tag:blogger.com,1999:blog-57035688076152638512018-01-15T08:46:11.756-08:00How 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.comBlogger219125tag: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.com0tag: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.com6tag: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.com2tag: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.com8tag:blogger.com,1999:blog-5703568807615263851.post-77000328344178175832017-12-26T08:45:00.002-08:002017-12-26T08:45:33.767-08:00Post Holiday MathWe are in day 2 of a 2 week holiday break. Day 1 was a holiday and I have a hard time convincing anyone to do any math. My kids sat around all day having fun, eating, chatting and helping with chores.<br /><br />Math starts today.<br /><br />Daily math is a prerequisite of the kids doing anything fun. The kids say, "I don't want to do anything fun and I'm not doing any math!" Then they read, do crafts, engage in an imagination-building-problem solving activity like Legos in order to not do any math. It's quite amusing to me when I walk by their room, and they are sitting there reading for hours, and they look at me like 'Ha, ha, I don't have to do your stupid math, I'm just going to read. I win.'<br /><br />Reading is way more important than math. The jokes on them and I'm not telling.<br /><br />Daily math started with the simple thought, "If a child becomes a strong reader and thinker because he reads daily, how is he going to become at STEM?" The answer was daily math. Around third grade, I thought "There is way to much homework to do each night. We'll just do daily math on the weekends" and that's where we've been ever since except summer and breaks.<br /><br />Math contains more than math, of courses. It contains anything I think they need to succeed at the time. This usually contains math. On Saturdays in the summer, this can be math, vacuum the basement, practice your instrument and do a reading comp question, fix the toilet, replace light bulbs. <br /><br />This year, the April MAP test is on our radar and I'm becoming slightly more organized with daily math. We overdid vocabulary between SSCC and 2nd grade and haven't done much in this area other than define and discuss any unknown word found in reading or reading comp. I am reintroducing vocabulary as part of math. With a vengeance.<br /><br />I like the MAP. It has a lot in common with the COGAT. The cognitive skill set is slightly different, but in both cases there is an advantage that can be gained from working on these skills simply because school doesn't really teach cognitive skills. Doing lots of practice, ala Kumon doesn't help at all, and learning algorithms ala Singapore sets up a train wreck (like ending up in the 90th percentile or less - I never really defined what a train wreck is but that's it). The problem with any program at all is that the child can get ahead and doing well, and the parent thinks that success has been obtained. The clock is ticking. Any time a child is practicing or applying or using things taught, learning may or may not happen, but skills building is not part of the deal.<br /><br />I remember when my goal was simply to cheat my kids into a GAT program. What actually happened was that we just ended up spending a lot of quality time together and I learned how to be a parent. The long term formula for academic success is Cognitive Skills + Interest + Will. At this age, and in the succeeding years while we caught up, it was all Cognitive Skills at the expense of Interest and especially Will. You can burn a kid out with daily math every day every year, so I tried (and failed) to take some years off. To compensate, I completely changed the approach to my formula of Baffled + Spending Time on the Question not the Solution + Get it Wrong + Check the Work. This created an environment of Zero Expectations and No Progress, and in that environment magic happened.<br /><br />Somewhere along the way, 'Will' came back, most likely because of chores or instrument practice, and I'm doing my best to stay as far away from 'Interest' as I can so as not to ruin it. A child can only develop interest in a vacuum that does not include the parent. Unless the parent is super sneaky.<br /><br />I'm thinking about 'Interest+Will+Skills' a lot because for the older child, my goal is that he does really well in AP Language Arts and/or History, with assumed A's in math of some kind. All of the math education is pointing in that direction for this child. I found that at one of the selective enrollment high schools in Chicago, a child can take Calculus as a freshman, followed by Linear Algebra/Multivariate Calculus, a course that's no longer on their website which I will demand be reinstated, and AP Statistics, and assumed A's in AP Language. This is 4 years of college credit math. We're going for it.<br /><br />The only way I can possibly think of achieving these goals is to do something creative, unusual, and different. Something that is more looking at things from a fresh perspective than hard work. Hard work is not going to do it.<br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com3tag:blogger.com,1999:blog-5703568807615263851.post-9369155278222733262017-12-23T11:55:00.000-08:002017-12-25T04:32:58.648-08:00The Makings of a ThinkerHere's a rough non-copyright violating approximation of a figure matrix question from my favorite COGAT practice test, grade 2. <br /><br />This is the last question in the book and the hardest.<br /><br /><div style="text-align: center;"><a href="http://3.bp.blogspot.com/-2t4B0QJsm9c/Wj6l3aWZ4CI/AAAAAAAAAmI/y3ih_HrqDTEw__f2_Z4twVk8PQCfU_A6wCK4BGAYYCw/s1600/testq.jpg" imageanchor="1"><img border="0" height="222" src="https://3.bp.blogspot.com/-2t4B0QJsm9c/Wj6l3aWZ4CI/AAAAAAAAAmI/y3ih_HrqDTEw__f2_Z4twVk8PQCfU_A6wCK4BGAYYCw/s400/testq.jpg" width="400" /></a></div><div style="text-align: left;">In this article, I'm going to show you how much mileage you can get from a single question.<br /><br />When I coach, usually at the behest of a parent who provides a compelling reason or academic puzzle that I want to add to my research, I'll start with whatever material they have available and do a single question. There are many other things I do with a practice test besides a single problem, but my favorite Academic Coaching Session Agenda is the Single Problem because the student picks up the most skills.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">This may be the only time I'm working with the child, and my primary goal is to train the parent who is lurking nearby, and I want an impact, so I do it exactly like I would with my own children. Like this:</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Step 1:</b> I instruct the child to do the problem. Take as long as you like, and before you answer the question, I want you to tell me that you're ready to answer the question but not what the answer actually is. I will probably announce that this is a really hard answer and I'm totally confused so I hope that the student can do it because I sure can't.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Step 2:</b> The child either announces the answer or announces that they are ready to answer. a) If they announce the answer and it's correct, I'll tell them I think it is the 2nd one and be prepared to prove your answer* b) if they announce the answer and it is not correct, my favorite case, I announce that they are wrong - try again and c) if they just announce that they have completed the question and are ready to answer, I announce that they probably got it wrong so go back and double, triple, and quadruple check the answer, followed by a) or b) when they announce the answer.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">*At some point during this training, the child will learn to check their answer. I am going to encourage this behavior in multiple ways including saying 'Check your answer'.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">This approach is the birth of skills. If the child answered incorrectly, then we're going to get double the skills from this exercise. It's not clear to most parents what these skills are. These skills are the skills of kids who will go into an accelerated history or reading course, teach themselves, and do well. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">When I announce to the child that they are wrong, they are probably wrong, or their answer does not agree with mine, the child can sense that I'm happy about this situation, and I genuinely am happy because we can learn something. I love mistakes, even the ones I make. Mistakes drive learning and it's one of the 5 core skills.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Step 3:</b> Explain the question to me. First of all, I want to know what the transformation is. The first shape undergoes 3 transformations. Zooming through problems is the way to miss subtleties like the height of the shape diminishing by about 10% before it is rotated 1/4 turn counter clock wise. Some kids say rotated 'to the left' which is OK with me provided 'to the right' always means clockwise.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">In this phase, we're learning how to see, the names of things (like rotate 1/4 turn counter clockwise or decrease in height slightly). I will correct the child's grammar or terminology, expecting that they eventually use the adult level words that I do in adult level sentences with multi-clauses. It's the opposite of Baby talk and the reason why my books have that awful looking graduate text book themed covers.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">When the child thinks they are done, I'll point out that explaining the question includes explaining what is happening in each and every answer. I would like to know what transformation took place to make each of the answer choices, or what transformation failed to take place. That's 4 additional problems as far as I'm concerned. </div><div style="text-align: left;"><br /></div><div style="text-align: left;"><i>I've never found a problem in a COGAT book that can't be solved with a thorough out loud explanation.</i> Sometimes when I'm working with my own material, I get the problem wrong, repeatedly, and I look at my answer and wonder what the heck I was thinking. Then I go through it the way using the steps I expect a student to use, and oh year, it makes sense again. When you say the transformations out loud (problem and answer choices) hard problems are turned into easy problems. I can't over stress the importance of this technique. This is why Shape Size Color Count is so verbal<br /><br />I call this skill 'Reading The Question' because most kids can't do it without a lot of training, and most parents lack the patience to wait. I know as a parent I used to lack the patience, and sometimes I still do. To accommodate my coaching inadequacies, I'll just turn over the material and go clean for 20 minutes before the teamwork begins, shouting out things like 'Read the question again' while I do my work. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">There is a prerequisite skill I call 'Seeing' that children have to develop. In this case, 'seeing' is visual and includes proportions and the ability to mentally rotate images. It takes some practice. In an academic household, those places of non-stop learning that produce GAT standouts, this practice started at age about 2. For the rest of us, COGAT practice is as good a time as any.</div><div style="text-align: left;"><br />I should point out that this is not a hard problem because it's missing the magic of the COGAT. The quadrilateral lacks symmetry. A problem like this would be practice for K. This is why practice tests are practice for the format of the test and not the thinking of the test. Also, there are 3 transformations, which you'd think would be good for working memory, but the shading transformation removes answer choices right away, making the problem easier, not harder.<br /><br /></div><div style="text-align: left;"><b>Step 4:</b> If the child can't get to the correct solution on their own, I'll mark the page and come back later. This question is still holding learning. If I have to announce that the shape is shrinking in height before turning, I just destroyed the learning opportunity. If there are 10 more questions with this transformation, I'm stuck having to announce it. It's a judgement call and depends on how much time is remaining before the big event. If you have a lot of time, you can back track by drawing 10 or 12 shapes, and ask your child to shrink one dimension and turn it 1/4 turn in one direction. Backtracking in this way is a version of finding an easier problem to solve before tackling the harder problem to solve. No branch of mathematics can withstand this approach, and every single super hard complicated advanced problem can be solved in this way if needed.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">For one child, we spent a solid 4 months doing cognitive skills training (including BTS and much much harder material of my own making). When we finally came back to math, we followed this approach from that point forward through SAT and calculus. I learned that these core skills are universally applicable. This is probably why the COGAT is such a great predictor of academic success. Take any topic, like fractions or exponents or roots of a 2nd degree polynomial, or multiplication or anything, and at one point we slowly went through a few problems using this approach and learned months worth of material with a small amount of effort.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">At some point during the actual test, the child will come to the questions that differentiate the 97th percentile from the 99th percentile. These are the questions that differentiate those kids who probably would do well at Stanford with a little effort from those kids who will be sitting in a GAT program next year because of the ridiculously high cutoffs in almost all states. The kid who gets these question correct will either be the child who is already 99% because his parents both have PhD's from those who have learned the skill set and go super slow on these problems:</div><div style="text-align: left;"></div><ul><li>They are not the slightest bit discouraged by not knowing the answer right away or being confused.</li><li>They take a long time to thoroughly investigate the problem</li><li>They have a few techniques to fall back on when it gets really, really hard. </li><li>They are not discouraged when they don't see their expected answer in the pick list. They try again as a matter of course.</li><li>They check their answer, and all the answers, at least twice if not more.</li></ul><div>I think the best way to teach these skills is to approach the training in the way I described above. You should see how the approach is consistent with these skills. It should also be clear that the other approach, I call this the school approach - explanations and lots of routine practice in the hopes of memorizing or mastering a set of question techniques - is not consistent with the skills needed at the top.</div><div><br /></div><div>For parents a week or two from the COGAT who reach out to me the first time for help, and have done zero of anything before that, this approach is the way to go. Of course, if you plan ahead, you'll be able to go much, much farther, but the approach is roughly the same.</div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com1tag:blogger.com,1999:blog-5703568807615263851.post-32897442340329005342017-12-16T09:01:00.002-08:002017-12-18T07:03:40.024-08:00Problem 123Testing season is in full swing in Chicago right now with the majority of test takers in K grade, followed by 1st grade.<br /><br />While sitting in the testing center, you may notice a members of a tiny but super intelligent articulate species talking to their adoptive parents about the composition of the earth's core. Then on the drive home, your child may sit in the back seat telling you in explicit detail about each problem he missed. These are both good reasons to buy a math book that your child won't see for 2 years and make him do it. It made me feel better.<br /><br />In this article, I'm going to demonstrate how to help your child work through material two years in advance. Problem 123 is short for the last problem in EDM Grade 2 book on page 123, and the context is going to be a 5/6 year old in Kindergarten who made it to page 123 despite not completing K math and having skipped 1st grade math. You can apply this context to other grades and other material (like a 2nd grader doing fractions), but if your child has been going to an after school math program for the last 2 years this is not going to produce experience for the child nor the same set of cognitive skills and you'll have to find a different challenge to achieve the same results.<br /><br />I owe a reader a discussion of fractions, and I'll use this article to warm up.<br /><br />Let's begin with my favorite email from parents and my common response. Here is a brief summary of the email: "This isn't working and I don't know what the heck I'm doing. I don't know how to teach math. What should I do?"<br /><br />Here is my response:<br /><ul><li>You are not teaching math. Focus on teaching the core learning skills and the child will teach herself math in the case you are blessed beyond belief with daughters, or himself math if you're like me and stuck with a bunch of boys. </li><li>The 1st few pages in the book took us about 3 weeks. Any page could take a week. Acceleration happens later in the process.</li><li>Our error rate was about 50% on a good day.</li><li>After about 30 minutes on this exact problem, I just gave up and made a note to come back to this topic at some point in the future (which was next week). I'm going to do it fully below because it shows you how to teach math to yourself which will make you a better math coach in the future. </li></ul>At this age, we're going to focus on the most important skill of Being Baffled, which is comprised of numerous subskills. Then I'll talk about the 'Reading the Question' subset which you will focus on through 4th grade. The other core skills like Getting the Problem Wrong (aka Making Mistakes) and checking your work are not discussed. <br /><br /><div style="margin: 5px; vertical-align: top;"><div style="align: left; float: left; width: 50%;"><b>Page 123, Lesson 5-6, #3:</b><br />Connect the points in order from 1 to 3.<br /><br />Find and name 3 triangles<br />__________________________<br />Try to name a fourth triangle<br />________________________<br />Color a four sided figure.<br /><br /></div><div style="float: right; width: 50%;"><a href="https://2.bp.blogspot.com/-fhG43yU5wjc/WjVCv3QMNYI/AAAAAAAAAk4/3xCF4i4noDQZ-VEyKnXqKCcDjhsPX2FVACLcBGAs/s1600/Drawing1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="641" data-original-width="1328" height="154" src="https://2.bp.blogspot.com/-fhG43yU5wjc/WjVCv3QMNYI/AAAAAAAAAk4/3xCF4i4noDQZ-VEyKnXqKCcDjhsPX2FVACLcBGAs/s320/Drawing1.jpg" width="320" /></a></div></div><div style="clear: both;"></div><br /><b>Step 1: Be Baffled</b><br />Say 'This is a hard problem' then leave your child alone for a minimum of 15 minutes to do the problem. I started this approach on page 1. Somewhere between page 1 and page 123, 15 minutes of doodling, yelling, and complaining became 10 minutes of thinking and trying and 5 minutes of doodling, yelling and complaining.<br /><br /><b>Step 2: Backtrack</b><br />The first challenge is that section 5-3 discusses the naming of line segments, like <span style="border-top: 2px solid black;">AB</span>, problems 1 and 2 in this lesson connect shapes with lettered dots, but it's left to the child to make the leap to naming triangles. A Kindergarten kid is not only not going to make the leap, but by this point they never mastered (or even got) the whole line segment naming business.<br /><br />Over the years, I've come to appreciate that 'Being Baffled' is a mandatory problem solving step, because it sets up the rest of the process, especially in BC Calculus. Being baffled relaxes everyone (especially the parent) and opens the brain to thinking. The opposite of 'Being Baffled' is frustration, impatience, and a subpar performance.<br /><br />Fortunately, the example at the top of this page (not shown) has the same triangle without the numbered points, so we need to backtrack a bit. Ask the child to name the line segments in the example triangle. We should get AB, AC and BC. Then ask the child to come up with a way to name the triangle.<br /><br />I'm rarely severe on vocabulary. At some point, I might just say that a triangle is named just like a line segment. A line segment is AB, but a triangle is ABC. What is the difference between BCA and ABC? Does this triangle have any other names? If the child is 8 years old and a boy, I would be disappointed if the child didn't say 'Bob'.<br /><br />If this were a problem like 72 - 49 = ?, backtracking might be a 1st grade workbook for a day or two.<br /><br /><b>Step 3: Dig into the question.</b><br />What is a triangle? Ask you kid to define it. It's a shape with 3 sides. How do you make a triangle? You put three sides together. Show your child 3 lines that don't touch and announce you created a triangle. Each side has to touch 2 other sides at its end point. I'm meandering through the question starting with the Stone Age and working my way back to 2017.<br /><br />There is a whole set of skills that formulates the skill of 'Seeing'. Some kids can do it, other kids have a lot of work to do. In this particular problem, there are 4 triangles. Two are obvious, one is not obvious, and one is hidden. This problem will show up on most competitive math tests in one form or another. Seeing is a big part of math and reading and science and innovation and internet startups. It's also one of the main skills of the COGAT.<br /><br />Ask the child to find all of the line segments in this picture. I see A1, 13, 3B for example. Then how many ways can you take 3 line segments that each touch 2 others at the end? We gave up after 3 named triangles.<br /><br /><b>Step 4: Give Up</b><br />You will give up on something. You are not working with a 2nd grade child, but a 5 or 6 year old. At some point, it's time to move on, and you have not achieved mastery over some math topic. Fortunately, EDM has some repetition so you'll see some topics again, just not this one. Fortunately, your child is going to get this material again in school, and they'll look like the smartest person on the planet when they see it again and figure it out quickly.<br /><br />After doing this for 8 or 9 months, children should be completing the work with reasonable accuracy in a reasonable amount of time, but I need to stress this child will never complete the work like an 8 or 9 year old would. My my goal of 'reasonableness' was met, and we stopped at about the 1/2 way point of book 2. That was good for 99% on the MAP for a while.<br /><br />Think carefully about what I did. I got a child to sit and work alone for 10 to 15 minutes on material he wasn't taught and didn't know before I would jump in and start helping. As the months go by, he gets less and less help, just more questions. I taught him (because math is a team sport and I was the missing team member as needed) to be baffled, to spend a lot of time on the question and to backtrack as needed, to make mistakes and be totally OK with that, to try over and over again and to check his work because he got most things wrong on the first try (not demonstrated above).<br /><br />With that skill set, and continued refinements over the next few years, it is reasonable of me to expect that he gets 99% on both sections of the MAP from this point forward, can handle accelerated work in all subjects with little or no help, can teach himself instruments and other things of interest to him, and go to Stanford for graduate school.<br /><br />On the other hand, what if I <u>trained</u> and <u>drilled</u> him on math topics during this period? What would I expect from a child who spent 4 years zipping through math because he was expertly taught and trained on math concepts? This is what school does really poorly and what after school math programs do really well. But it's not the skill set I want. You wouldn't notice a difference between either approach if you just looked at math and you just looked at a 2nd or 3rd grade performance on a math test of some kind. The difference will show up elsewhere and it will show up later.<br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-31454467610756704862017-12-08T16:18:00.001-08:002017-12-08T16:18:37.563-08:00Fractions One<b style="font-weight: normal;"><div dir="ltr" id="docs-internal-guid-e44e0e40-389f-81bc-4e85-d71f912b9bf0" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">There are a lot of good math curriculums that teach the mechanics of fractions. I’ve seen step by step diagrams to add fractions with different denominators and add mixed fractions. With a thorough explanation and lots of practice, a young child can do fractions without any increase in academic skills or knowledge of math whatsoever.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">So we’re not going to learn fractions this way.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The MAP test distinguishes kids who are ahead in math from the rest in the early grades. In later grades, it distinguishes kids who can figure out new math on their own. That’s what we want. </span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The starting point for fractions is for the child to tell me what they know about fractions. Some kids have not learned to articulate math, so we can work on this gap, It is most likely going to take some time for their brain to digest fractions on its own WITH NO HELP so I’m willing to wait. Plus, i need to find out where they are. Plus, they need to figure out what they already know because they are going to have to use it.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Start with ½, ⅓,¼ etc. What are these? Order them biggest to smallest? Can you draw it? If we put 2 in the numerator position, what do we get?</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">If you wanted me to teach fractions to your 7 year old who has never seen fractions before, we wouldn’t do more than 1 or 2 problems a day. Each problem is on par with a really good science experiment that spurs the imagination. Doing a bunch of problems is pointless to the learning process. Once the imagination is engaged, we’re learning, and during the thinking process WITH NO HELP learning skills are being generated that I’ll need in 3 years when I plunk down an SAT book.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">What is the difference between ⅖ and 2 divided by 5. I want to know. Let’s do it. Suppose we divide 2 by 6 and then by 7. What’s going on? I want to know. Tell me, or we can figure it out together.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">By the way, mathematicians never use the “divided by” sign. We always use ⅘ and say ‘4 divided by 5’ when we mean divide by or four fifths when we mean fractions, because these are the same and the divided by sign is lame.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Over the next few days or once a week, we’ll continue forward or repeat this conversation while it sinks in. If this kid is learning fractions now, then we’ll be decomposing 2nd degree polynomials soon and I won’t be in the mood to help. That’s why I won’t assign a fractions worksheet. Instead, I’ll ask them to decompose every number 1 through 100 and circle the prime numbers. When they need this, they won’t know it so I’ll have to tell them, but they are just kids.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">From experience, the most important thing the kid needs to know is the answer to this question: If i add 3 pieces of cloth to 2 T-shirts, how many T-shirts do I have now? (10 minutes later) It’s the same with fractions. Either you make a T-shirt out of the 3 pieces of cloth and add it to the 2 T-shirts to get 3 T-shirts, or you rip each T-Shirt in half and add it to the 3 pieces of cloth to get 7 pieces of cloth. But you can’t add T-shirts and pieces of cloth without doing something.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Then I would take a single question of each type and we’ll do it together and look at it. By ‘together’ I mean I’m not going to help at all. Maybe I’ll give hints. Once they get it, we can do a harder version of that question type later. Or we try a different one. Ore we draw pictures, try an easier version, split it into 2 problems, or sometimes just iterate through all integers with that version of the question, starting with 1/1 and ½, ⅔, etc until patterns emerge. Or turn it into a word problem that is relevant to their world. Or all of the above.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Can you imagine what a little child who wants to be a piano expert does to become better? They practice the same piece over and over and over again. They drill and drill and scales and scales over and over.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Math is not like the piano at all. Math is learning to think, to analyze, to find patterns, to impute and make logical deductions, inferences, leaps. To put 2 unrelated things together. Drilling teaches none of this. Doing a single hard problem for 15 or 30 minutes while the parent is silent or asks questions is the prerequisite of thinking.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">If I were starting from scratch with your child, I’m guessing this might take 1 to 2 months, maybe more to get to the really hard fraction problems. It would require very little effort on either of our parts. Just a lot of staring, questions, and thinking.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">Where did I get the ability to teach fractions? We were doing fractions for the first time and I had 25 minutes of silence to stare at the problem while the work was in progress. I asked ‘what are fractions anyway’ and started to look at them anew. </span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">At some point, you might want to assign a workbook page or the whole thing to get the ball rolling. When and how is your preference. I would never assign a fractions worksheet ever because a 7 or 8 year old doesn’t need fractions, and they will get smart enough by doing fractions to determine that math is useless, boring, and lame. This is my personal opinion. What I do instead is assign material that has lots of problem types, including fractions, and I assign that. It’s more sneaky. I just download tests of all kids and we do the problems that are appropriate. On these tests, either the problem is within reach, we skip it, or I’ll do it because they won’t see it again for a year.</span></div><br /><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline;">The big issue to keep in mind is what your child did in the last few years. By the time we got to fractions, we had already been through this type of experience a few times and had done material that was less math topic and more hard core thinking. If you have less practice with this, then fractions will be your boot camp.</span></div><br /></b><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-3083065750599007432017-12-05T04:15:00.002-08:002017-12-05T04:15:50.839-08:00Advanced Math and Little KidsI have about a dozen questions from readers that have been swirling in my brain, all on the topic of casual work-ahead At Home Schooling in math. I've been trolling parent forums and reading amazon reviews while a new round of 1st through 3rd curriculum shows up from my latest buying spree.<br /><br />Let's take the first question first. <i>How do I teach my child fractions</i>?<br /><br />Here is my step-by-step*:<br /><br /><ol><li>You do a complete inventory of all of your child's skills and your skills as a parent that are required for your child to teach herself fractions.</li><li>You fix the ones you can fix immediately and work on the rest at the appropriate pace and the appropriate material. You can work on fractions if you want while you do this.</li><li>Your child teaches herself fractions. You help by reinforcing the 5 core skills which you can see while your child struggles with the material on her own, with no help learning the actual math.</li></ol><div>#1 is the problem, of course. It's also the problem with parent forums and helpful parent advice. It is also a problem with teachers, even good ones, but not the really great ones who have taught for 20 years. #2 is easy once you get it, and looks impossible before you actually see it work, then it's total magic. #3 is our goal.</div><div><br /></div><div>*I will present a more detailed step-by-step but we've got a lot of ground to cover first.</div><div><br /></div><div>Back to parent forums and book reviews. Parents are blind to the cognitive skill set of their child and where this fits relative to other children, not to mention their own skills as an At Home academic coach. They find something that works and then state with no further thought that it should work for other parents. Maybe, maybe not. If the parent mentions either a) my child reads 6 hours a day or b) my child got 99% on both the COGAT and the MAP or c) my child got 99% on the MAP but didn't do so well on the COGAT then I have a pretty good idea where this child is on the skill spectrum. a, b, and c are three totally different places, but I've spent enough time investigating so many children in these three cases that I can just prescribe the medicine. The rest of the world needs more analysis. </div><div><br /></div><div>Wouldn't it be great if you could follow really 100's of successful parents around for 10 years and take notes and build a program based on what they did to put their kids at the top of the heap? That's exactly what I did, and not just in math.</div><div><br /></div><div>Recently I've been getting questions related to a certain famous math curriculum. I haven't seen this material in 5 years since I reviewed it and then gave the books to a tiny little test case and followed up every week. It wasn't right for my children, but I found a little girl who I thought would benefit for her specific case and she did.</div><div><br /></div><div>The books are arriving and I'm really disappointed. It's not about the core skills at all. It's about explicitly showing the child how to do mathematical operations. It skips learning. Even worse, the questions tend to be the one-shot deal, as in one sentence that is pretty clear that the 2 numbers have to be added. The inevitable result is a child who is told how to do math, never develops the skill set for #3, does pretty well on tests, and then has to be taught fractions.</div><div><br /></div><div>In the last few months, I've gotten to personally know the Amazon drivers in Chicago because they show up at my house so much delivering material. The last time I did this I was so disgusted that I wrote Test Prep Math. Not much has changed. I've also pulled down at least a dozen curriculums (sic) from the web and gotten to know their creators from doing a little research. I've come to the conclusion that the Test Prep Math series is the best material math material anywhere.</div><div><br /></div><div>This is hard to say. Authors have warned me that once you publish, you face a life of insecurity from that point on. They were right. I've freaked out when one mother told me that her child who's at the 99% found the books easy. OK, I can deal with that. The book is designed<i> to get the child to 99%</i>. Just skip ahead until it gets hard. There is a review on Test Prep Math 2 where the reviewer slams me because the book is confusing and the answers are wrong. As explicitly stated in the introduction, it is supposed to be confusing, and even I get the answer wrong when I speed through it and forget that it was designed for multiple readings on purpose, for you to see you skipped something or blindly assumed the wrong thing. Those are core skills #1 (dealing with confusion) and core skills #2 (spend more time with the question - a lot more time - like 3 weeks if that's what it takes for the skills to emerge for the first time). The book was returned and I feel personally responsible that the reviewer's child is going to eventually fall short in school. </div><div><br /></div><div>I've gotten a lot of emails and a few comments from readers who state 1) my child finished TPM Level 2 and is finishing TPM Math Level 3 and 2) what do I do next? When I get this type of email, the questioner probably has no idea that they have a friend for life. I'm planning to put TPM Level 4 on a free website, mostly because it's going to take me a lot of time to piecemeal the material out there and my new friend for life won't have time to wait, and I'm still weeks away from TMP Level 1 and it's taking up time.</div><div><br /></div><div>By the way, in my ongoing effort to make kids so ridiculously smart that they blow away the COGAT, which was my original goal before I decided a math chair at MIT was also a good idea, I've finally perfected my ability to deliver figure problems to 6 year olds that are 3 times harder than anything they'll ever see again. It's much easier with older children to take away the net. Never underestimate the importance of the COGAT. It measures skills that kids need to teach themselves fractions. It doesn't care if they can actually do fractions or any other type of math. The COGAT wants kids who already know how to learn and can go from Kindergarten to fractions in one year, which is what happens when you enter certain gifted and talented programs.</div><div><br /></div><div>Test Prep Math 4 launches the math career. It's all about math. The skills continue to refine and develop, and the fifth core skill (problem solving skills) becomes wider and deeper on it's march to passing the AP exam in BC Calculus. When you child chooses a joint major in English and Music instead of a STEM career, those problem solving skills explode yet again and you discover why so many CEO's and law firm partners have English or music backgrounds, but you wanted a doctor so we blew it.</div><div><br /></div><div>Here are the Test Prep Math Level 4 milestones. By 6th grade, your child will have finished all of the practice math tests in at least one SAT book. You will have administered at least a rigorous Algebra 1 final where they will encounter some pre-algebra and many algebra topics for the first time. They will have been introduced to important concepts in high school geometry, Algebra 2, trigonometry and calculus and you're holding off on the ones that require maturity to grasp. If you've ever seen TPM, you won't be surprised to find out that TPM 4 includes the reading comp portion of the SAT as well, but you have to go a bit slower because of all that unfamiliar vocabulary. If you were fortunate enough to do Pre-K Phonics Conceptual Vocabulary and Thinking, and followed the directions with regard to the Word Board, the SAT vocabulary goes pretty quickly. Some day, when my youngest completes his 7th and 8th grade high school enrollment nightmare, I'm going to spell out in detail why we're doing this. Until then, just go with the flow.</div><div><br /></div><div>We're not even going to look at the SAT until the summer after 4th grade and really get into it a year later. Before then, we've got a lot of ground to cover, and it includes fractions.</div><div><br /></div><div>I'm going to need 2 articles to do it, and they'll probably be long. The first article is going to lay down the ground rules that apply to math starting in Kindergarten and that you will use thereafter if you want your child to learn. </div><div><br /></div><div><br /></div><div><br /></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com2tag:blogger.com,1999:blog-5703568807615263851.post-42873330557808675252017-12-01T08:23:00.000-08:002017-12-01T08:23:48.789-08:00Pick the Right At-Home Math CurriculumI spent the last few days thinking about the comment I received from Anonymous asking about current+2 curriculum for a 2nd grade child. The last two articles on this topic were experimental and not helpful, and I'll delete them some day.<br /><br />Taking a step back, here is a better version of the question: "What is the best way for a 2nd grader to work through 4th grade math so that she (or he) obtains all of the grit related benefits from doing so, learns more math, subject to the following constraints":<br /><ol><li>You've only got so much time to help and you're not a teacher</li><li>You need a high MAP score and teacher recommendation for the GAT program</li><li>You may or may not have to pass the COGAT this year</li><li>This child is only 7. And not necessarily good in math. </li><li>You can't afford a tutor or an after school math program. Plus you hate driving.</li><li>If your child does get into a GAT program, you want them to be the best.</li><li>If you run into problems, you're going to send 19 emails a day to getyourchildintogat@gmail.com so this advice better be good.</li><li>Math curriculum from US publishers stinks</li></ol><div>I updated the article <a href="http://www.getyourchildintogat.com/p/chapter-6-math.html" target="_blank">How To Create A Math Genius</a> to be more clear about this situation. You might want to refer to the content starting at first grade. In this article, I'm going explain why my curriculum choices are counter intuitive and logically valid. </div><div><br /></div><div>My top 2 choices for curriculum are Go Math from Houghton Mifflin and Eureka Math. A few years ago, a teacher suggested I review Eureka Math for 4th grade and I had a pdf of the whole book but I can't find it. It's totally spoon feeding math, not only in the book but in the problems. Go Math has a more intuitive approach, which means more concepts and less actual math. For a kid who's already been through the advanced math exercise, he can do the Go Math homework for current+1 on the bus while playing Minecraft and discussing Star Wars memes. And get them all correct.<br /><br />If I was more worried about the MAP, I'd go with Eureka. If I was more worried about the COGAT I'd go with Go Math. I would probably pick Go Math anyway.<br /><br />The target of Eureka and Go Math, and the rest of US curriculum, are the 50% of below average kids in the US with parents who know nothing about math and don't care. This is perfect for a 2nd grader attempting 4th grade work, because the 2nd grade is starting way, way below average and her parent has zero experience teaching 4th grade math to a 2nd grader. Really great 4th math curriculum is designed for bright, talented, engaged 4th graders with a parent who knows something about 4th graders, or at least has had 9 months of experience with a 3rd grader. <br /><br />If your 2nd grade child works through 4th grade math, and you follow the rules, #1, #2, #4 and #5 are taken care of. #8 makes this possible. For #3, you need more material beyond advanced math. The COGAT is looking for kids with generalized problem solving skills who will be <i>strong academically in the future</i>, not kids who are ahead now. But if you want your advanced math to impact the COGAT score, start with 100 (average) and add 1 point for every leading question you ask, add 5 points every time your child makes a mistake and you just shrug your shoulders because you don't care, and subtract 1,000 points every time you tell your child how to do something. This will be an indication of their final score on the COGAT.<br /><br />#6 will happen on it's own. Most GAT programs only go 1 year ahead on math so your child would see the exact same math for a second time.<br /><br />I'll take care of #7 right now. "My son/daughter has been working on one of these books for 3 weeks and gets them all wrong and has only done 2 pages." This is exactly what I expect. This is the path to gifted. The secret is just to keep going even though it doesn't make sense. This is so counter intuitive that only about 10% of parents are willing to try it, and only 1% of parents are willing to follow the guidelines of an encouraging learning environment at home under these conditions. That's why only 1% of children make it into the top 1%.</div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com2tag:blogger.com,1999:blog-5703568807615263851.post-55102910129919907722017-11-30T04:36:00.000-08:002017-11-30T04:36:08.153-08:00Teaching Algebra To A Fourth GraderI'm really excited about yesterday's algebra post and the worked the followed last night proving I was totally wrong. I'd delete the post entirely if it wasn't chock full of good advice that sets the stage for today's topic, which is teaching Algebra to a 4th grader. Which is going super well, thank you, and after I complain that this is insane and ruining our children, I'll show you how.<br /><br />There is a branch of math curriculum that is not very mathy. It's fuzzy and intuitive and wholelistic and verbal and it doesn't really care if the kid currently or will ever know anything about math. I love this type of math. It's used in our school, chosen by a group of teachers who have about 9,282 years of teaching experience between the 4 of them. One is named Yoda, just so you know.<br /><br />What I've found is math that works for average or below average children in the US will work for your slightly above average child much earlier. I think the best math curriculum of all time, even surpassing Sylvan's Kindergarten math book is the middle school math Jo Boaler created. It involves no math at all, and then she just walks kids into 'WHAM' real math. Her problems show up in CMP math, which is what our school uses.<br /><br />On the other end of the spectrum is Singapore math. I've decided that Singapore math is now Public Enemy #1, replacing Kumon as the worst thing you can do to your child. One of my early famous articles describes Anti-Kumon, a program that I felt so strongly about that it ended up being the Test Prep Math series. I also hate Mathasium and Level One. I'm going to hunt down Singapore math grades 5 and 6 ASAP and start using them. I've already recommended Kumon pre-algebra grade 6, a good book once you rip out the part at the beginning that spoon feeds how to do each problem and the part at the end called Solutions.<br /><br />What Singapore found out is that you can train your child on advanced math and they'll look pretty capable as a result. The top high schools in the country are full of overstressed, overanxious kids spending long hours doing homework and beginning the teacher to just please please tell them exactly what to do to get an A because they've never been given the opportunity to learn and don't know how. The Singapore material itself isn't such a bad idea (which is why they're about to get an order for books from me), it's what parents do with the material that is detrimental to their child's future.<br /><br />Recently I conducted a search for problem solving books. I've developed my methodology based on Poyla's 1945 book and was wondering if anyone else came up anything else that was helpful. (The short answer was The Art of Problem solving that came out 10 years later and is helpful for wealthy people who live in suburban Connecticut.) For the 8 weeks prior, all of my Google searches were 'Algebra II problems', for the older brother, and Google's search engine is nothing if not intuitive, so it gave me an extensive list of books and websites devoted to detailing the step-by-step solution to every algebra problem ever devised. I was horrified. This is where math training leads. A drug addiction to solution guides.<br /><br />Anyway, I'm going to apply hard core Poyla to 2 problems. The first problem is below, and the second problem is that you have to get your child to learn it on their own, no cheating. In yesterday's post, there were two problems, and children naturally gravitate to the the second one. I should have recognized this one as a necessary step for the first one but I blew it. <br /><br />Here we go with the harder question.<br /><br /><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 12px; text-align: justify;">There were three times as many jelly beans in Jar A as in Jar B. After 2685 jelly beans in Jar A were sold, Jar B had twice as many jelly beans as Jar A. How many more jelly beans were there in Jar A than in Jar B at first? </span><br /><br />We followed exactly the problem steps from yesterday's article, including a diagram that was totally unhelpful, but there was no way to solve this equation without extensive backtracking and #7 the missing element. I hate the missing element technique. It is absolutely fundamental to geometry proofs, but it takes a lot of work for a child to derive the missing element in 1 hour that took brilliant mathematician's 250 years to derive. The secret is #8 use everything you ever learned that points to the missing element, and if you haven't actually learned it yet, you need backtracking.<br /><br /><b>Step 1: Backtracking</b><br />For backtracking, I used IXL and Khan Academy algebra problems with parenthesis. I did this a few months ago. These are real powder puff exercises, like 4(x - 10) = 23. I look for parenthesis because kids who grow up with wholelistic language-based thinking math take many months to remember how parenthesis work no matter how many ways you spoon-feed it to them. I finally created Kumon style parenthesis worksheets and told them just to memorize it.<br /><br />I'll tolerate estimate-iterate for a while (is x 3? How about 30? What about 12.2?) because it's good arithmetic practice and builds the type of number sense needed for statistics, but eventually I'll resort to something like 1/x(23 - x) = x<sup>1/2 </sup>so they quit guessing and ask for help.<br /><br />The missing element is the equation x = 3(13 - 2).<br /><br />What makes x = 3(13 - 2) a better problem than 1/x(23 - x) = x<sup>1/2</sup> or 4(x - 10) = 23? The answer might take multiple 30 minutes daily discussions. The answer is that in the easy equation, x is on one side and all of the numbers are on the right. In fact, the easiest equation of all is x = 33. x on the left, a number on the right. The goal of algebra is to get x on one side and the numbers on the other side, in the cheatiest least effort way possible. The goal of prealgebra is to handles all types of numerical operations including exponents. Algebra adds 'x' and mixes things up.<br /><br />From that point forward, we had an 8 week battle to see whether or not the stubborn kid could solve the problem without resorting to algebra, no matter how long it took, or whether he had to learn the fundamental principle of algebra: you can add/subtract/multiple/divide/power up/power down each side of the equation by the same factor (whether it's 5 or (x - 2)) and the equation will take a step in the direction of 'easier' if you didn't screw up the parenthesis again.<br /><br />We spent so much time analyzing what was wrong with equations (the x is not on the opposite side as numbers) that it qualified as a principle on which to build.<br /><br /><b>Step 2: Derive the Equations</b><br />In the problem above, this wasn't an issue because our math program is founded on convoluted complex word problems with double reverse logic. We lost a few minutes because one of the unfortunate side effects of this approach is a kid smart enough to point out how stupid the problem is. "Who buy's 2,685 jelly beans? Like they're going to sit there and count them. This is a dumb problem."<br /><br />For some kids, backtracking might include writing equations from word problems.<br /><br />So we got 3B = A and A - 2685 = 1/2B. <br /><br />The second equation was rewritten as B = 2A -5310. The reason is that at one point in our backtracking, I told him if he see's x in an equation (aka a variable), then there is a 100% probability he'll have to work the equation with transformations to derive the answer, so stop wasting time trying to solve it in your head. <br /><br />The three important principles for this step that we haven't come to terms with fully are:<br />a) The best way to determine the correct equation is to write down the crap you know is wrong and fix it<br />b) don't write the two equations buried in a bunch of pictures<br />c) if the older brother wants to interrupt math with the new Avengers trailer, you're going to lose 20 minutes<br /><br />No matter how many times I encourage mistakes and do overs, each new step up the math ladder is greeted with this expectation of getting things right the first time. Mistakes are the fastest way to the goal. Perfection is a hard stop on the road to learning. We would save a lot of time if he would just write 2,685 - B = 2A, realize it's wrong, and fix it.<br /><br /><b>Step 3: Wait for the Leap</b><br />At some point during this problem I started cursing Anonymous for putting me in this position. This would be a great problem for a long weekend. To solve it, my kid has to figure out how to solve simultaneous equations, on his own, and all we've got are our problem solving techniques.<br /><br />I am 100% sure that 100% of Singapore kids are told what simultaneous equations are and shown how to solve them, then they can practice this technique, get high test scores and great grades, without ever have experienced true learning. It's like taking a Grade A steak and grinding it into dog food. For my buddies from Southern India, I don't have a good analogy. I once made Indian food and proudly brought it to work. My coworkers told me it was 'bachelor food'. All those great spices mixed into a tasteless mess. That's what happens to Singapore math when it's trained and not learned.<br /><br />My son pointed out that he can't solve the equation, and then complained and glared at me.<br /><br />Why? "Because it's got a B and an A. It could be anything."<br /><br />I asked him to specifically point to what is wrong with the equation. After about 5 minutes, he pointed to "2A" in the equation B = 2A -5310. So I asked him to fix it.<br /><br />We had already established algebra is about fixing equations. He knew the way to do this was transformations. In the first 7 or 8 minutes, he just stared trying to determine how to transform the equation. No luck. Then he got really intense because somewhere in the pictures of his bear and a girl named 'Amy', he could sense 3B = A plays a role.<br /><br />In Poyla, one of the foundations of understanding the question is 'use ALL available elements of the problem'. This becomes really important in geometry. We haven't spent much time on it. I asked him if anything else could help. Since 3B = A was buried in doodles, I asked him to show me all of the pieces of this problem. I'm not sure this was necessary, but it was getting late and he had science homework and my spouse was yelling at me. (Solution strategy #9, when your spouse is yelling about how late it is, start asking questions that direct your child.)<br /><br />We had 7 or 8 minutes of silence and I could see he was becoming really excited in an intense concentrating way. He said "2A is 6B" and wrote 5B = 5310. When you're excited about learning, you can do 3 transformation in one step and I'm not going to complain. This is how brainiacs get to the point where they solve things mentally to the consternation of their teachers.<br /><br />What did I do? I did three things.<br />1. I didn't look up the solution and explain it to him.<br />2. I didn't help other than ask questions and suggest one of the 8 problem solving techniques. In this case, I suggested all 8 and we used all 8. I will continue to do so until I'm banned from helping by my son, which is scheduled for middle school, at which point I will solidify my role as the dumbest, lamest parent on the planet and my child will reach self sufficiency.<br />3. I waited, and waited, and was prepared to wait for the next 3 weeks if that's what it takes.<br /><br />I was rewarded in 3 big ways.<br />1. I concluded the whole session by mentioning that 2 equations with 2 variables is called 'simultaneous' equations. I pointed how that he taught himself how to solve simultaneous equations and this is a big deal. He already knew at this point that he taught himself and it was a big deal to him.<br />2. 3 months ago, it was horribly painful for him to transform x - 3 = 6 by adding 3 to both sides. Now he was doing 4 steps in once (multiplying 3B = A times 2, substituting 6B for 2 A, subtracting 6B from each side of the equation and multiplying each side by -1). I have repeatedly told parents to look for this effect, starting with phonics and first math when you get 3 weeks of zero and want to quit. It's nice to see anyway.<br />3. As a parent, I took a big leap myself in problem solving skills under the problem of how NOT to teach my child how to solve simultaneous equations even though Anonymous put me into this awful spot.<br /><br />We are not going to have to practice simultaneous questions to perfect it. It's been earned, not trained. I don't like perfection, it removes the problem solving aspect that will be gained the next time the topic comes up, which will probably be this weekend with 8th grade simultaneous linear functions because I'm totally psyched.<br /><br />In the last 6 weeks, I've come to the realization that the approach behind Test Prep Math is not at all compatible with Singapore math before grade 4. Test Prep Math tries to avoid math at all costs while building up the skills underlying math, logic, and reading convoluted problems to earn the first 3 foundation problem solving skills that I covered in yesterday's article. These are 2 wholly different world views. I'm betting the farm that by middle school and then again in high school I will inevitably be proven correct. I'm standing on a mountain of research, logic, and common sense from qualified teachers that I stole (problems solving technique #10). By why wait until then? 4th grade is a great time to crush a few years of Singapore math.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-21534618189805710602017-11-29T13:56:00.002-08:002017-11-29T13:56:20.465-08:00Teaching 4th Grade Math to a 2nd Grade ChildI received this great question from Anonymous that deserves at least one post, if not a book. Your child and skill level may vary, but from my stand point, it's the same question. <br /><br /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">I'm struggling with 4th grade math materials. What's the best way to teach my second grader how to solve these questions? </span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;" /><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">There were three times as many jelly beans in Jar A as in Jar B. After 2685 jelly beans in Jar A were sold, Jar B had twice as many jelly beans as Jar A. How many more jelly beans were there in Jar A than in Jar B at first? </span><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;" /><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;" /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">Aileen and Barry had an equal number of postcards. After Barry had given Aileen 20 postcards, Aileen had five times as many postcards as Barry. Find their total number of postcards.</span><br /><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;"><br /></span><div>I'm going to provide a step-by-step guide, and this is going to be a long article. Brace yourself.</div><div><br /></div>There are many great reasons to teach a 2nd grade child 4th grade math. Here they are ordered from most important to least important.<div><ol><li>You didn't think to teach your child 2nd grade math when they were in Kindergarten. Frankly, it won't matter by middle school when you begin, but the earlier you start, the more time you have to block out all of the memories of frustration until you just remember what a great idea it was. An earlier start imparts more technical skills and a later start imparts more grit, but grades are high in science and language arts, which is what you really want.</li><li>You want to imbue your child with unmatched grit and generalized problem solving skills so that the rest of their academic career will be easy no matter what the challenge.</li><li>You want your teacher to notice that your child is bored in math and recommends your child for an advanced or accelerated program.</li><li>You are blatantly cheating your way to a high score on the MAP test.</li></ol><div>This problem is from Singapore math. Be very careful with Singapore math because like Kumon, it shows the kids how to do the math and undermines a host of more important skills like how to think. There are problem solving guides that come with these types of math courses and they short circuit learning. You can destroy your child's thinking ability in one shot and it's hard to undo the damage.</div></div><div><br /></div><div>One more thing to keep in mind with Singapore math. 4th grade math compares with 5th grade or 6th grade math the way we normally refer to math curriculum in the US. I've seen 2nd graders do 2nd and 3rd grade level Singapore and come out ahead. You might want to think about switching to 3rd grade Singapore math or 4th grade lame standard US math.</div><div><br /></div><div><b>Rule #1: Don't, under any circumstances, teach math. </b></div><div>You don't want your child to learn math. If you focus on the more important skills, they will learn really advanced math on their own. But if you try to teach them math concepts to solve these two problems, they are not going to learn math or anything else. It's not about math. The child is in charge of math, and you are in charge in an environment and experience where learning will explode.</div><div><br /></div><div><b>Rule #2: It's going to go painfully slow at the beginning.</b></div><div>It's really hard to watch a child tackle a problem that requires basic problem solving skills while they pick up basic problem solving skills. It's painful. If you want your child to learn how to learn, you can help by being confused, by being patient, by asking questions, but you can't just tell them how to do it.</div><div><br /></div><div>It does not surprise me when a child takes 2 or 3 days to get past the first problem. It does not surprise me that they forget something we did or said 10 minutes ago. But I'm always totally shocked that in a few months they're zooming through 4th grade material like a slightly below average 4th grader, and I'm pleasantly surprised that test scores are now 100% across the board.</div><div><br /></div><div>I'm always happy to receive an email from a parent that starts out with "I was doubtful at first because we got no where in the first 3 weeks..." because I know exactly where it's going. If your child does ballet every day, they will probably become adept at ballet. In the same way, success is inevitable on 4th grade math. Give it time.</div><div><br /></div><div>I like to say "of course your child can't do 4th grade math, because she is only a 2nd grader". But she will. These problems, however, are challenging for a 6th grader. At Math House, we've worked through much more inappropriate problems, so I say go for it.</div><div><br /></div><div><b>Rule #3: Let's teach something besides math.</b></div><div>Language is probably the most important. In the 2 problems above, there are at least a dozen words that your child could read and not understand, at least not in the context of the problem. I'm going to provide some solution strategies that will help you in the first few weeks, but you need to get to a discussion of the problem as the primary way to work through it, not just because you want a high reading comp score as a bonus, but because <u>understanding</u> of math and <u>language</u> are linked. I'm not sure math itself is linked to language, probably, but understanding math definitely is.</div><div><br /></div><div>In the first few passes of each problem, invite your child to explain it to you, word-by-word and sentence-by-sentence. For many parent-child teams, this will be total culture shock. It takes changing gears and practice. If your child can't articulate the question on the 7th try, word by word, you may ask for a picture or try again the next day.</div><div><br /></div><div>Being confused, having to read a question 5 times, and getting it wrong are 3 important skills that have to be practiced and developed. If your child doesn't become an expert at these 3 skills, and you as the primary academic coach aren't totally on board, more advanced work is going to be a real struggle. </div><div><br /></div><div><b>Rule #4: You need solution strategies to survive.</b></div><div>You, the parent need the solution strategies. My kids know all of them and are ready to tackle graduate study of Lie Groups, but if they use them, they use them behind my back. I've never met a problem anywhere that can't be solved by these, so when they are stuck, I just shout out random solution strategies and we're back in business.</div><div><br /></div><div>Now about that solution.</div><div><br /></div><div>The challenge with the 2 problems above for a 2nd grade child is "2685" and "five times". I don't care if my 2nd grader picks up an understanding of 4 digit numbers and multiplication/division. That's his problem. I want him to understand the essence of the logic and problem definition.</div><div><br /></div><div>If the child understands the problem, in second grade, we're way ahead of the game. Moving forward with strategy and solution will follow in time. I prefer the child to get there when they get there, on their own.</div><div><br /></div><div>By the way, you can just google these problems, tell your child the solution framework, and set your child up for failure down the road. It's your choice. </div><div><br /></div><div>Here is the parent tool set:</div><div><ol><li>Draw a picture. This doesn't work really well with 2,685. Plus, this strategy is appropriate to geometry and should only be used as a fallback when your child is really frustrated. Drawing is relaxing. In this case, I would ask them to draw a diagram to show me the before and after (with colored bars instead of cards) just so I could see that they understand the problem. Given the difficulty level of these problems, a drawing is inevitable, or acting them out with a stack of pennies.</li><li>I tried algebra. Total failure in 2nd grade. The 4th grader is now starting to get it because I told him it's total cheating. Yahoo answers recommend algebra for 4th graders, but if you are successful, by the time your child gets to 4th grade they will just look at the question, stare at it silently, and announce the right answer. They will be using elements from the rest of the list.</li></ol><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">There were three times as many jelly beans in Jar A as in Jar B. After 2685 jelly beans in Jar A were sold, Jar B had twice as many jelly beans as Jar A. How many more jelly beans were there in Jar A than in Jar B at first?</span></div></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;"><br /></span></div>This problem needs #3: Make a simple problem. In competitive math and math after calculus (like infinite series), a simple problem is followed by incrementally harder problems until we've developed a generalized algorithm. In this case, we just want to understand the problem.<div><br /></div><div style="text-align: start;"><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">There were three times as many jelly beans in Jar A as in Jar B. After </span><span style="background-color: white; text-align: justify;"><span style="color: red;">25</span></span><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;"> jelly beans in Jar A were sold, Jar B had twice as many jelly beans as Jar A. How many more jelly beans were there in Jar A than in Jar B at first?</span></div><div><br /></div><div>Now we've got a problem that a 2nd grader can work through, although it's going to take a few days at 30 minutes of concentration time per day. I would recommend getting a bag of jelly beans after the first day. Hopefully, you have lots of pennies, but now we've got a problem that deserves a picture. Regardless, going back to 2,685 is going to add nothing to the problem for 2nd grade.</div><div><br /></div><div>How did I pick 25? I estimated and iterated (solution technique #4 which kids get really good at for problems like this after a few months of work).</div><div><br /></div><div>Lay out the 25 sold jelly beans, and ask your child what we don't know. (Many readings of the question later and some discussion) and we don't know how many beans are in Jar B and how many beans in Jar A were not sold. You can do this on a 3 part diagram and place the sold beans in part 2 of Jar A.</div><div><br /></div><div>Then invite your child to start putting down beans in the 2 missing places (#4 estimate) until we've got the beans left in Jar A to equal those in Jar B. Finally, have your child read the question out loud and explain the answer to you. Here's a tip. Start with 1 bean in A for the part left after the sale (solution strategy #5 - start with 1) and ask how many need to go in B to establish twice. Ask whether or not 1 in A and 2 in B satisfy the initial condition. Your child is going to go "What does initial condition mean" so you have to read the problem again and write down the 2 conditions the beans have to satisfy. As your child adds beans so that the part in A that is not sold is 1/2 of the part in B, see whether or not you got the solution.</div><div><br /></div><div>In this way, a 2nd grader will build number sense, learn multiplication/division from the ground up, and have to concentrate really hard to get through it. All great skills. If you throw in discussion skills, your child is going to make a lot of progress. It is unlikely that your child will get any where near competent on 4th grade Singapore math. This has never been part of teaching current+2, but eventually it will happen. The first year is mainly about grit.</div><div><br /></div><div>On to the next question. Solve these in order:</div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">Aileen and Barry had an equal number of postcards. After Barry had given Aileen 1 postcard, Aileen had two times as many postcards as Barry. Find their total number of postcards.</span></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">Aileen and Barry had an equal number of postcards. After Barry had given Aileen 2 postcards, Aileen had three times as many postcards as Barry. Find their total number of postcards.</span></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">Aileen and Barry had an equal number of postcards. After Barry had given Aileen 4 postcards, Aileen had four times as many postcards as Barry. Find their total number of postcards.</span></div><div><span style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 12px; text-align: justify;">Aileen and Barry had an equal number of postcards. After Barry had given Aileen 20 postcards, Aileen had five times as many postcards as Barry. Find their total number of postcards.</span></div><div><br /></div><div>In addition to problem decomposition (inherent in these problems), estimating+iterating, and diagramming, I recommend solving these problems in reverse. #5 Start with the end state and see if you can work your way backwards to the initial condition. It's good practice on an important solution strategy.</div><div><br /></div><div>Those 4 versions of the problem are not just a variant of start easy and work your way up, but have an element of what I call 'Backtracking'. When we do 'work ahead' these days, we'll come across something like arithmetic in the complex plane and have to take off time from the problem to practice adding etc complex numbers. It can happen on any problem. In your case, it could be arithmetic with multiple digits or decimals. Be prepared.</div><div><br /></div><div>On that note:</div><div><br /></div><div><b>Rule #5: Get a Fallback Book for Bad Days</b></div><div>I've used boring current+1 workbooks which just have pages of fill in the blank when we're having a bad day because at least I want daily math to be an established pattern during the current+2 year. In your case, I highly recommend Singapore Math Grade 3, or grade 3 if some publisher stole this question, because you may find that the grade 3 book is already 2 years advanced over 2nd grade and end up switching to it. Then get a boring 3rd grade fill in the blank book for bad days.</div><div><br /></div><div>Plus, I can't help every day, and it's nice to have a worksheet that I don't have to grade.</div><div><div><br /></div></div><div>Plus, we may need it to backtrack on missing math topics and a 3rd grade book would do it.</div><div><br /></div><div><b>Rule #6: You'll Never Succeed</b></div><div>You'll never succeed in a 2nd grader doing 4th grade math like a top notch 4th grader. You don't want to, so don't set out with this goal in mind. You want your 2nd grader to be an amazing kid in all subjects, prepared to take on the best of the best. But a great 4th grade mathematician will crush him. If you want a child to work quickly and accurately 2 years ahead at the end of 6 months (which may happen a few years in the future on its own), you'd have to spoon feed, memorize, and train, and you'd end up with a dummy who hates math.</div><div><br /></div><div>Instead, after you get to about the 75% mark of the book (or the 3rd grade book in this super hard series once you come to your senses), when your child is only misses half of the problems and takes forever, look for amazing things in all subjects. Take a year off of math and do other things if you can. Then be prepared to spend the rest of grade school feeding your child advanced math so they aren't bored.</div><div><br /></div><div>The original experiment for current+2 never got beyond adequate, although he works nicely on his own. Sometimes he does really well with current+3 or current +5, and sometimes it's 100% wrong. Recently, I created a new website for our Boy Scout troop. He sat at the computer next to me because he wanted his own website. [Insert eye rolling here, because that's what I was doing.] I sat there stunned when he typed html from scratch. Who types html from scratch? He certainly didn't learn this in school. Then started adding detailed styling and animation like he has a programming gene. The level of learning skills when he's motivated is at about current+7. That's what I'm talking about. I didn't give him a fish when he was hungry. I didn't give him a fishing pole or a net. Apparently by focusing on problem solving skills and not helping or caring about the answer to a math problem, I gave him a whole fleet of fishing trawlers. That's what I'm talking about.</div><div><br /></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com1tag:blogger.com,1999:blog-5703568807615263851.post-14040730952255829212017-11-27T08:16:00.000-08:002017-11-27T08:16:37.895-08:00Add 20% To Your Child's Score<div><a href="https://www.minneapolisfed.org/~/media/files/publications/studies/earlychild/lessonslearned.pdf?la=en" target="_blank">Here is a thorough</a> paper summarizing early childhood studies. It's slightly dry if you're not in to this sort of thing, but it's very inspiring how much success has followed investment in at risk children living in poverty.</div><div><br /></div><div>The general conclusion is that taking kids who live in a home devoid of eduction and putting them in a top notch academic program is going to have a big impact. Early studies found that when you send a kid back into the original environment, the scores and grades plummet back to where they came from. It's nice to see later studies address this issue.</div><div><br /></div><div>These authors ask an open question that I have already answered. It's a really big question and has a big answer.</div><div style="margin-left: 20px; text-align: left;"><i>...many early child interventions are conducted with at-risk children living in poverty. There are many reasons to suspect that the same results may not occur if the same intervention were conducted with affluent children. </i></div><div><br /></div><div>"Affluent" in this case means a home with education and stability. I would agree a child from an "affluent" home may not see much benefit from a program designed for an inner city child with a single parent who didn't finish high school, even though some of the at risk kids in these programs saw IQ leaps from IQ = 92 to IQ = 130. That is one friggin' big leap.<br /><br />Since I don't have any at risk kids in my home, I asked a different question <i>"What type of radical dramatic change would I need to do around here to go from 110 to 125, or 125 to 135, or to 160 just for the day of the big test?"</i></div><div><br /></div>Step 1: I'm going to give myself 18 months. It turned out that it took 14 months just for me to get my act together as a parent, followed by 2 months for my child to get past radical core skill therapy (in one case barely in time for the test) and then 2 months to ramp up to a new level. You can get your act together on day 1, and I'd be happy to provide a list of mistakes not to make, but if you've been reading my blog I think you're past that.<br /><br />Step 2: I want my kids to experience the same shock that these at risk kids experienced walking out of poverty into an advanced academic program run by a bunch of PhD's and taught by their graduate students. <br /><br />Step 3: We're not going back. I am on constant watch against video games, surfing, online chatting, and fun of any kind as my kids try their best to have a normal life. It turns out that we only need about 20 or 30 minutes a day of heads down concentration on something inappropriately hard, but I've made those 20 to 30 minutes a prerequisite of fun.<br /><br />Step 2 is formalized into Test Prep Math. I want a single shocking 25 minute problem a day at first. (Yes, I ramp up slowly because some kids cry and more adept kids can just zoom ahead feeling confident before the 'wham'.) I want mistakes and confusion. This is the birth place of problem solving skills. If you present a child with a doable problem, there is no need for problem solving skills. How about just easing your child along with some step-by-step and scaffolding? You're not going to get a leap of 20+ points like these studies have found taking baby steps.<br /><br />But the work is not done. There are two problems I'm dealing with in my own research. <br /><br />On one end, I just got 1 started on Amazon. The reviewer complained "the book has so many errors". Those "errors" are alternate solutions. I stole this directly from the COGAT and love it. You do a problem, get it wrong, don't understand the solution, and then dig in for 20 minutes to figure out that you assumed adding but the only available solution uses multiplication. If you don't like confusion, don't by the book, because this is the most important skill and the base of the whole GAT skill pyramid. I'm always worried about printing issues, so I'm getting a new copy just to check the solutions for the 10th time. My other copies keep getting 'borrowed' by neighbors.<br /><br />On the other end of the spectrum are kids who have really great math training and skip right past the confusion and problem solving steps because they already know how to do the problems. The COGAT is a big stumbling block because it demands problem solving ingenuity. A child never learns to solve problems if they are formally taught math, and if your child goes to a great math program like Mathasium, Level One, or Singapore, they have completely different academic world view than the COGAT. It's not a bad thing, and could be a good thing, but it's the opposite of what I want for my children. I'm laying awake at night wondering how to fix these kids. It's one thing to lead a horse to water and they refuse to drink. It's another thing if the horse is drinking gallons of water and is still thirsty. <br /><br />I'm thinking of just adding more bonus question to Level 2. I am the master of giving a child a question that he can't answer without 20 minutes of logic and solution strategies, but it would just make people like the 1 star guy more baffled. I could spoon feed everything in the solution, but this will just help others avoid the learning process. I hate solutions. Too many parents think that the whole purpose of test prep and math is to have your child know something. It's not. Think more radically, like 20 points radically, whether this is from 79 to 99 or from 99.1 to 99.7. Step 0 is big goals.<br /><br /><br /><br /><br /><br /><div><br /></div><div><br /></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com2tag:blogger.com,1999:blog-5703568807615263851.post-30097647317744366862017-11-25T11:00:00.000-08:002017-11-25T11:00:03.260-08:00Math Over 20 Minutes a DayI'm back in the daily math business thanks to the break. It beats listening to 2 boys make up video games and verbally describe the action because they are not allowed to play real video games unless they do some really serious math, read, practice their instruments (together without fighting) and clean the kitchen and vacuum the place.<br /><br />Each child began their official math career with 6 months of math at a level of current plus 2. (This was Every Day Math, hard but not too hard.) It's a right of passage and a way to impart senior executive functioning skills, problem solving skills, core learning skills, and grit. The exercise below is exactly the exact identical same situation, just with different math. Since then, I haven't worried about an organized program.<br /><br />When the video game talk became pushing and shoving, I upped the ante. The fourth grader would get a 6th grade math test from Virginia and the 7th grader got a rigorous high school Algebra II final.<br /><br />For math at an inappropriate level, we follow these rules. First, the kids do it. Since they are missing vocabulary and concepts, because I haven't done current+2 in a long time, we do it again together the second time. (We've been skimming current+4 and current+6).<br /><br />I'm going to describe how we do some of these problems so that you'll see that it really isn't about math at all. It's about a high degree of analysis and problem solving because a) the MAP is a big deal this year for us and b) multi-digit multiplication is 100% useless and distracting from important skills.<br /><br />Here are the rules for doing math at home:<br /><ol><li>Let the child do the work on their own first with no help.</li><li>When you go through it, pause to take the material on it's own terms because the child hasn't seen it yet and he started with a final and not the actual text book.</li><li>Figure out a way to cheat.</li></ol><div>#3 is the key to everything including academic and life success. It's why I expect my kids to open the book the first time the night before the Chemical Bio Organic Genetic Engineering Chemistry final and ace it the next morning.</div><div><br /></div><div>Here's how it works in action. As you can see from the picture, we got off to a slow start on the very first question.</div><div><br /></div><div style="text-align: center;"><a href="http://4.bp.blogspot.com/-cgpe_qNv49U/WhcJSlKI0fI/AAAAAAAAAjo/xHQNeyi0NDAoNyHO90imN6Ipp25d4ja0QCK4BGAYYCw/s1600/WIN_20171123_11_42_44_Pro.jpg" imageanchor="1"><img border="0" height="260" src="https://4.bp.blogspot.com/-cgpe_qNv49U/WhcJSlKI0fI/AAAAAAAAAjo/xHQNeyi0NDAoNyHO90imN6Ipp25d4ja0QCK4BGAYYCw/s320/WIN_20171123_11_42_44_Pro.jpg" width="320" /></a></div><div><br /></div><div>The way to cheat on this question is to note a) the answer is in the vicinity of 25 or 26, and since no addend ends with 9 in the 10,000th place, the answer has to be C. Much more gratifying than multi-digit addition which is used no where in life or in any other class or in college.</div><div><br /></div><div>Question 3: 6x + 3 = 3(2x + 3)</div><div>Here are my comments: <i>Every time you see x in an equation, be prepared to rearrange and transform the equation.</i> This is a good place to learn how parentheses work without the spoon feeding and repetition of Pre-Algebra. "x" requires a few long discussions under the heading of Power Bucketing (aka setting up future math) but we already had those discussions. <i>The equation becomes 3 = 9. Now pick the answer. </i>On the SAT, we'll switch to looking for a subset relationship to find the answer and other cheatiness, but for now they need to learn transformations.</div><div><br /></div><div>Question 5 was even more fun.</div><div><br /></div><div style="text-align: center;"><a href="http://3.bp.blogspot.com/-gttMLnREJzw/WhcL8w0evlI/AAAAAAAAAj0/csL2CtRdQrcAiEOfxgr-wdiLPgj3R9-PgCK4BGAYYCw/s1600/WIN_20171123_11_55_47_Pro.jpg" imageanchor="1"><img border="0" height="232" src="https://3.bp.blogspot.com/-gttMLnREJzw/WhcL8w0evlI/AAAAAAAAAj0/csL2CtRdQrcAiEOfxgr-wdiLPgj3R9-PgCK4BGAYYCw/s320/WIN_20171123_11_55_47_Pro.jpg" width="320" /></a></div><div><i><br /></i></div><div>It took a while, but we settled on putting 6.23 x 9.3 within the bounds of 6 x 9 and 7 x 10. You can see this work in the middle of the page, and you can see on the right the framework my son used to actually calculate 6.23 x 9.3 using successive digits. The cheaty-est way requires the most work, higher order problem solving skills, more creativity and more time. I love it when a student is excited that cheating turned a 5 minute problem into a 20 second problem, never stopping to think that it took us 20 minutes to get there. </div><div><br /></div><div>By the way, one reason to let the child do the work first is because children will most likely resort to calculations and they all need practice in arithmetic. The main reason is that whatever they answer is expected to be wrong, and Math House loves mistakes. </div><div><br /></div><div>Question 6 in the picture is awesome. It involved a wiki definition of "statistical" followed by an evaluation of each statement on those terms. 'Statistical' is a summary or characterization of the data, and 3 of those answers ask for a single number. The last one is seeking an average. Also, statistics usually follows the rest of the material in a math course and in terms of timing usually ends up being taught after the you-know-what test. I'm not sure how the little one ended up with the correct answer the first time.</div><div><br /></div><div>The Algebra II final was loaded with solution strategies, most of which were not discussed yet and ended up being more boring to re-work than the 6th grade test. The breadth of the Algebra II test was good so it was worth it. On both tests there was this little gem:</div><div><br /></div><div><div style="display: inline; float: left; width: 45%;"><div style="text-align: center;">Alegra II</div><div style="text-align: center;">Evaluate 3n/(n + 3) + 5/(n - 4) </div></div><div><div style="display: inline; float: left; width: 45%;"><div style="text-align: center;">Pre-Algebra</div><div style="text-align: center;">Order 1/4, 1/5, and 11/40 </div></div></div></div><br /><br /><br /><i>In both cases, you can't compare apples and oranges, or 1/5 and 11/40. And you can't directly add things with different denominators. What happens if you multiple something by 1? Does 100/100 qualify as 1? What about (n + 4)/(n + 4)?</i> These are my comments as we meandered to comprehension.<br /><br />Many parents complain that they don't feel qualified to understand math in a child's terms, let alone teach it. Here is my response. What they are really saying is that they don't want to take the time to understand and solve the problems of a) the math on it's own simple terms (the 'simple' takes time to get there) and b) the problem of working slowly with the child until the child has learned some skill. And yet they expect their child to magically acquire patience in analysis and problem solving skills?<br /><br />You've got a third problem, which is that at school the child is learning boring spoon fed repetitive work that values memorization, speed, and 100% accuracy. So if they don't learn the important skills at home from you, they won't learn it.<br /><br />Learning starts with unknown, slow, and 0% correct. I'm happy if you feel like you're at this point too.<br /><br />First, acknowledge that your baffled. You can be baffled on how to teach this while the child is baffled on what to do. This sets the right tone and makes everyone comfortable.<br /><br />Next, look at what you know about the problem. a) Your child stinks at parentheses, isn't 100% conversant with variables that span R, doesn't see the need for common factors and b) you don't know how to teach them.<br /><br />Third, come up with a strategy. It will have the following components: a) it will take a long time, b) it will be step-by-step, c) you have to back track on something simpler, like having the older child do the fraction problem first and having the younger child compare 1/2 and 1/3 first, d) you will have to reevaluate and try again.<br /><br />The preceding paragraph is going to be the child's take away. Someday they'll understand "n", common denominators, how to use parentheses, algebraic transformations and the rest of it. At least they'll be comfortable when they get to it in school or on a test. But those problem solving skills starting with 'Baffled' and ending with 'Try Again' are so powerful both of you are on a path to 99%.<br /><br />I'm going to conclude with a warning about accelerated math in school or after school. It is now common to teach Algebra II in 7th grade and Geometry in 8th grade, or to skip to Geometry in 8th grade, despite the compelling evidence that the result is many kids quit math early in high school and reporting hating it. At this young age, speeding along, the kids memorize and learn to use the concepts. There is little if any time devoted to the key skills that are taught in high school, especially in Geometry, learning adult level problem solving skills doing Geometry proofs. I would be surprised if any 8th grader could prove to me that a straight line is straight, let alone prove each building block of Euclidean Geometry all the way up to trig, but that's what a rigorous high school class teaches, because it is essential to Calculus. It's essential to thinking.<br /><br />We've been doing high school Geometry proofs for the last 6 months with both kids. Algebra II is a belated detour. You might imagine that the approach is dramatically different than an accelerated school math program. In 14 months I'll tell you why this is so important.<br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com3tag:blogger.com,1999:blog-5703568807615263851.post-14790646825803573292017-11-23T08:14:00.002-08:002017-11-23T08:14:59.664-08:00The WISC V<div>It's time to take a closer look at the WISC V.</div><div><br /></div><div>I haven't looked at this test since I began my early research. It is a combination of the Word Board, the COGAT, and an IQ test. I studied the concept of IQ extensively, and once I realized it was a myth I turned my attention to cognitive skills. IQ is not just a dumb concept, it is detrimental to cognitive growth. I believe that studying for the COGAT when done properly has an immediate impact on the child's academic, problem solving, and cognitive abilities. If the WISC preparation is done properly, growth will occur in the parts that are not designed like an IQ test. The IQ part should be learned elsewhere. It takes a bit more time, but it's doable.</div><div><br /></div><div>Some school districts include the WISC in their GAT screening, and a seat in a gifted and talented program can is worth it so let's beat the WISC IV and V. The WISC is often paired with the MAP and the COGAT, and these 3 tests have some overlap, not to mention the fundamentals of thinking skills.</div><div><br /></div><div>If you want to know what is on the WISC, take a look at <a href="https://www.criticalthinking.com/articles/test-preparation-practice-for-wisc-assessment">critical thinking's page</a>. I like some of the material, but it's way too easy to get to the cutoff scores in almost all school districts. Even worse, there is a chart showing indicating how fast a pace you would keep to get through BTS Level 1 for a first grader. Working slowly through this book in K develops deep skills. Going through this whole book quickly leads to what I don't know. Nonetheless, I noticed their "Suggested Test Prep Plan" is chock full of best practices, as is the concept of a timing chart, but this content could use about 50 pages of explanation. I'm a big fan of their website and how they've improved it over the years and if you're really facing 4 weeks to the test, get a practice test and do what they say. (Someone once accused me of making money off my recommendations but it should be pretty obvious that companies wouldn't pay for this type of analysis.)</div><div><br /></div><div>My starting point for a WISC refresh was the authors' books on comparing the WISC 4 to the WISC 5 and the new practitioner's guides. Then I looked at adult level IQ tests and asked how I could present permutations of fundamental concepts to little kids so that they could understand the question but not get it right, apply the underlying skills, and thereby learn something.</div><div><br /></div><div>The list of question types doesn't hint at the grilling your child is going to get on the verbal section of the WISC. It's all Word Board. Get a <a href="https://www.sadlierconnect.com/vw/vocabularyworkshop.com" target="_blank">vocabulary workshop</a> book, post the words on the fridge, and ask your child about similarities, synonyms, used by, part of and the rest. If you have a 4 year old, get <a href="https://www.amazon.com/Pre-K-Phonics-Conceptual-Vocabulary-Thinking/dp/154045620X" target="_blank">Pre-K Phonics Conceptual Vocabulary and Thinking</a> and then you won't have to worry about vocabulary, reading, or grilling until the 7th grade MAP. </div><div><br /></div><div>Matrix reasoning, picture concepts, symbol search, perceptual reasoning and arithmetic are question types that would benefit from COGAT practice.</div><div><br /></div><div>That leaves the IQ portion. Sequencing, Cancellation and Symbol Search stand out as blatant attempts to measure IQ, but elements of IQ skills can be found in other question types as well by design when this test is properly administered.</div><div><br /></div><div>The difference between measuring cognitive skills (COGAT) and IQ (WISC) is the difference between measuring the student's ability to solve a novel problem given enough time, and the student's ability to quickly solve a novel problem because they have had so much practice doing it in the past. Some school districts want to find children that have the potential for a strong academic performance and use the COGAT. Others want to see evidence that the child loves school so they add the MAP. The most short sighted school districts only want kids who's parents have PhD's so they add the WISC.</div><div><br /></div><div>The student develop the additional IQ related skills from an early age because they love to read and solve puzzles and do crafts and play with Legos and other activities that would give school districts confidence that this student lives in a primarily academic household and will perform in an accelerated program in the long term because the parent is actively involved in making the house a learning environment with no TV or screens.</div><div><br /></div><div>School districts that use the WISC wasting a lot of academic potential in their student population. They are also avoiding the problem of program full of kids who prepped for the test and then ended up with a subpar academic record by middle school. The latter case can be solved with a better program. The former case is called a city where you don't want to raise your children.</div><div><br /></div><div>There are 2 challenges with teaching IQ skills. First, turning your house into a top notch learning environment requires a lot of time and effort on the part of the parent. You have to do it, but it takes time to make up for 20,000 hours that you spent with your child not acting like you have a joint PhD in literature and biology. The second challenge is that training your child on sequencing and memory skills is counter-productive. You are taking the thinking out of thinking, and giving your child a time limit on anything also takes learning out of learning.</div><div><br /></div><div>The solution is working memory, as in working + memory. In Test Prep Math, the word problems, quantitative and visual spatial sections all have multiple problems superimposed. The original intent was to slow the child down to the pace of learning by replacing one-step problems with multi-step problems, and cheat the cognitive skills tests by getting the child used to something 2 or 3 times as comlicated. The magic number for working memory is 3 but substeps tend to push the ceiling. For the word problems, I add confusion to the question (why ask how many they have altogether when you can ask it in 100 other ways?) and the result is that work to identify the equations to be solved, putting them in memory while uncovering the rest, and then keep them in memory while being doing the work. Kids who have had Level One or Mathasium are forbidden from using a pencil because they've already had training in problem solving (instead of learning) and lose the 'working' part of working memory.</div><div><br /></div><div>The result is the natural tendency of children to form their own algorithms and techniques to manage this process and not have to sit their for 25 minutes solving a problem 5 times to get the correct answer. Those internal algorithms evolve naturally on the student's own terms, and once they are there, we step beyond solving novel problems to applying solution techniques. When a child takes less time and makes less mistakes on a series of problems that continues to grow in complexity, we've stepped from cognitive skills into the realm of IQ skills. What I don't like about after school math programs is that they skip the internal process and explicitly the methods to the child. We get a child who appears to be great at math, but didn't make the internal effort and is not going to gain the long term benefit. It's like a performance enhancing drug instead of a fundamental long term improvement; long term research is ongoing.</div><div><br /></div><div>But Test Prep Math is for 2nd and 3rd grade. I've gotten complaints from the very beginning that there is no Test Prep Math for 1st grade. Almost there. In the mean time, with what ever material you use, give your child space to grow their working memory. If you don't help, at least for the first 10 minutes, or help by just asking the child to walk you through each micro bit of the problem in excruciating detail, you're letting memory work, as in holding things longer and letting those little analysis and problem solving skills develop on their own. </div><div><br /></div><div> </div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div></div>Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com3tag:blogger.com,1999:blog-5703568807615263851.post-55975713830672881962017-11-14T07:44:00.000-08:002017-11-15T07:28:23.819-08:00Blanket Parenting AdviceI often get questions about different situations under the heading of 'Is This A Problem?' and while I'm struggling for an intelligent and informative response, I'm thinking <i>Your child is awesome. You should help me with my parenting issues.</i><br /><i><br /></i>The spouse of one of my Power Dads told me her mother directed her to add " by Kindergarten" to each of her questions to diffuse the anxiety of younger parents. "Is my child going to learn to use the potty?" becomes "Is my child going to learn to use the potty by Kindergarten?" and an issue magically becomes a non-issue.<br /><br />Our pediatric physician was more direct. This person will easily have 90,000 people at his funeral because he was so awesome. Throughout the entire time we qualified for his practice, no matter how serious our worries were, his answer as always "this is not a problem." Looking back, I can see that he meant either a) this is not a problem, or b) this will take care of itself in a few years so stop worrying about it.<br /><br />In the academic space, a bit more advice is needed because there are deadlines. In most school districts, these deadlines reappear every year to provide second and third chances, although in some school districts there are far fewer seats after the first test. Middle school provides a whole new round of opportunities, as does high school. Frankly, the later opportunities are the only important ones in the long run, but this is not helpful if you have a shot at a great elementary school.<br /><br />Here is my advice for academic excellence. If you want a child who is far above average, you as the parent need to act far above average. Average approaches are going to produce average results, except in cases where you've been doing something unusual for a long time and neglect to mention it to me. When I ask parents how their child scored a 99% on the COGAT and they respond "We didn't do anything" or "the kid just taught himself how to read" there has been much more going on than the parent realizes. It's usually a case of the parent doing all the right things in a hand-on/hands-off environment without knowing it.<br /><br />The material to grow cognitive skills is well known at this point. I'm looking for a change in testing to respond to the routine high scores these days and I'm seeing early evidence. There are programs, classes and books behind the rise in test scores. The average outcome of this approach is great but no guarantee of 99%. But there are thousands of parent-child interaction hours and when research takes the time to observe and measure the parent-child hours, the statistical importance of everything else diminishes. The what is important, obviously; a child can't exercise cognitive skills if the child is not exposed to anything that requires these skills. The how is the deciding factor.<br /><br />Ask yourself this question. What is a GAT parent? Am I measuring up? How would a GAT parent spend their time? How would a GAT parent show interest in things? How would this person answer questions? What books should I bring home? Does a GAT parent use scaffolding, and if so, how much? Should I push my child into something over their head or let them walk their step-by-step? If you're looking to send your child somewhere to become GAT you might be looking in the wrong direction.<br /><br />In the past few years, I've answered all of these questions and the answer always involves both options (if there are 2 options) or all options (if there are more than 2). In our case, we forgo anything that involves the car or a building that is not our house, but that's our choice. The one thing I learned from home schoolers is that you can teach your child in 20 minutes what would take 3 hours in a classroom setting. The key is that we do a lot less and we stretch things out a lot more. It's not the only key, but it's a good start.<br /><br />In the face of little available information, my starting point was the simple observation that if lots of people do something, we don't want to do it. I don't want that outcome. I don't expect this road to be easy on anyone. In fact, we've become quite adept at doing things that aren't easy because we've done so much of it. But we'll make it easy anyway by following the Zero Expectations and Lots of Mistakes Are Good rules. There's the "both" again.<br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-73826414146961509162017-11-07T17:41:00.000-08:002017-11-07T17:41:04.565-08:00Simple Down and EstimateI'm amazed at how 2 solutions strategies grow and develop in children year over year.<br /><br />The estimation strategy started as more of a graduate level proof strategies before I turned it in to a learning experience for 5 year olds. It's related to start with a simpler version of the problem which I refer to as 'Simple Down' in the title to this article for lack of space.<br /><br />Here's how the estimation strategy works. A child is looking at a super hard problem that they know how to do, but they can't quite work out a strategy for decomposition (2 easy steps are better than 1 hard step) so I ask the question: <i>Is it 1? </i> Hopefully, I'll get the half eyelid you dummy look, but it usually takes a few times until the kid is on to me. "No, it's not 1." <i>Is it 2?</i> "No, that one doesn't work either." <i>What about 3?</i> Eye rolling. <i>How about 4? </i> Sighing.<br /><br />What I'm looking for is a whole bunch of more advanced super skills to emerge. It takes restraint for me to explain how to do the problem, but this will destroy a tower of synaptic connections, not to mention their academic future. So I'll just ask about 5 and maybe 6.<br /><br />Inevitably, the child will be totally frustrated and bored by my useless guidance and will try 10. A few more times, and the child might look at the picklist and see "9 12 15 19". I hope this doesn't happen right away, because iterating through 1, 2, 3 and 4 might produce answers like 5, 7, 9, 11 and suddenly we're developing causal function sense, the Estimate Iterate skill. Once they see that the answer set only requires 4 solution calculations, we've got head down the path of efficient time management.<br /><br />These variants are just the tip of the skill ice berg, and to get deeper I believe very strongly that describing and explaining the solution strategy prevents the child from an internal mechanism that opens the door on more sophisticated methods that they will invent on their own in a few years. Plus I tried just describing and recommending this approach and was ignored. I'm disappointed when I meet a child who knows how to solve problems of all types. It's unlikely they figured this out on their own. There are many popular books describing solution methods for algebra problems of all types. You will need one of these if you teach your child how to do a math problem at a younger age.<br /><br />The second strategy involves a simpler variant of the problem looks a bit like estimation but is used when your child is in over his head. A 6 or 7 year old seeing multiplication for the first time, a 5 year old struggling with double digit addition, an 8 year old dealing with complex numbers, or a 9 year old graphing 2<sup>x</sup> over the positive and negative rational numbers*. 23 + 89 too hard? Start with 10 + 10 and work your way up from there. When the child gets back to 23 + 89, he will own it. You are one step closer to never seeing a math grade again or caring.<br /><br />These 2 solution methods are why I prefer one hard problem to six medium problems. There is a much bigger payoff and it just builds on itself. Suppose we're doing a few problems on a worksheet and get to a problem needing one of these methods. I'll stretch out the time just on this one problem, so that the lesson stays with the kid and is not drowned out by more problems. I don't see strong readers iterating through worksheets like "Jane eats corn. Jane eats pie. Jane eats broccoli. Jane makes pie. Bill makes pie..." This is what most math worksheets look like to me. The math version of a book is a single worthy problem that unfolds a whole new world of awesomeness. (Readers read books to become strong readers not worksheets.)<br /><br />I've seen these skills grow over the last 8 years. What is amazing is all of the different manifestations of the subskills I didn't know exist until they happened and how these skills are applied elsewhere. <br /><br />*No one actually appreciates an exponential graph but me. That was a fail. Buy the square root of -1 is pretty cool.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-11698535427657377592017-11-04T05:19:00.002-07:002017-11-06T11:51:48.954-08:00Practice, Training, and LearningA few weeks ago, I re-reviewed the COGAT practice tests. Then I pondered how different practice is from cognitive skills development. I've been pondering ever since.<br /><br />My goal for the period leading up to the test is to increase a child academic, cognitive, and problem solving skills. There's very little difference between these skill sets. The only academic skill that is not on the list of cognitive skills and problem solving skills is how to survive a 50 minute math class when you figured out next month's chapter in the first 60 seconds of class.<br /><br />The first rule of cognitive skills development is that it's not going to happen if the child sits down and does more than 1 problem. This is impossible for most situations, so the next best thing is a few problems for decoration surrounding 1 problem that will result in cognitive development.<br /><br />The second rule is that if the child knows the rules, recognizes the problem format and knows what to do, then no cognitive development is going to take place. Think about that. I'm going to great lengths to make a problem confusing and hide that it's really just a plain old boring math problem, except when it's not a plain old boring math problem.<br /><br />My absolute favorite conversation to have with kids goes like this: "Mr. Math Guy, what does this mean?" <i>You tell me</i>. "I don't understand it." <i>Then explain it to me.</i> "How can I explain it to you?" <i>Read it again. </i>"Read it and still don't get it." T<i>hen tell me what the first word means</i>. "Really?" <i> I've got all day.</i><br /><br />The conversation works better if you use a 1970's Clint Eastwood western accent. When this conversation happens, we're on the verge of a cognitive explosion and this kid is not just going to learn math, they are going to learn 5 or 6 really powerful life changing skills. I'm currently working on suggested content for these kids when I get mentioned in Nobel Prize speeches.<br /><br />The third rule is that you can't tell the child anything. Telling is the opposite of learning. This is really hard to do when the kid starts at square one so feel free to cheat a little.<br /><br />The fourth through nth rule (for lack of time) is that you can't hurry, mistakes are required, you're going to end up on tangents, and any time your child gets anywhere near the Big Five problem solving skills, clear the decks and do not, under any conditions, do another problem after that because you may ruin the whole experience. You can't use a Big Five if you have a whole bunch of work to do, and I don't trust either child or parent to live in the moment and make it a life lesson if you follow up using one of these skills with more problems.<br /><br />Of course, you can't do any of this 2 weeks before the test by zooming through practice tests. Plus, practice tests are nowhere near as hard as the convoluted knot that is in Test Prep Math. (Reading comp skills are an added bonus.)<br /><br />So far, I've directly addressed the problem wherein the child does not have skills, by prepending easier problems. I've addressed the problem wherein the parent does not have any skills by adding direction. I've addressed the problem of what do you do if you end up with a braniac (section 2) I've addressed the problem with children who have unusual skill gaps but are competent in other areas (section 3).<br /><br />The problem I'm working on now is children who are highly trained in math, like after school or weekend managed math program, and don't need the problem solving skills.<br /><br />This is a pending disaster. It's my worst nightmare and keeping me up at night thinking new problems. I put my contact information right in Test Prep Math. If anyone has any questions or problems, I get a call and the clock starts ticking on me fixing it. I didn't get any calls for 12 months, other than 'great book, my son thinks your book is not lame' or 'great book, my daughter loves math now' but in the last 2 months, I've a few calls like "my son is already in the 99th percentile in math but can't pass the COGAT". The culprit appears to be Level One and Mathasium. I don't think it's the extra math. These aren't bad programs. The culprit is that being really great at math precludes the need for high level cognitive skills, the skills that are so important we should probably form a cult around them. The COGAT, on the other hand is remedial math heavy on extra problem solving skills. There's a disconnect. It looks like managed math programs take a short cut and just teach and practicing math, then hard math, then really advanced hard math. No skills required. Then there is an add-on program for test prep skills, but it's too late. The damage is done. This is not going to end well.<br /><br />I'm on the case.<br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-86891619343377586172017-10-25T06:30:00.002-07:002017-10-25T06:30:40.710-07:00The Gifted Grab Bag Mega ArticleI've been so busy with my latest research project so I'm just going to cram a months worth of articles on ancillary topics into one Mega Article.<br /><br />I talk to a lot of parents about their kids. The conversation includes a score and some questions. Other times I just observe. Over the years, some things strike me as odd.<br /><br />I've seen kids who are good a puzzles. Anything else? "No, he just likes to do puzzles." Is that the secret to passing the test? Here's how it works. You get your kids puzzles starting at age 2. The kid can use them as chew toys. Every birthday, Christmas or whatever include puzzles with a small number of big pieces. Your child will toss it aside in favor of something shiny and branded and rediscover them a few months later. By about age 4, you can find puzzles that have big pieces on one side and small ones on the other. When a puzzle gets solve quickly, the next one will have smaller pieces in a greater number. Ramp up slowly. Sometimes you leave one on the dining room table and a piece at a time gets added, but someday your child will just sit down for 3 or 4 straight hours doing a singe puzzle. At this point, you have won. After talking to a more experienced mom about puzzles and interviewing her 4 year old, I invented this recipe. Thanks for that, Puzzle Mom.<br /><br />But kids end up doing well GAT programs who don't do puzzles.<br /><br />At age 3, there are numerous craft books about cutting, pasting, folding and drawing. These are a life saver if you are juggling a pre-K kid, a toddler, and a baby, especially if you need quiet time. I think my wife bought 2 or 3 thousand of these books and 3 or 4 laundry baskets full of felt, googly eyes, pipe cleaners, colored pencils and crayons of all types (there are a lot of types of crayons, especially German ones). Our house is littered with crafts and origami characters. Once you get past K, there are really cool books with cutout-fold-glue robots and monsters. I'm not sure this guarantees 100% on COGAT folding questions, but it makes test prep easier to have a child who is used to sitting down and concentrating on shapes.<br /><br />You'd think that sports would be counter productive but there are gifted kids who do sports morning noon and night. What about kids who do Tai Kwon Do or ballet? Does this give them an advantage? There is really good research that says yes and I believe it. But it probably wouldn't give an advantage to someone else. Maybe it's kid specific. So I invented fast walking while talking about math. <br /><br />We are faced with math facts again, my nemesis, this time with multiplication. Timed math facts exercises have been banned by our school (perhaps the top school in the universe now that Aristotle and Plato are not around anymore). But as every teach knows, a kid who hasn't learned their math facts is going to struggle on more advanced material. Our teacher sent home a cryptic letter explaining that timed math facts tests are banned, but if you untwist the logic and read behind the lines she just announced that our class is doing them anyway. So on our last Math Walk 2 miler, I introduced our newest exercise: Explain to me, using parenthesis, how to do "6 x 7" using the least amount of mental energy. Then we argued whether (3 + 3) x 7 is easier to do than (5 + 1) x 7. The first one doubles 21 and the second one has 1 x 7 in the distribution step which has a mental energy level of zero. We'll cover all math facts eventually this way, but we ended the walk with 1700 x 17 and there are 3 different ways that make this an easy problem to do on a walk. Take that Math Facts. The reason I like this exercise is that I can't get 9 year olds of any shape, size or color do comprehend parenthesis, at least in the context of a worth 9th grade problem. But I can't get any kid who is an expert at memorizing math facts to understand pre-algebra at age 9.<br /><br />I've always been really impressed with kids who spend an hour or 2 hours practicing an instrument with multiple lessons each weak from qualified musical experts. Their accomplishments are really impressive outside of school and I suspect that they've gotten through the test and through the program with out a lot of effort. These kids give stunning concerts. This would never work for us. We don't have 2 or 3 hours a day for practice what with the puzzles and math walks<br /><br />So I invented Do-It-Yourself music in 20 minutes a day or less. It works this way: Here's the book, here's the instrument, here's the fingering chart, here's a copy of the Empire March. Give me 20 minutes of squeaking and fumbling and complaining. I'll check youtube to find out why we're squeaking and fumbling and fix things occasionally like finger placement. Mostly I'm just happy that we get 20 minutes of squeaking and fumbling each day. Once a song is played with the right tempo, we move to the next page. I've found that as the year goes by, we actually achieve some sort of competence, not exactly the level of the competition from the last paragraph. This still leaves plenty of time for crafts and puzzles and Minecraft programming and talking about what is canon in Star Wars and what is not and of course Math Walks.<br /><br />There are ancillary benefits to the DIY music approach. The summer before band, the little one went from zero to skipping the first year and joining the intermediate band on a new instrument. Even more impressive is what is about to happen in Karate Recorder once his class gets their recorders. Look it up, it's a great exercise and you should do it with a 3rd or 4th grade child. Last weekend he found his older brother's recorder so I printed a fingering chart and the 9 songs for this program. He started with the Black Belt song, and in about 90 minutes memorized all of them. I should point out that gifted programs are zero competition - not even the slightest bit. They just work together in teams. This is both a really good thing and a really disappointing thing to a parent at the same time. So my kid is going to walk in and trounce the other kids in Karate Recorder on the first day. The older one warned us both that there are 29 other kids who are all super smart and they will gang up on him and crush him, which is why you don't want to do this. Wise beyond his years. But still, why pass up the opportunity?<br /><br />I'm not taking any chances on the negative effects of sleep deprivation. We've always had a 7 p.m. bed time because I like to get up really early and write. Lately, we're still working on things past 9 pm, but at least we're doing it in PJ's and with teeth brushed. Nonetheless, there are really great kids excelling who routinely get zero sleep. But there are many more kids who don't get enough sleep and it ruins their education.<br /><br />I'll have to finish my mega article in the next article. I tried writing the two topics but they are too big to fit and too important. <br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com4tag:blogger.com,1999:blog-5703568807615263851.post-72070021528129648102017-10-21T13:21:00.000-07:002017-10-21T13:21:26.141-07:002017 Review of Practice TestsI've completed my practice test review. I already have a page for this so I just updated it. <a href="http://www.getyourchildintogat.com/2014/06/cogat-test-prep-books.html">You can find it here.</a><br /><br />It was fun to lay the books out side by side for a full comparison. Most of the market is in the K to 2nd grade range, so that is where I focused my efforts. <br /><br />The review left me with an overall sense that any of these books would work. I noticed that some were harder than others and the original ones from past reviews still had a format that was closer to actual test. Is it worth sacrificing format to save $15? Maybe, maybe not. It depends on the child and where the child is in their test prep program.<br /><br />Some of the best new books were careful to mention the proper role of the practice test and it's value, which is both limited and critical. Over time, other publishers have been marketing their books as Test Prep. I'm not comfortable with this definition. Preparing for a cognitive skills test means primarily developing the cognitive skills of your child. A large quantity of practice problems is not the way to do this. It doesn't hurt, and it helps at test time in certain ways, but kids at the 99% level of the academic bell curve generally didn't get there by practice tests. I think this holds true for the math and verbal sections, especially verbal, where I recommend very little time with a practice book in most but not all cases.<br /><br />In the few weeks leading up to popular test times, I get quite a few questions about what to do, and the time limit dictates a practice test and not much else. This is a good start, and might be just enough in some cases, but it's important to me to provide direction and hope when asked. There is always hope and there is always next year.<br /><br />What I'm not going to mention in the review because I don't want to put anyone off is that I coach kids with material that is 3 to 5 times more complicated, more moving parts, more advanced that what is in a practice test. It seemed obvious in theory and it worked really well in practice. To get a 98% on a really hard test, over 100 questions in a 60 to 90 minute time frame, the the best way to prepare is to develop concentration, analytical skills, logic, soft skills, grit and working memory at the 130% level or higher, and that means a few problems a day that are more thorough.<br /><br />If you happen to have a boy who is facing a test, but not before January, and you want to be part of my over the top research project for 1st grade, please send an email to getyourchildintogat.com. I'm working on Test Prep Level 1. Ideally, you have tried and not passed the test before. I won't guarantee that your child will pass the test, but I will provide custom material to close any gaps I find.<br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-45242553740519577872017-10-17T04:49:00.001-07:002017-10-21T05:01:25.412-07:00Time For A Practice TestTest Prep season is almost over for some school districts. Others will begin testing in December and continue through March. I've been busy with cognitive skills training since about April and I'm ready for a break.<br /><br />A practice test is the last step in test prep. I recommend switching over about 2 weeks before the test. In preparation, I bought practice tests from the two newest publishers that I don't have on my shelf. The books will be here in a few days and I will lay out all of the books side-by-side against my charts of skills and report back my findings.<br /><br />Teaching cognitive skills is, in general, counter intuitive and it's hard to get parents to switch gears to cognitive skills methods and away from the approach that schools use with school curriculum. This has been the focus of my research lately - training parents to be GAT parents. Using a practice test is also an odd exercise.<br /><br />The goal of a practice test is to make sure the child understands the format and basic rules of the test, to prevent any mistakes or confusion from ruining the test, and to relax.<br /><br />It is very common for a bright child to make up their own rules. You can identify and correct this problem with a practice test. It's common for children to forget to check all the possible answers before answering for 71 consecutive questions even though you told them to check all possible answers before answering on the last 70 questions. Your voice will echo in their brain during the test, but many children won't give you that satisfaction during practice.<br /><br />It is very common for a child that has already gotten a 98% on the test last year, and who is poised for a 99.7% on the next test - brace yourself - to get half or more questions wrong with a practice test. The child's brain has a section dedicated to increasing anxiety and frustration in the parent, and this part, called the Frustracampus, is in charge of taking a practice test.<br /><br />Understanding the format of the test and it's basic rules has been proven to add 4 points to a child's score. It's not good for much more. Two weeks is not enough time to turn a 65% child into a 99% powerhouse, but 4 points is 4 points so I recommend this step.Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-64250423259095580722017-10-12T18:00:00.000-07:002017-10-15T12:12:55.488-07:00Why The Word Board Is So ImportantIn most school districts, gifted and talented entry is based on the score sheet, and the score sheet includes an a line on it even scarier than test scores: The teacher rates your child. It's called the teacher inventory.<br /><br />It doesn't matter how smart your child or how high the test score if the teacher rating is low. There is a simple solution to the teacher score. First, you need a creative, engaged, dedicated student. That will help. But most of all you need an articulate student who raises his hand first and can express himself articulately at a level far beyond his peers. Or her peers, as the case may be.<br /><br />Like everything else that most people think is an innate gifted, talkativeness is a learned skill.<br /><br />For this reason, The Word Board is much more important that I ever mentioned before. Here is a little background.<br /><br />The Word Board was originally conceived as a way to accelerate the process of mastering phonics and conceptual vocabulary in the context of Delia.<br /><br />Delia was less than two years old at the time. My child was in a mom and tot group with Delia. Delia was reading a book, pointed to a picture, and said, "Look mom, it's the Eiffel Tower". Once the other mothers got over the shock that Delia spoke in a complete sentence, they hovered over the book to verify that it was in fact a picture of the Eiffel Tower. I heard about it for a week.<br /><br />At the time, my research consisted of devouring studies and articles on the impact of vocabulary. In his papers, the author of the COGAT mentioned that all cognitive skills are present during the process of learning to read (a fact known since 1911), that vocabulary is a thread that runs through all parts of a cognitives skills test, that a simple vocabulary test has about 75% of the predictive power of a cognitive skills tests. I think these are nicely summarized in a chapter of Welcome to Your Child's Brain. The more talking at home, the higher the level of vocabulary. A higher level of vocabulary predicts a strong academic performance. And of course cognitive skills tests are designed to predict academic performance. The bottom line of all of this is vocabulary, whether you are staring at a figure analogy, a folding question, or a quantitative puzzle. It's not intuitive until talk through a math question as described in the previous article. And then it works.<br /><br />Flash cards are the main competitor of the Word Board, but flash cards are about learning words or sounds or vocabulary. The Word Board is about learning to think and answering questions. It's about owning the answer to some inane question I just thought of. The Word Board steps up to talking, defending, thinking, making things up on the spot. On the spot is crucial.<br /><br />Here's how the Word Board works:<br /><br />1. You put the unit on post it notes on the refrigerator. This unit could be a phonics lesson, Vocabulary Workshop, Foss science vocabulary on the rocks unit, Wordly Wise for 6th grade, or freshman Chemistry (before freshman year, of course). The kid has to <b>earn</b> it before a word comes down. For a 4 year old, this could be reading the word adequately and making a face (in the beginning, but we're going to ramp up after that) and for a 2nd grader facing a GAT test, it may be parts of used by sounds like made of similar to and all other parts of the analogy skillset.<br /><br />2. The parent needs to pick up 2 important skills. The first skill is to have a book or wiki or online thesaurus or map handy. If the kid defines sap, that's good for lesson 5, but by lesson 43 "fleck" is going to need some differentiation between spot and bit and all things small. The kid doesn't know these, so you'll just have to put up some more post it notes for the next trip to the Board. You are going to do a lot of talking because you are the primary educator of the child. By the next lesson, the bar just got raised. In one session ( 2 years later) we started with cobble and pebble, and then I just kept adding words until I ran out of post it notes. That first year I went from reasonably over educated to All Knowing Knower Of All Things.<br /><br />3. The second skill is grilling your child in an encouraging productive way so that the child is unable to leave the Board without a proper dissertation defense of whatever words are there. As long as you have Zero Expectations and are OK With Mistakes and as patient as a pile of dirt, this will always go well. With this approach, it's hard to do the Word Board without laughing about something. I find, however, for most parents, especially the high strung ones with a GAT program in mind, these are totally learned skills. You will know what I'm talking about when you are talking about the 6 words related to "fleck" and your child remembers zero of these until the third week.<br /><br />Picture a child with a unit of 10 vocabulary words doing exercises and reciting definitions off of flash cards. Then picture a child facing those 10 words on post it notes surrounded by 20 more that I just thought of and having to answer a bunch of questions on each all the while I'm sharing things off the map or new related words. Some days, you may picture silence, but bad days are par for the course.<br /><br />What I got out of this was a child who woke up at 6:30 am, started talking as he came out of his room, talked non stop the rest of the day and talked for about 20 minutes after his door was shut at bed time. There's also hyperlexia, but I'll describe that later. Plus so many words so fast the kid learns to listen carefully and memorize immediately. But mainly I can ask difficult questions and get well thought out answers that go on for a long time.<br /><br />Take that teacher inventory.<br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com4tag:blogger.com,1999:blog-5703568807615263851.post-33165322766717389712017-10-06T06:12:00.000-07:002017-10-15T12:12:26.663-07:00The Panic ButtonThis is the time of year that my inbox fills up with panicky questions from parents. In this article, I'm going to tell you exactly what to do when your child misses easy practice test problems and you panic. I've said this before but you need me to repeat it over and over again and you don't ever check your answers.<br /><br />This is much better than the time of year (rapidly approaching) in which I'll get 100 questions like "I just found out that my child is taking a test called the CoGAT in 2 days. Do you have any advice?" I actually have an aswer.<br /><br /><div style="text-align: center;"><b>The Practice Test Panic Button</b></div><b><br /></b><b>Step 1 - Stop Panicking</b><br />You're children are way smarter than my children were at that age and it doesn't matter because I used even way harder problems than you are using, and my kids missed most of them. If my child got the problem correct, it would be a waste of time, and with the clock ticking, we can't afford any time wasting.<br /><br />On normal not super hard problems, I usually observe a 50% error rate going into the test. The parent voice doesn't kick in until you are not in the room. Then in the child's brain it's like 'read the question reread the question look at all the answers choose one no guessing do it over check your work' and the child will need therapy after the test.<br /><br /><b>Step 2 - Backtrack</b><br />I used to talk about backtracking 6 years ago. It was my go-to-crutch. I demphasized it in my books because step 3 is faster and more effective, but Step 3 requires more time per question.<br /><br />Backtracking is very useful in test prep situations, trying to do advanced math after skipping a year or two, and dealing with bad days for kids under 8 years old.<br /><br />When you are struggling with folding questions, get out the paper, scissors and a whole puncher. Spend some time doing the basics. Cut out some shapes for the figure matrices and build your own figure analogies. Even if you don't devise a corporate skills based training program in shapes, you'll take the pain out of test prep and it's a nice break.<br /><br />Feel free to take a break and have your child make up their own questions one day.<br /><br /><b>Step 3 - Make An Easier Question</b><br />This is my new go to method and it has a bigger payoff but is harder to do. Reduce the problem to the simplest variant you can think of. The quantitative/visual-spatial problems in Shape Size Color Count are based on this method, as is problem solving in Geometry and Calculus, competitive math, and every thing in between. It's more than powerful.<br /><br />The premise of this approach is that you take all factors out of a hard problem and slowly add them back in so that your child can take an intuitive leap on each factor and own the complicated logic behind it. We're looking for a light bulb to go off.<br /><br />He are some examples:<br /><ul><li>The simplest version of the figure matrix you are struggling with is the top row with a piece of paper over the rest of the problem. Slowly introduce the next 5 shapes (the bottom row has 1 shape and the answer set has 4 more).</li><li>For quantitative problems, the simplest problem is x = 1 or shape = 1 or even 1 = 1. You can add elements back in. I know this sounds silly, it takes experience to start with the right level and you can't go wrong with 1 = 1.</li></ul><div>This teaching method goes way beyond super powers into the miraculous.<br /><br />By the way, this year I've been watching 4 year olds who are doing Shape Size Color Count + Pre-K Phonics and Conceptual Vocabulary and the results are amazing as I predicted. If your child is going this route, warn me at the end of K because I've got something special in the works.</div><br /><b>Step 4 - The Blind Coach</b><br />All 9 sections of the test rest on a foundation of vocabulary and cognitive processes that manifest themselves in verbal skills. Vocabulary is behind the whole thing, including the shape that gets wider instead of bigger.<br /><br />Take out a blank piece of paper and ask your child to tell you how to draw the problem. Take liberties on vague terms and don't put things where they belong unless instructed to do so. This will frustrate some kids - what with having to think and do work and all - so you can draw a smiley face on a shape because he never said <i>not</i> to do so.<br /><br />Expect about 5 iterations while your child learns to articulate what he sees. What is actually happening is that the child realizes that <u>what he sees and articulates is not what is actually on the page</u>. There's a lot more. Light bulb.<br /><br />For the verbal section, there is a variant called <b>The World's Dumbest Parent</b>, where the child has to explain every word to you and you just don't get it. You kind of get the word 'spatula', but not quite. Who uses it? If it's in a group of things, what is that group called? What is it used with? Doing what? Etc. That only leaves 6 more words to work through before you can actually do the problem. I'm hoping that experience sticks with your child when he's confused on the test.<br /><br />I'm shooting for the verbal version of 'draw a picture'. Draw a picture is a great problem solving strategy but lousy for problems that already start out as a picture. I realize that some kids have different learning styles: visual, verbal, auditory, kinetic, etc. These are all founded on a variety of previously learned skills and burned pathways. During cognitive skills practice, I want to develop all of these learning styles.<br /><br /><b>Step 5 - Don't Do Things The Normal Way</b><br />There are a variety of other tricks I use with different age groups and different skill gaps. For example, with fast answerers, we go through the whole book focusing on this question on each problem "what is the trick in this question" or "tell me an easier way to solve it" and I am not the slightest bit interested in the actual solution because I threw them away after I bought the book. Or I announce the solution I like, which is the wrong one, and make the child prove to me that they are correct. Or instead of giving the answer, I make them prove to me that their answer is the best one, choice-by-choice.<br /><br />At some point you need to tell your child what to do when they are stuck on a question. More importantly, in this article, I'm telling the parent what to do when stuck on a question. Something's going to rub off on the child, either panic and frustration and impatience, or let's take a step back and try something different. It's hard not to smile when I'm drawing the worst version of a matrix per instruction, staring with 1 = 1, or taking 20 minutes to do a single 3 minute question because I'm so dumb.<br /><br /><br /><br /><br /><br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0tag:blogger.com,1999:blog-5703568807615263851.post-36289389692153532752017-10-04T04:16:00.000-07:002017-10-04T08:44:06.547-07:00The Apple QuestionLately I've been experimenting with small questions that pack a punch.<br /><br />To qualify, a question has to have a small number of words (obviously) but the question should require the child to step out of their comfort zone and include some words that seem harmless or innocent but are in fact very demanding. The question has to challenge the core skills with the exception of working memory which may not be possible under the circumstances. The question can't be like a brain teaser that requires some outside trivia to answer.<br /><br />Test Prep Math throws quite a few punches, especially in bonus questions. The effect I'm looking for is "You can't expect me to answer that question. My boring math book at school doesn't expect me to answer questions that require thinking. This is not fair." But small question that packs a punch would stand on it's own in terms of time requirements, and frankly 12 words on a page would look stupid, especially if some lucky kid takes 60 seconds to answer it. Maybe I'll do some more experimentation for the 4th edition.<br /><br />Here is the apple question. I think this is suitable for ages 6 to 9 or 10. I'll answer it below.<br /><br /><div style="text-align: center;"><span style="color: blue;">Describe in detail the third best way to eat an apple.</span></div><br /><b>Some Background First</b><br /><br />This line of research came from this question: "Name the 4 arithmetic operators".<br /><br />When teaching math, quantitative reasoning, or quantitative test prep to children under the age of prealgebra, it's pretty much all adding, subtracting, multiplying and dividing. For younger kids, it's halving and doubling instead of multiplying and dividing. Countless times a child has been totally baffled by a question, and if they just took a step back and asked 'which of the 4 operators is this unusual diagram doing or word problem asking for?' then they could eliminate 3 of them and do the work.<br /><br />When I first pointed out to my own child "It's got to be one of the arithmetic operators, just try them all and see which one works" he responded "what's an arithmetic and what's an operator?" If this were reading, I would just explain away (of course the bear has an ulterior motive, let me explain greek tragedies...) but this is thinking practice, and a parent is not allowed to answer questions. This question came up recently and it was a fun for me not to answer it with someone else's kids. When you can get a child to tell you what 'arithmetic' and 'operator' mean and answer the question, you've got real learning going on. This question packs a punch for the parent.<br /><br /><b>Back To The Question</b><br />The first response I get to the apple question is total bafflement that I would ask them a question like this so out of nowhere. I've only asked this question only to kids who have at least started working with Test Prep Math so they all know they can't get out of it and I'm not going to help. The older ones ask me to repeat the question and the younger ones just stare at me so I repeat it anyway.<br /><br />That covers the first skill which is to be baffled without tears or frustration.<br /><br />The range of answers I get is breath taking. The best answers are kids who are thinking "Well, I eat it. That's the normal way. Sometimes mom cuts it up." Then they are totally out of ideas and have to invent a convoluted apple eating machine or something. Ideally I'll watch them attempting and discarding ideas before they announce the answer. Other kids go a completely different route and think of apple recipes. By the way, did you ever wonder why apple sauce was invented? You'd know the answer if you were a German in 1870 and you were staring at a bountiful apple harvest rotting in the barn.<br /><br />The answer is always wrong. (Core skill #3, get it wrong).<br /><br />Sometimes the kid names the method so we'll start reading the question again in more detail. (Core skill #2). It says 'describe in detail'. I'll get a correction with more detail.<br /><br />But in analyzing the question, there are the words 'third' and 'best', and these require a much more complete answer. "Are you correct? Prove it to me." I'll ask. Because there is no solution manual for this problem, this requires naming the other 2 (which is the most fun when the child has already forgotten what they are) and then explaining why the third one is not as good as the first 2.<br /><br />There are 2 more even punchier punches behind this question.<br /><br />Years from now, if you can see into the future as far as 3rd or 4th grade, you might see your child turn in a project or paper that is almost complete. You might even see a limited effort. This is unlikely because in 3rd or 4th grade the rubric is usually very detailed. By middle school detailed rubrics don't help. You'll see a range of work from 'good job' to 'way over the top extraordinary' and the kids who hit 'way over the top' impute all of the extra demands from a limited number of words in the rubric. That's what I'm going for.<br /><br />But the most punchy punch of The Apple Question is that for the kids at a certain level of skills, it only takes this single question for them to totally get it. Children usually respond to follow-up punchy questions by demonstrating that they won't get fooled again.<br /><br />An evaluation of long term results are under way.<br /><br /><br /><br />Norwoodhttp://www.blogger.com/profile/09462923179883891369noreply@blogger.com0