The very first thing I ever did as an academic coach was to teach incomprehensible material.
It was 8 weeks before our gifted and talented test. The school district did not reveal the name of the test. I assumed that googling "how to prepare for mystery test" would be a waste of time, so I made up my own material.
What is the best way to prepare a 5 year old for a test that doesn't require any learned knowledge, a test that will be used to identify top academic performers? Common sense told me a bunch of ridiculously confusing problems on material he's never seen before.
There is a much longer list of sub skills that will help a child get a passing score, but looking at ridiculously confusing problems and trying to figure them out is good for about 90%. I've recently written an article on mistakes, an important topic for ongoing academic work at high levels (aka higher levels that your child's current level). Dealing with mistakes has an official role on the test, but the whole purpose of the test is new and hard problems to see if your kid blinks. A blinking child isn't going to get far enough in the problem to worry about mistakes.
There are other sub skills on the test to see if your child is exposed to rich language or does some math at home, but the test is heavily weighted toward kids who are just going to take their time and figure out a problem. No one is going to take the time to figure out a problem if they are put off by problems that take time to figure out. Kids who have done nothing at all, can't read, no math, no test prep, get into GAT programs because they are OK with hard problems.
Last night I sat down with my kid to cover the 12 math problems I left on the breakfast table before heading off to work. He made a good effort, but he only completed 3 problems, and got them all horribly wrong. We spent about 30 minutes redoing them. Here's how it went:
Me: You're supposed to do the problem this way.
Son: No, YOU'RE supposed to do the problem THIS way.
Me: Stressing random words doesn't make you right.
In these 3 problems were a variety of math topics he hasn't mastered yet. These topics are introduced in 3rd grade, taught in 4th grade, and drilled extensively in 5th grade. For example, fractions. Fractions are presented in school math in this way: 3 1/2 - 1 2/5 = ? This is completely useless, and any child with a shred of intelligence learns that fractions are a waste of time. Even the word problems are completely irrelevant. But by Algebra 1, you see 3 1/2 - (1 2/5)x = -4, and suddenly all of Pre Algebra is needed in order to solve x, including fractions, order of operations, negative numbers, and equation transformations.
Will my child master Algebra at a young age? No. He will become adept at Pre Algebra, and when he see's Algebra for the first time in school it will be really easy because it's all sitting in buckets in his brain waiting for light bulbs to go off. But mainly, he'll be used to taking a long time to figure out really hard material with a lot of moving parts. For little kids, I call this skill "Being Baffled", and it's the biggest skill of all. For older kids, it consists of being patient with a lot of new syntax like dx/dy, limit of f(x) over d as d approaches 0, the word tangent, as he comes to terms with calculus. Someday in college, when all of the kids are baffled in Organic Chemistry or Chemical Engineering, one baffled kid is going to just keep chugging along.
I've been at this for 7 years so far with my kids and a few other kids that I've worked closely with over a long period of time. I'm going to present my refined curriculum in the next article. I never expected that I'd be teaching calculus to a 12 year old who hates math, but that's where it leads. In the link on the upper right Chapter 4 - How To Create A Gifted Mathematician I presented exactly what I did as I did it, updating this page every 18 months or so, and now I can confidently state that it works way beyond expectations.
Wednesday, June 28, 2017
Tuesday, June 20, 2017
Dealing with Mistakes
A reader posted a comment on the last article asking for clarification on my comments about mistakes. I'm probably not going to get this right on the first try, but here is my Policy Statement on Mistakes. I owe everyone this because I have been advocating doing math at grade level + 2 starting in Kindergarten or 1st grade (if you're late and catching up) and of course no kid can actually do that. Until they do.
My Policy Statement on Mistakes
When I sit with younger children, I witness numerous skills emerging that I see fully matured with older kids on more advance material. I've got 2 kids who are 3 years apart, and I work with each of them one after the other on Saturday and Sunday so I see it every week. Before I did any of this, I read George Poyla's manual on how to do high school Geometry proofs and rewrote it for a 5 year old.
I see some really cool skills develop. I need to get these skills to a very high level so we can do very cool things by high school or later. Also, these skills are needed to survive in our GAT program and to get really high scores on tests.
Go www.IXL.com/Math. You can click on each grade and see a list of things that you probably think are skills because school refers to these as math skills. (You can do this for other subjects as well.) They are not skills. Comparing a rational number is not a skill (if you picked 6th grade). Almost nothing your child is going to do in a math workbook is even remotely a skill. I'd like hack into their website and leave a virus so that after each item, for example "Division facts for 2,3, and 4", the virus would append "is not a skill".
Let's say I sit down with your 5 year old and give her this problem: XII - IV = ?. I actually did this with a table full of Kindergartners. They all got it wrong. One kid wandered away from the table. What I did next depends on the kid and where they are with their own personal skill set level. I brought out little bags of Doritos.
Some kids think that math is all about a problem that already has a solved solution. I'm going to assume they get this from their overly stressed out helicopter parents. These kids are a mess. This is level 0. These kids hurry through problems and will do anything to get the right answer so they can move on to the next problem. If they get it wrong, they are upset.
For these kids, I change the question. I want to know how they solved it. I want to know how XII and IV work. What are the rules? It turns out each of these is a mini math problem in disguise. What are the mini math problems?
I'm usually working with material that is more complicated that a one step 3 + 7 = ? problem so I want them to restate the problem into 2 mini problems. With something that is way over their heads, I want to start with something easier like I + II = ? and just work our way back to XII + IV even if it takes many days, which it usually does until they really get it.
After a few weeks of this, it should be clear to the child that we're working with material that they are not the slightest bit competent on so I'm not really interested in XII + IV = ? I'm interested in how to solve this problem even though you don't know what XII + IV is. We're lucky to get through 2 or 3 problems in one sitting. Maybe even 1 problem.
If the child has a working memory deficit (thanks to school curriculum), the child has a really hard time keeping XII (the mini problem) and IV (the other mini problem) and XII + IV (the third mini problem) in their brains the whole time and is always lost. This is going to take at least 6 weeks for working memory growth to kick in. This is a big problem on GAT test prep. If you jump ahead with a 5 year old to EDM Grade 2, every problem is 3 problems in one for a 5 year old. This is why we always work ahead. Once they get XII + IV, it's only one problem to them and they are no longer using skills.
Never, ever, ever in my whole coaching career have I cared if the child can do arithmetic properly. 3 x 7 = 21 will come on it's own because we are going to encounter this a lot in the next few years. By the time they master 3 x 7 = 21 we'll be on to 1/3 + 1/7 = ? and then 1/3(x + 1/7) = ? so they'll never actually be at the point where they are zipping through problems they mastered. They are struggling the whole time trying using survival skills, and this is where skills develop.
So if the kid struggles with 21 + 13 and actually solves it, but gets 45, and it's because they added 20 + 10 and got 40, and 1 + 3 = 5, we'll write 20 + 10 and 1 + 3 together and do it again. Or not. Depends on my mood. I'm in no hurry. I know with 100% confidence that the skills will kick in during the next few months and we'll probably stop doing 2nd grade math by about 8 months later because it will no longer be challenging.
After a few weeks of this (maybe 6 weeks), some rudimentary skills have developed, and I can move on to the next stage. I call this the "Wrong" stage. This is the most awesome stage where the majority of skills develop. Here is my dialog:
My Policy Statement on Mistakes
When I sit with younger children, I witness numerous skills emerging that I see fully matured with older kids on more advance material. I've got 2 kids who are 3 years apart, and I work with each of them one after the other on Saturday and Sunday so I see it every week. Before I did any of this, I read George Poyla's manual on how to do high school Geometry proofs and rewrote it for a 5 year old.
I see some really cool skills develop. I need to get these skills to a very high level so we can do very cool things by high school or later. Also, these skills are needed to survive in our GAT program and to get really high scores on tests.
Go www.IXL.com/Math. You can click on each grade and see a list of things that you probably think are skills because school refers to these as math skills. (You can do this for other subjects as well.) They are not skills. Comparing a rational number is not a skill (if you picked 6th grade). Almost nothing your child is going to do in a math workbook is even remotely a skill. I'd like hack into their website and leave a virus so that after each item, for example "Division facts for 2,3, and 4", the virus would append "is not a skill".
Let's say I sit down with your 5 year old and give her this problem: XII - IV = ?. I actually did this with a table full of Kindergartners. They all got it wrong. One kid wandered away from the table. What I did next depends on the kid and where they are with their own personal skill set level. I brought out little bags of Doritos.
Some kids think that math is all about a problem that already has a solved solution. I'm going to assume they get this from their overly stressed out helicopter parents. These kids are a mess. This is level 0. These kids hurry through problems and will do anything to get the right answer so they can move on to the next problem. If they get it wrong, they are upset.
For these kids, I change the question. I want to know how they solved it. I want to know how XII and IV work. What are the rules? It turns out each of these is a mini math problem in disguise. What are the mini math problems?
I'm usually working with material that is more complicated that a one step 3 + 7 = ? problem so I want them to restate the problem into 2 mini problems. With something that is way over their heads, I want to start with something easier like I + II = ? and just work our way back to XII + IV even if it takes many days, which it usually does until they really get it.
After a few weeks of this, it should be clear to the child that we're working with material that they are not the slightest bit competent on so I'm not really interested in XII + IV = ? I'm interested in how to solve this problem even though you don't know what XII + IV is. We're lucky to get through 2 or 3 problems in one sitting. Maybe even 1 problem.
If the child has a working memory deficit (thanks to school curriculum), the child has a really hard time keeping XII (the mini problem) and IV (the other mini problem) and XII + IV (the third mini problem) in their brains the whole time and is always lost. This is going to take at least 6 weeks for working memory growth to kick in. This is a big problem on GAT test prep. If you jump ahead with a 5 year old to EDM Grade 2, every problem is 3 problems in one for a 5 year old. This is why we always work ahead. Once they get XII + IV, it's only one problem to them and they are no longer using skills.
Never, ever, ever in my whole coaching career have I cared if the child can do arithmetic properly. 3 x 7 = 21 will come on it's own because we are going to encounter this a lot in the next few years. By the time they master 3 x 7 = 21 we'll be on to 1/3 + 1/7 = ? and then 1/3(x + 1/7) = ? so they'll never actually be at the point where they are zipping through problems they mastered. They are struggling the whole time trying using survival skills, and this is where skills develop.
So if the kid struggles with 21 + 13 and actually solves it, but gets 45, and it's because they added 20 + 10 and got 40, and 1 + 3 = 5, we'll write 20 + 10 and 1 + 3 together and do it again. Or not. Depends on my mood. I'm in no hurry. I know with 100% confidence that the skills will kick in during the next few months and we'll probably stop doing 2nd grade math by about 8 months later because it will no longer be challenging.
After a few weeks of this (maybe 6 weeks), some rudimentary skills have developed, and I can move on to the next stage. I call this the "Wrong" stage. This is the most awesome stage where the majority of skills develop. Here is my dialog:
- Kid: 45
- Me: Wrong. Try again.
- Kid: 33
- Me: Wrong. Try again
- Kid: 43
- Me: Wrong. Try again.
- Kid: 35
- Me: Show me how you are doing this step by step.
- Is it 44?
- Me: Your just guessing. Prove it to me.
This dialog is not possible with a child who is at level 0, but it is possible at level 1. You'd think it would be more productive if I just asked them to explain it to me after the first wrong attempt and you would be right. But I need to practice saying "Wrong" with no emotion because I don't care. This is hard to do. I still need practice after all of these years.
If the child doesn't figure this out after a month, I'll just explain it to them, it being this: It's much easier to do math if you do it right the first time and check your work (aka do each problem at least twice before asking if you got the right answer). The stubborn ones don't believe me, but eventually I catch them cheating (aka doing it twice) in order to save time.
If the child doesn't figure this out after a month, I'll just explain it to them, it being this: It's much easier to do math if you do it right the first time and check your work (aka do each problem at least twice before asking if you got the right answer). The stubborn ones don't believe me, but eventually I catch them cheating (aka doing it twice) in order to save time.
Once the kid can explain what they are doing, as in "I add 20 and 10 and then I add 1 + 3, and then I add 30 and 4", they are at level 2. At level 2, they spend a lot more time thinking about the problem and less time worrying about the solution.
At level 2, we can dive into the solution more and I start to demand that I want more than an answer. I want them to figure out how to do each problem in a cheaty way on each and every problem. I'm not longer happy with 20 + 10 = 30, I want them to explain how to do 20 + 10 without thinking. My own kids actually counted on their fingers 10 times from 20, which is great, but now I want them to look at it and think about it. Let's try 20 + 20, 20 + 30, 20 + 40, 30 + 30, etc. until they see patterns. This is listed on the IXL page as a skill, but the skill is actually the kid figuring out how to do this without being taught. I have to provide a) the opportunity, b) the request to do it and c) no help whatsoever. I usually have to do this again next week and again the week after this until they get it on their own.
As a parent, I'm so tempted to explain it to them. As an older parent, I know that if I break down and explain something, I undercut learning and will end up having to explain math the rest of their lives. So I don't explain, and 2 days of work is suddenly 2 weeks of work. It pays off in the end but for those 2 weeks you're thinking that it's a waste of time and your child should just learn a trade and forgo college.
As a parent, I'm so tempted to explain it to them. As an older parent, I know that if I break down and explain something, I undercut learning and will end up having to explain math the rest of their lives. So I don't explain, and 2 days of work is suddenly 2 weeks of work. It pays off in the end but for those 2 weeks you're thinking that it's a waste of time and your child should just learn a trade and forgo college.
At level 2, the kid has already been through the "Wrong" dialog enough times to know where it's heading and spends more time redoing the work and breaking it down and explaining it to himself to reduce the "Wrong" iterations.
In the course of doing this from 1 + 1 through calculus, I haven't found a problem yet that can't be solved by Poyla's two most powerful tools: break the problem down into 2 smaller problems or find an easier version of the problem and just work your way up from there back to the other problem. Sometimes we come across a math concept that the kid needs but doesn't know at all, and we'll go to IXL or Khan and just look for easy spoon feeding problems for the next week or so. Eventually the kid gets to the point where they can devise clever ways to solve a problem on their own on the spot with a brand new complicated problem. But this is level 3 and they won't get there until after TPM.
It's rare that we get past 3 or 4 problems in one setting. The EDM Grade 2 workbooks have 6 problems per page, but this pace is not sustainable for more advanced math, and we didn't actually get up to 6 problems per day in EDM for a few months. Test Prep Math is heavy on logic, working memory, and problem solving skills and ends up being 1 or 2 problems a day.
In EDM, there were days at level 2 where I witnessed exemplary problem solving that resulted in 50% incorrect answers. I grade the work, announced good job and moved on. Some days we had 100% wrong answers and we went out for ice cream, which is the house rule. In subsequent years, I could raise the bar and we don't call it quits until all mistakes are corrected. After 4th grade, I started to apply this approach to reading, science, and writing and it worked.
Summary
If your child is doing math worthy of thinking, your child will be making a lot of mistakes. If your child is not making a lot of mistakes, then they are picking up the bad habits that I described in the beginning of this article, so they are actually getting dumber so move on to harder material.
If your child is making a lot of mistakes, and you and your child are having a hard time dealing with this, then you can concentrate on overcoming your bad attitude toward mistakes and not worry about any other types of learning. This is the big step, a key difference between GAT and average, and the roadblock to the other skills which I've explained in past articles.
There are great ways to deal with the pain of mistakes, including the pain of making a mistake because your child in fact doesn't know how to do the problem and won't ever know without some help.
If your child is making a lot of mistakes, and you and your child are having a hard time dealing with this, then you can concentrate on overcoming your bad attitude toward mistakes and not worry about any other types of learning. This is the big step, a key difference between GAT and average, and the roadblock to the other skills which I've explained in past articles.
There are great ways to deal with the pain of mistakes, including the pain of making a mistake because your child in fact doesn't know how to do the problem and won't ever know without some help.
- Ignore the mistakes and just move on. This is a signal that it's not about right or wrong anyway, which it isn't.
- Do the work over. You should do the problems and get them wrong too.
- Split the problem up into mini-problems and do those. My kids needed a lot of help learning to split problems up. We had to take time off to do all of our math facts the splitting way. (Eg, 6 + 6 is really 2 hands and the 2 invisible fingers, as in 5 + 5 + 1 + 1.)
- Take time off and do something else. Like an IXL page that practices the thing they should have learned but didn't because you skipped it, or a grade level workbook.
- Try an easier problem and make it harder and harder until it looks like the one in the book that's causing trouble.
Because of those last 3 bullet points, my kids are really good at problem solving even though we took so long to get through math workbooks. The silver lining is that eventually your kid gets really fast. I'll talk about that later.
Wednesday, June 14, 2017
The Key To GAT
I'm not sure I can live up to the bold title I chose for today's article, but I was pretty inspired by my last article, so I took my own advice last weekend. Like most of my articles, you have to read it twice to find the good advice because I bury it in off track commentary.
My kids are in a GAT program and doing well because I gave them material that they couldn't do and stopped answering their questions. In the case of the first one, it was 2nd grade math at age 5, which was the introduction to both of us of academic work at home. With the younger one it was Shape Size Color Count in Pre-K.
Does this sound drastic? Their school day is filled with projects, plays, and self directed time. The older boys like to use the self directed time to gang up on unsuspecting victims of network video games because they hacked into the school network and outsmarted the security system that is supposed to prevent this. Last year, they used 6 different math books, none for very long. I had a hard time figuring out what was going on. In other words, it looks like the GAT program doesn't bother to teach anyone anything because this would just bore self learners. So I was right.
I remember the point in which I officially just gave up trying to teach advanced math to a kid who couldn't even do grade level math adequately. It was that point when we started to make real progress. I didn't give up assigning advanced math, just expecting anyone to actually get it.
So I'm doing it all over again. What follows might sound shockingly insane to parents of 4 year olds. Parents of older kids will know that it's shockly insane, but it works. Instead of bothering to teach math at all, I just taught kids how to learn. Here's a bunch of concepts that you have no clue what any of it means nor how to do it, and over the next few weeks (or more - whatever it takes) we're going to do this. In other words, if you take my advice and start doing math at home, I feel your pain because I'm in the same boat.
The other thing I did and am doing right now is to go to IXL and Khan Academy when we come across new math concepts that we skipped and that is causing mistakes. I've got a few other work books (maybe a hundred, but one decent grade level workbook is usually good enough) that I'll read through just so I know what makes up math curriculum for each grade. I think both of these sites have matured to the point where the workbook might not be necessary. IXL has a great table of contents for this purpose. It's harder with Khan Academy but if you start with lesson 1 of some grade and just keep going, you'll find out where your kid is stuck.
Last weekend, the 6th grader and I started calculus. A lesson on Saturday to deal with derivatives and a lesson on Sunday to deal with integrals. I think this is about the 5th or 6th time we've tried something like this and I'm finally at the point as a parent where it goes smoothly. When he was crying his way through 2nd grade math (this was before I learned not to care whether he was getting it, which he didn't), you would have pointed out that he was not only NOT gifted, he was probably behind grade level. Sunday night, I asked him to explain to me what the field of calculus is all about. He gave me a pretty good explanation, but I didn't bother to tell him that the ability to find the slope of a curve or derive the equation of a curve from the equation of the slope turns out to be tools to solve much higher order problems. He's 12, after all, and is not particularly fond of a field that he's so good at. I'll wait until he's 13 to break the news.
The 8 year old is much more stubborn. He kept trying to solve algebraic polynomial equations by staring at them and iterating between possible values of x until he narrowed it down to the answer. So it took a whole week to get Mr. Stubborn to try transformations, which he kept screwing up. He would transform an equation in the wrong direction until it was too complicated, and make mistakes every single time. 4 problems from Khan did the trick, although we had to do the 4 problems twice, and then 4 more problems. It was really hard for me not to teach him the rules of transformation. He'll learn these himself, and in the process learn something about learning.
If I cared that either of them would actually master a math topic, I'm convinced neither of them would master anything. But if they learn how to learn because I'm not helping (other than finding supplemental exercises on IXL or Khan to close gaps), they are going to master a lot more than math.
So what does it mean to be in GAT? For that matter, what does it mean to score at the top on the ITBS, the COGAT, the MAP test?
Have you ever met a parent who's kid not only plays little league baseball, but practices daily with their child, and put the child on 3 traveling teams? Yes, I said 3 travelling team. I know these parents. I know parents of little gymnasts who not only do the same thing but spend a lot more money doing it. Well, GAT is almost nothing more than a kid who spends a lot of time in the academic gym. GAT is the travelling team of academics.
I once asked a travelling team parent how we could improve our baseball skills and he lectured me on all sorts of clever ways. "Get squishy balls and a plastic bat, go into the basement, and throw the squish balls at your little batter as hard as you can. Repeat nightly." I never thought of that. And I never bothered to do it, or visit batting cages each weekend or much of anything else in baseball. The bit more of GAT beyond spending time in the academic gym is doing insane things others don't, and the insane things including letting the child struggle with their work without helping and giving them work they can't do. Travelling team dads also throw hard balls outside at their kid as hard and fast as they can. I do the same thing with math, and vocabulary, and occasionally reading. Usually not reading, because I don't want a kid who hates to read because he has to read a book I chose, but I always do it with math.
The MAP test is our favorite travelling team. Each question a child answers correctly is followed by a question for the next grade level. I think it stops at trigonometry, but we're a few points shy of 99 right now, which is why we're looking at calculus.
I think for both the MAP and possibly the ITBS, grade level + 2 is required to score consistently beyond 95%. I have evidence that a child doesn't actually have to be good at grade level + 2 to get there. A child can master grade level + 2 once, as in one single year, but if the child doesn't master learning this pace will not be sustainable and scores will eventually plummet.
In 2nd and 3rd grade, we took off school math and delved into Test Prep Math. The learning skills in this book are formidable and I don't think further training is on core learning skills is necessary. In prior articles, I reported the research that proved teaching high school geometry to 8th graders results in a poorer performance in math during high school. I think this research has one shortcoming that I'll discuss later. I'm now looking 6 years down the road and see a shot at AB Calculus by freshman year.
My kids are in a GAT program and doing well because I gave them material that they couldn't do and stopped answering their questions. In the case of the first one, it was 2nd grade math at age 5, which was the introduction to both of us of academic work at home. With the younger one it was Shape Size Color Count in Pre-K.
Does this sound drastic? Their school day is filled with projects, plays, and self directed time. The older boys like to use the self directed time to gang up on unsuspecting victims of network video games because they hacked into the school network and outsmarted the security system that is supposed to prevent this. Last year, they used 6 different math books, none for very long. I had a hard time figuring out what was going on. In other words, it looks like the GAT program doesn't bother to teach anyone anything because this would just bore self learners. So I was right.
I remember the point in which I officially just gave up trying to teach advanced math to a kid who couldn't even do grade level math adequately. It was that point when we started to make real progress. I didn't give up assigning advanced math, just expecting anyone to actually get it.
So I'm doing it all over again. What follows might sound shockingly insane to parents of 4 year olds. Parents of older kids will know that it's shockly insane, but it works. Instead of bothering to teach math at all, I just taught kids how to learn. Here's a bunch of concepts that you have no clue what any of it means nor how to do it, and over the next few weeks (or more - whatever it takes) we're going to do this. In other words, if you take my advice and start doing math at home, I feel your pain because I'm in the same boat.
The other thing I did and am doing right now is to go to IXL and Khan Academy when we come across new math concepts that we skipped and that is causing mistakes. I've got a few other work books (maybe a hundred, but one decent grade level workbook is usually good enough) that I'll read through just so I know what makes up math curriculum for each grade. I think both of these sites have matured to the point where the workbook might not be necessary. IXL has a great table of contents for this purpose. It's harder with Khan Academy but if you start with lesson 1 of some grade and just keep going, you'll find out where your kid is stuck.
Last weekend, the 6th grader and I started calculus. A lesson on Saturday to deal with derivatives and a lesson on Sunday to deal with integrals. I think this is about the 5th or 6th time we've tried something like this and I'm finally at the point as a parent where it goes smoothly. When he was crying his way through 2nd grade math (this was before I learned not to care whether he was getting it, which he didn't), you would have pointed out that he was not only NOT gifted, he was probably behind grade level. Sunday night, I asked him to explain to me what the field of calculus is all about. He gave me a pretty good explanation, but I didn't bother to tell him that the ability to find the slope of a curve or derive the equation of a curve from the equation of the slope turns out to be tools to solve much higher order problems. He's 12, after all, and is not particularly fond of a field that he's so good at. I'll wait until he's 13 to break the news.
The 8 year old is much more stubborn. He kept trying to solve algebraic polynomial equations by staring at them and iterating between possible values of x until he narrowed it down to the answer. So it took a whole week to get Mr. Stubborn to try transformations, which he kept screwing up. He would transform an equation in the wrong direction until it was too complicated, and make mistakes every single time. 4 problems from Khan did the trick, although we had to do the 4 problems twice, and then 4 more problems. It was really hard for me not to teach him the rules of transformation. He'll learn these himself, and in the process learn something about learning.
If I cared that either of them would actually master a math topic, I'm convinced neither of them would master anything. But if they learn how to learn because I'm not helping (other than finding supplemental exercises on IXL or Khan to close gaps), they are going to master a lot more than math.
So what does it mean to be in GAT? For that matter, what does it mean to score at the top on the ITBS, the COGAT, the MAP test?
Have you ever met a parent who's kid not only plays little league baseball, but practices daily with their child, and put the child on 3 traveling teams? Yes, I said 3 travelling team. I know these parents. I know parents of little gymnasts who not only do the same thing but spend a lot more money doing it. Well, GAT is almost nothing more than a kid who spends a lot of time in the academic gym. GAT is the travelling team of academics.
I once asked a travelling team parent how we could improve our baseball skills and he lectured me on all sorts of clever ways. "Get squishy balls and a plastic bat, go into the basement, and throw the squish balls at your little batter as hard as you can. Repeat nightly." I never thought of that. And I never bothered to do it, or visit batting cages each weekend or much of anything else in baseball. The bit more of GAT beyond spending time in the academic gym is doing insane things others don't, and the insane things including letting the child struggle with their work without helping and giving them work they can't do. Travelling team dads also throw hard balls outside at their kid as hard and fast as they can. I do the same thing with math, and vocabulary, and occasionally reading. Usually not reading, because I don't want a kid who hates to read because he has to read a book I chose, but I always do it with math.
The MAP test is our favorite travelling team. Each question a child answers correctly is followed by a question for the next grade level. I think it stops at trigonometry, but we're a few points shy of 99 right now, which is why we're looking at calculus.
I think for both the MAP and possibly the ITBS, grade level + 2 is required to score consistently beyond 95%. I have evidence that a child doesn't actually have to be good at grade level + 2 to get there. A child can master grade level + 2 once, as in one single year, but if the child doesn't master learning this pace will not be sustainable and scores will eventually plummet.
In 2nd and 3rd grade, we took off school math and delved into Test Prep Math. The learning skills in this book are formidable and I don't think further training is on core learning skills is necessary. In prior articles, I reported the research that proved teaching high school geometry to 8th graders results in a poorer performance in math during high school. I think this research has one shortcoming that I'll discuss later. I'm now looking 6 years down the road and see a shot at AB Calculus by freshman year.
Saturday, June 10, 2017
COGAT Test Prep Books
The most common question I get is "what test prep book should I get?" The second most common question I get is "how do I get my child to 98% in the shortest possible time with the least amount of effort?"
The answers to these questions are the reason I started this blog in the first place. In 2011, there was no list, no one thought you could take a child from 50% to 99%, and for certain age groups, there was very little material available.
Almost all of material on the market targets K and 1st Grade. A link on the upper right of my website lists these books. This is where the majority of testing happens in the US. What does a parent do for other age groups, like older or younger children?
The easiest, best, most thorough way to create a long term gifted child is simply to start in Pre K, and for those who think ahead, there's Shape Size Color Count and Pre-K Phonics Conceptual Vocabulary and Thinking. I'm fascinated to read the single 3 star review on Shape Size Color Count. I read the reviewers other book reviews and her children moving to third grade material after age 5. My kids didn't start 3rd grade material until 1st grade, because they went into a 3rd grade program at this time, and we bought a fewer books than she did. In fact, we used just these 2 until we got to the K and 1st Grade COGAT test prep material.
After 1st grade, it gets progressively more challenging to find test prep material, and this week I got questions about 5th through 9th grade. Finding material is a real challenge, especially the visual-spatial variety that is the subject of the tests like the COGAT, NNAT, and Raven. For these age groups, the second above question is much more important.
Take a step back and think about these tests. They are used to identify students with strong academic skills, students who are self-learners, students who will do well in a program that is a year or two ahead. Do these students have some innate visual spatial skill that gives them an advantage in literature and science? Of course not. These students have an advantage in solving problems they've never seen before.
There's only one way to teach a child to solve new problems they've never seen before. Give them new problems that they've never seen before that require concentration, rereading, mistakes, fumbling, do-overs, and, in short, learning skills. This is the approach of Test Prep Math in a nutshell, but since it only covers grades 2-4, after that we turn to advanced topics. I've tried quite a bit after this age: advanced science, SAT test prep books, pre-algebra through 8th grade math. I've settled on things that work for us and put the rest on the shelf for later.
In my experience, the difference between a gifted student who gets past the score cutoff and a student who falls short is a parent who lets their child learn versus a parent who doesn't think progress is happening because their child is struggling and intervenes to explain things.
I like material when I observe that the student has to struggle over a long period of time to figure it out and doesn't quite get it while it's being solved. This is where skills grow. My job as a parent or academic coach is to watch it all unfold and assure the student that this is all totally OK. I've written about this extensively in articles on this website.
The biggest challenge I face is when we get stuck on a term or concept that the material expects the child to know and he doesn't know it. This will happen at all ages, but gets more challenging with age. The fact that this setback stretches out the learning experience is a bonus, but it's still a challenge. Depending on whether this is math or not dictates the approach.
We never call a problem "solved" without spending some time analyzing it to see what other gems it holds. What is odd or unusual about the question? Why is it tricky? Is there something fundamental or are their wide applications of what we just did? What lesson did we learn that can help with the next problem. (This is a very long list that includes non technical things like check your work, read the question carefully, don't be fooled by double meaning, it's OK to be clueless, and many other things.)
Our approach to the COGAT or MAP or anything else is to do a few hard problems instead of a lot of problems. If there are 40 questions following a chapter of something, I'll go for the last 2 usually. I'm looking for quantity - as in quantity of time spent on a single problem, and not quality, as in the ability to answer a whole bunch of problems quickly and accurately.
We never really master material, instead we master the ability to navigate and figure out the material. Based on the results, you think my kids know things thoroughly, but they usually don't pick up solidified knowledge until much later. The only thing I'm concerned with is mastering how to learn. Actual knowledge is not my goal, and it's not the goal of the COGAT.
The answers to these questions are the reason I started this blog in the first place. In 2011, there was no list, no one thought you could take a child from 50% to 99%, and for certain age groups, there was very little material available.
Almost all of material on the market targets K and 1st Grade. A link on the upper right of my website lists these books. This is where the majority of testing happens in the US. What does a parent do for other age groups, like older or younger children?
The easiest, best, most thorough way to create a long term gifted child is simply to start in Pre K, and for those who think ahead, there's Shape Size Color Count and Pre-K Phonics Conceptual Vocabulary and Thinking. I'm fascinated to read the single 3 star review on Shape Size Color Count. I read the reviewers other book reviews and her children moving to third grade material after age 5. My kids didn't start 3rd grade material until 1st grade, because they went into a 3rd grade program at this time, and we bought a fewer books than she did. In fact, we used just these 2 until we got to the K and 1st Grade COGAT test prep material.
After 1st grade, it gets progressively more challenging to find test prep material, and this week I got questions about 5th through 9th grade. Finding material is a real challenge, especially the visual-spatial variety that is the subject of the tests like the COGAT, NNAT, and Raven. For these age groups, the second above question is much more important.
Take a step back and think about these tests. They are used to identify students with strong academic skills, students who are self-learners, students who will do well in a program that is a year or two ahead. Do these students have some innate visual spatial skill that gives them an advantage in literature and science? Of course not. These students have an advantage in solving problems they've never seen before.
There's only one way to teach a child to solve new problems they've never seen before. Give them new problems that they've never seen before that require concentration, rereading, mistakes, fumbling, do-overs, and, in short, learning skills. This is the approach of Test Prep Math in a nutshell, but since it only covers grades 2-4, after that we turn to advanced topics. I've tried quite a bit after this age: advanced science, SAT test prep books, pre-algebra through 8th grade math. I've settled on things that work for us and put the rest on the shelf for later.
In my experience, the difference between a gifted student who gets past the score cutoff and a student who falls short is a parent who lets their child learn versus a parent who doesn't think progress is happening because their child is struggling and intervenes to explain things.
I like material when I observe that the student has to struggle over a long period of time to figure it out and doesn't quite get it while it's being solved. This is where skills grow. My job as a parent or academic coach is to watch it all unfold and assure the student that this is all totally OK. I've written about this extensively in articles on this website.
The biggest challenge I face is when we get stuck on a term or concept that the material expects the child to know and he doesn't know it. This will happen at all ages, but gets more challenging with age. The fact that this setback stretches out the learning experience is a bonus, but it's still a challenge. Depending on whether this is math or not dictates the approach.
- We solve an easier version of the problem first and then make it slightly harder on each iteration until we're back to the problem at hand. I have, on occasion, gone back to 1 + 2 and worked my way back to something really complicated.
- For something like parenthesis or fractions or or cosine, we take a break to find something that covers the topic, like IXL or Khan academy.
- For vocabulary, science or otherwise, we take time off to explore the word, its origin and uses, and the word is posted on the refrigerator. For simple vocabulary, I just explain the word, but it still goes on the Word Board.
- It the word is technical concept outside of math, we start a quick research project. 99% of the time, the internet gets the job done. Sometimes we have to mix vinegar and baking soda.
I call this backtracking and we do it a lot. If the child actually knew the material before hand, it wouldn't be "learning how to learn" training in the first place. I think this is the second most common place where most parents get stuck. The first most common place is doing a problem that should take a 5th grader 30 seconds, but doing it with a 3rd grader who needs 40 minutes.
Our approach to the COGAT or MAP or anything else is to do a few hard problems instead of a lot of problems. If there are 40 questions following a chapter of something, I'll go for the last 2 usually. I'm looking for quantity - as in quantity of time spent on a single problem, and not quality, as in the ability to answer a whole bunch of problems quickly and accurately.
We never really master material, instead we master the ability to navigate and figure out the material. Based on the results, you think my kids know things thoroughly, but they usually don't pick up solidified knowledge until much later. The only thing I'm concerned with is mastering how to learn. Actual knowledge is not my goal, and it's not the goal of the COGAT.
Wednesday, June 7, 2017
The Summer of Awesomeness
Every year I eagerly wait for summer so we can plow ahead with some awesome academic work while the rest of the country goes to soccer camp. (For those of you who need soccer camp because you both work, our summer work is about 45 minutes each day so you have no excuse.)
I used to speculate that my average, normal, rotten kids were average, normal and rotten. Since then I've had the opportunity to coach a lot of kids because their parents were struggling to build an At Home curriculum to supplement school (aka the place where learning dies), usually because they were doing Test Prep Math and wondering how it is possible to actually do it.
Every one of these kids I've coached, every single one, is way smarter than my children and every coaching session was ridiculously easy compared to my experience at home when we were getting started.
I realize that summer is also test prep season for many readers. Some of the things listed below are related to the COGAT, but most to the ITBS or MAP test. We don't face a high stakes test again until May of 2018, and it is the MAP.
In each case, if you watched us starting out on a new project, you would think we had no business doing it and my kids should just learn a trade like plumbing and forego college, but I can assure you that plumbing is a very technical field with some brilliant workers, so I think we're stuck with college, and then graduate school, and probably post-doc.
Most of my summer efforts involve putting together an Over The Top Reading Program of books that are so good I read them as well. While this may be the most important part of every summer, it's also the most boring for me to write about so I won't.
When we started Every Day Math 2nd Grade at age 5, my first child was barely adequate at Kindergarten math. Sometimes a single problem would take 2 days. After the first week, we got through 1 page, and I had to get a 1st grade book to help out. He mainly got it wrong. 9 months later, he was zipping along in the 2nd Student Journal and we called it quits because the challenge was gone.
This is the single most important lesson I have learned as a parent and academic coach, and it characterizes everything else we've ever done.
After 3rd grade, I subjected him to the my working draft of Test Prep Math Level 3. His grades were pretty bad and his test scores were falling. He would spend 1/2 hour reading the problem and yell at me because I was making him think. Then we both learned to take our time (probably more me than him) and his progress picked up and the arguing stopped. 2nd most important lesson I've ever learned.
The 2nd child was subject to Shape Size Color Count at age 3 and 4, not to mention Test Prep Phonics (only phonics book written by an engineer) and 1st grade math and EDM 2nd grade went quickly with little to no involvement from me. He also benefited from a summer of test prep where we did Building Thinking Skills through the 4-6 Grade version. I recommend Building Thinking Skills a lot, because there's not much else to choose from, but I think it targets the average. If anyone is thinking 'oh no, my child doesn't find it easy' then read the paragraph above on EDM because I have a whole different approach to what is easy and what is hard, and different expectations for the outcome.
After I got the kids past the basic skills, our summers have really taken off. As a reminder, the basic skills are: be comfortable not knowing what the heck you are doing, read the question as many times as it takes to understand it, make lots of mistakes, and build working memory while you juggle a bunch of new vocabulary words and try to figure out a problem at the same time. Plus go slow. And always have zero expectations so you aren't disappointed.
Here are some examples to inspire you:
I used to speculate that my average, normal, rotten kids were average, normal and rotten. Since then I've had the opportunity to coach a lot of kids because their parents were struggling to build an At Home curriculum to supplement school (aka the place where learning dies), usually because they were doing Test Prep Math and wondering how it is possible to actually do it.
Every one of these kids I've coached, every single one, is way smarter than my children and every coaching session was ridiculously easy compared to my experience at home when we were getting started.
I realize that summer is also test prep season for many readers. Some of the things listed below are related to the COGAT, but most to the ITBS or MAP test. We don't face a high stakes test again until May of 2018, and it is the MAP.
In each case, if you watched us starting out on a new project, you would think we had no business doing it and my kids should just learn a trade like plumbing and forego college, but I can assure you that plumbing is a very technical field with some brilliant workers, so I think we're stuck with college, and then graduate school, and probably post-doc.
Most of my summer efforts involve putting together an Over The Top Reading Program of books that are so good I read them as well. While this may be the most important part of every summer, it's also the most boring for me to write about so I won't.
When we started Every Day Math 2nd Grade at age 5, my first child was barely adequate at Kindergarten math. Sometimes a single problem would take 2 days. After the first week, we got through 1 page, and I had to get a 1st grade book to help out. He mainly got it wrong. 9 months later, he was zipping along in the 2nd Student Journal and we called it quits because the challenge was gone.
This is the single most important lesson I have learned as a parent and academic coach, and it characterizes everything else we've ever done.
After 3rd grade, I subjected him to the my working draft of Test Prep Math Level 3. His grades were pretty bad and his test scores were falling. He would spend 1/2 hour reading the problem and yell at me because I was making him think. Then we both learned to take our time (probably more me than him) and his progress picked up and the arguing stopped. 2nd most important lesson I've ever learned.
The 2nd child was subject to Shape Size Color Count at age 3 and 4, not to mention Test Prep Phonics (only phonics book written by an engineer) and 1st grade math and EDM 2nd grade went quickly with little to no involvement from me. He also benefited from a summer of test prep where we did Building Thinking Skills through the 4-6 Grade version. I recommend Building Thinking Skills a lot, because there's not much else to choose from, but I think it targets the average. If anyone is thinking 'oh no, my child doesn't find it easy' then read the paragraph above on EDM because I have a whole different approach to what is easy and what is hard, and different expectations for the outcome.
After I got the kids past the basic skills, our summers have really taken off. As a reminder, the basic skills are: be comfortable not knowing what the heck you are doing, read the question as many times as it takes to understand it, make lots of mistakes, and build working memory while you juggle a bunch of new vocabulary words and try to figure out a problem at the same time. Plus go slow. And always have zero expectations so you aren't disappointed.
Here are some examples to inspire you:
- Last summer, we discovered that our inability to do competitive math didn't actually preclude doing competitive math. So we've been printing 5th through 8th grade released tests and doing them. You may watch my 8 year old do this and wonder why we bother, but read the paragraph above again about our first experience with EDM and you'll see why an 8 year old is now crushing 8th grade competitive math tests.
- I bought an SAT test prep math book a few years ago as a follow up to TPM. Those first few questions were a disaster. The summer after 5th grade, some of the math practice tests were finished. This year, we turned our attention to the reading comprehension questions after finishing all of the math tests in both books.
- The summer after 5th grade, we decided to try the 8th grade math book in the hopes of getting it out of the way early. The first few weeks were nothing but frustration and dashed hopes for me. You'd think a dad who calls his home 'Math House' would have sons who like math. By the end of the summer, we only completed half of it and had to continue through November to finish. Lesson 3 - summer projects may continue past summer.
- I followed up 8th grade math with Algebra, which was painful, and Trig, which went really well because his insane Chemistry teacher taught the kids the basics of trig with right triangles, and all I had to do was the advanced part.
- We've done writing projects, as in you've got 30 minutes to write something impressive on this topic, but neither of us can stay motivated because his writing assignments are generally really good during the year. It's just in math that schools can't seem to get their act together. But a kid who did 6 essays in the summer is a kid who did 6 more essays than any other kid.
Every few years I think about letting my kids take off math entirely. This year my older child reminded me that I have done this in the past, so I gave him a high school Chemistry book. The table of contents are posted on the refrigerator. His "math" is to take a section, explain it to me, and then complete some of a test that I find online concerning the topic at hand. This is the first time since EDM that things didn't start out on a disappointing note. High school chemistry books are spoon-feeding compared to TPM. Maybe I should have gotten the AP version. I'm pretty excited about this summer project regardless.
I'm also posting vocabulary words 100 at a time on the refrigerator. This hearkens back to the days when we did this for Test Prep Phonics and Vocabulary Workshop. I'm getting these from the SAT books. There are about 20 new words per page in the SAT book that are new to a 12 year old. Anything up there after 2 weeks that isn't crossed out is a word that he'll never care about, so we move on.
The 3rd grade child is a problem. We can't do competitive math forever. I tried his older brothers 8th grade math books, and he could do it, but he doesn't have the maturity to know what he is doing. I bought him his own SAT book, and he can do it, but it seems pointless. He learned some algebra but doesn't have the maturity to really appreciate it. We did some html, css, and java script, but he's more interested in marketing his stupid you tube channel with his website than learning how to program.
I told the 3rd grader that we're not going to look at math again until he's finished with 4th grade, and the heck with his grades and test scores. 4th grade math just teaches a child how not to think anyway. So this summer, he's going to be writing. It will probably be marketing copy, but it will at least be writing.
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