Tuesday, December 5, 2017

Advanced Math and Little Kids

I 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.

Let's take the first question first.  How do I teach my child fractions?

Here is my step-by-step*:

  1. 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.
  2. 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.
  3. 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.
#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.

*I will present a more detailed step-by-step but we've got a lot of ground to cover first.

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.  

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.

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.

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.

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.

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 to get the child to 99%.  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.  

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.

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.

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.

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.

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.

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.  


  1. I have a second grader and he is ready to do 4th grade math next month. We're already doing your test prep book 3. Also I am debating between singapore math and beast academy 4. Which one do you recommend? Both are pricey for the entire grade level books but I want to invest in either one of them or both.

    1. I like both of these. Which Singapore math books are you going to get? Which version? The problem is that either course has 1700-2000 problems for 4th grade. If you had 2 sets, you wouldn't have time to do everything, which you won't anyway, so you have to chose material and problems. It's easier just to take one series and go start to finish. I also like Challenge Math, but not as a curriculum. I'm leaning toward Singapore math. I've been reading parent boards, but all of their complaints about curriculum (and every curriculum is the subject of complaints) have to do with their limitations as academic coaches.