Saturday, December 16, 2017

Problem 123

Testing season is in full swing in Chicago right now with the majority of test takers in K grade, followed by 1st grade.

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.

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.

I owe a reader a discussion of fractions, and I'll use this article to warm up.

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?"

Here is my response:
  • 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.  
  • The 1st few pages in the book took us about 3 weeks.  Any page could take a week.  Acceleration happens later in the process.
  • Our error rate was about 50% on a good day.
  • 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.  
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.

Page 123, Lesson 5-6, #3:
Connect the points in order from 1 to 3.

Find and name 3 triangles
Try to name a fourth triangle
Color a four sided figure.

Step 1:  Be Baffled
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.

Step 2:  Backtrack
The first challenge is that section 5-3 discusses the naming of line segments, like AB, 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.

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.

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.

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'.

If this were a problem like 72 - 49 = ?, backtracking might be a 1st grade workbook for a day or two.

Step 3:  Dig into the question.
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.

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.

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.

Step 4:  Give Up
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.

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.

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).

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.

On the other hand, what if I trained and drilled 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.

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