expected of 4th graders. You can also look at grades 5 and 6 because fractions is going to appear every year from now on. I didn't read any of it because it's too boring.<br /><br />Instead, like all topics in math before calculus, with the exception of geometry, we simply have to state the obvious. How to you add, subtract, multiple, and divide fractions? Throw in 2 more operators (greater than and less than) and transformations (aka equals) and that's pretty much our goal. This is exactly 8 things to learn (transformations are 2 things - equivalent fractions and transformation to and from mixed fractions).<br /><br />This little exercise is going to be repeated with rational numbers, exponents, complex numbers, and other pre-pre-algebra topics. When this child is doing algebra for the first time at age 9, and is stuck while trying to reduce a really complicated algebraic expression, I say 'Dude, you've only got 4 possible operations - addition, subtraction, multiplication and division, just try all 4 of them to see which one works.'<br /><br />When your child sees decimals and percentages some day, we'll have 2 additional transformations involving fractions.<br /><br />Where did I get all of this material? I spent a month thinking about it. Your child's teacher does not have a month to spend on fractions because there are typically 6 to 8 topics each day, plus statistics. With some math topics, I also wiki and read about Egyptian or Babylonian history. Your child's teacher won't have time to do this either. She has 8 subjects and 30 kids of cognitive profiles to teach. You have 1 child and fractions.<br /><br /><div style="text-align: center;"><b>The Student</b></div><br />Children are natural learners. Once the parent is prepared (95% of the battle), the rest is easy. Just give your child as long as it takes and don't help at all. Ask the questions and expect your child to work things out mentally, when your child doesn't succeed, ask them to draw the picture. Help as needed, but only after the child has exhausted their mental faculties. I generally observe mental exhaustion takes place at about 20 or 25 minutes (because I always choose really hard material), and I'm prepared to sit there, sometimes silently, for 20 or 25 minutes.<br /><br />If you hand a 4th grade book to your child, there will be gaps hidden in 2nd and 3rd grade material. The child will get stuck on a problem, and the way forward is material that they either never had or never mastered. Be prepared at all times to go back to 2nd or 3rd grade material as needed. Suppose they get stuck on a really hard problem, and you can see that it involves transforming from mixed fractions or comparisons. Take a few days off and do some problems involving mixed fractions or comparisons. IXL is good for this.<br /><br /><b>Step 1 - Comparisons and Transformations</b><br />I'm not sure why a book would be needed at all. The most important fractions are 1/2, 1/3, 1/4 ... 1/10. If the denominator is greater than 2, then you've got 2/3, 2/4, 2/5 ..., 3/4, 3/5, 3/6... and so on. Then you can multiple any fraction by 2/2, 3/3, 4/4 and you've got a set of un-reduced equivalent fractions.<br /><br />Pick any 2, and ask for >, < or =.<br /><br />If your child was adept at division and had a really strong number sense, I would not create flash cards to drill my child on fraction comparisons. If your child did not have a strong number sense because they never had really great curriculum at age 4 or 5 that built number sense, I would not only create flash cards, but I would create spread sheets with 100's of problems from the fraction list and drill the child until their number sense was invincible. In our case, we did this at age 4 with SSCC and never looked back. Except when we did this again. And one other time.<br /><br />You can search the internet for "comparing fractions worksheet" and see thousands of examples. If I never met your child and you only gave me 30 minutes to address "comparing fractions", I would print 3 of these: One with pictures, one with simple fractions, and one for harder fractions (involving primes versus composite numbers, like 12/13 versus 10/12) and I would find out quickly where they are.<br /><br />This exercise requires transformations - like comparing 5/6 and 10/12. This is a two step problem. 5/6 and 9/12 would be a more obvious two step problem.<br /><br />Throw an integer in, like 2 1/3, and you've got the other transformation to get to 7/3. We never go in the other direction, from 7/3 to 2 1/3. When I see this in a book, I comment that this is lame. In higher order math, we only work with 7/3, or 142/25, and never mixed fractions. Also, as I mentioned before 6 ÷ 3 = 6/3 (this is impossible to write in a vertical line, but basically I'm writing division problems as fractions and never using ÷ again).<br /><br /><b>Step 2 - The Other Arithmatic Operators</b><br />Once we 'get' fractions and practice transformations, we have to tackle addition and subtraction, then multiplication and division.<br /><br />Addition and subtraction involves transformation. We can't add apples and oranges. We have to transform one or both. This is why transforming and comparing fractions is a prerequisite.<br /><br />Pictures might help if you didn't spend any time doing step 1. We usually just skip to the hard parts, but you need to read Step 4 below to see why.<br /><br />Note that this is a 2 or 3 step problem. These types of problems reward a child who works slowly and a parent who doesn't expect correct answers. If the child is expected to do a lot of problems, expected to get them correct, and expect to do them quickly, the child will fail at multi-step problems. Because of this, I have settled on one or 'a couple' of problems as our daily routine until the child builds speed.<br /><br />If this child was 10 years old, I would expect the child to devise and explain a formula for adding fractions. Before this age I never even hint that there is such a thing as a formula. I want the child to go through the 5 or 6 substeps every time, using working memory, because amazing and surprising subskills will develop in that child's brain that will pay off in a big way later on.<br /><br />For an 8 or 9 year old, I would want to see a picture and an explanation of what is happening. I would also try out 1/2 + 1/3, 1/3 + 1/4 etc from the list I explained above. But I would do this every time he was stuck on something like 5/11 + 2/3, because this age desperately needs intuition number sense and now's the time to develop it. This is really going to slow down the topic, but if you do it right, you'll save many years later on not having to explain math topics.<br /><br />Multiplication and division require starting all over again with this article, both parent and child section, with each operation. What does it mean to divide 3 by 1/2 or 7 by 1/2? What does it mean to divide 1 by 1/3? How about dividing 4/5 by 2/3? The same basic questions are asked about multiplying fractions. What is 1/3 times 3/4? Before algebra in about 6th or 7th grade, I would want this child to think through the meaning of these problems every time instead of just turning 4/5 x 2/3 into (4 x 2)/(5 x 3), because if the child skips thinking through these each time, they will get to algebra ready to calculate but unable to understand. This approach precludes some problems and precludes lots of practice. This approach involves a few problems over a much longer period.<br /><br />Diagrams work really well in understanding multiplication and division. These will be articles on their own so I'm not going to cover it here. Have you ever read a history book that starts with the beginning of time, evolution, 40,000 years ago etc until it gets to the main topic, which might be 1972? That's how I handle these topics.<br /><br /><b>How Bad Can It Be?</b><br />The biggest challenge with teaching your child math is coming to terms with how stupid your child is. You're doing something that you just did the day before, and your child not only forgot what he learned the day before, he can't even add. He does a single problem in 30 minutes and it's totally wrong. There are 29 problems on the page that are not completed. It's a disaster.<br /><br />This is the make or break moment in your child's academic career. You have the choice between a future surgeon with join doctorate degrees in Sumerian literature and Bioengineering, or a kid who drops out of community college to form a rock band. The choice is yours.<br /><br />I'm usually pretty pleased and announce that will pick up problem #2 the next day. I can do this because in the futile mess I see cognitive skills developing. Within a few months, my child is making adequate progress and I'm looking for books on Sumerian literature on Amazon.<br /><br />Sometimes I am discouraged and ask how he could possibly screw up such a simple problem. After I say something like this, he will spend the next few weeks perfecting a base guitar riff.<br /><br /><b>How Good It Can Be</b><br />Once you've taken on a few topics like this once, each successive topic is easier and more fun. The key is that 6 to 8 months of hard work pays off, and you can see that doing a single problem for 2 weeks and getting nowhere is normal and leads to ripping through pages down the road and eating math for lunch. For a parent, it requires nothing short of faith to get through the first few weeks.<br /><br />For those of you who took my advice to do EDM Grade 2 in Kindergarten, you already know this. For those of you who do TPM, which is not all that mathy but is really thinky, you're ready to start. Unfortunately, in both cases, nothing ever gets easier and you still have to go through the whole painful learning curve with new maths. But doing Algebra II with a 9 year old and going through a painful learning curve is much more gratifying than doing decimals and going through no learning curve.<br /><br />Last week, my child was struggling on a problem from his Algebra I final exam. We stopped using math books altogether and just take tests, figuring things out on the spot. Sometimes, we'll take a break and do some worksheets on a new topic. Anyway, there were 4 maths involved in this topic, and he didn't know 3. He didn't even know the formula for the area of a circle. It took us over an hour to do a single problem, what with all the backtracking.<br /><br />Then I realized I accidentally grabbed the Algebra II final. When we went back to the Algebra I final, he had 6 questions of the form "What is 42% of 66?" and <i>didn't know how to do them</i>. Arrrgggghhhh!<br /><br />In each case, we took apart, figured out, and mastered new topics on the spot. This is the skill set that I want. This is the skill set behind the MAP test, for very important reasons. If you can get this skill set down early on, say fractions, then it's just a matter of plowing through pre-algebra, functions, algebra, geometry, trigonometry, calculus (AB and BC), linear algebra, real analysis and series, and then statistics. <br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com8