When I set out to be a better parent edjumacation-wize, I chose 3 goals:

- My children would get
*98.6 or higher*on the COGAT - So they could
*succeed*at the really hard program they qualified for with that score even if we cheated to get in - They would learn how to
*teach themselves*math and thus do well in all subjects and life because I'll be darned if I'm going to teach them math.

The 3 goals are the exact same thing; not close, not related, but identical.

Unfortunately, teaching your child how to learn is counter-intuitive and very frustrating. 89% of parents will not let their child learn how to learn enough for the child to get into the 90's on the COGAT. 94% of parents don't go far enough so that their child gets to 95. You get the picture.

Most parents are happy when their child does slightly challenging material like math facts or fractions, practices until mastery, followed by a baby step in complexity and practices a lot until ready for the next baby step. I get really frustrated when working with these kids. I ask them to show me how they did the problem, and they provide polished mechanical algorithms that were invented by an adult. Some kids understand these mechanics, some kids don't care.

When children invent their own mechanical algorithms, their innovations have breathtaking complexity and apply widely to a variety of fields. It takes very little brain power to learn an algorithm. It takes a lot of brain power and a long time to invent one. Each time the child invests an algorithm, their brain increases by 15% in size.

The worst part of letting your child learn to learn is that it doesn't appear that anything is happening. Most of the time, it looks like they are just getting dumber. It's horrible. It's very hard for a parent not to yell at their child while they are learning to learn. With the math fact step-by-step approach mentioned above, it looks like the child is getting brighter because their brain is filling with the mastery of learned math concepts. At least they have a high ITBS score to show for it.

Yesterday, a Power Mom complained about question 15 in Test Prep Math Level 2. The author and Test Prep Kid spent three days on the question and have yet to reach an agreement. I consider it one of those questions where learning to learn takes place.

In response, I got on Skype with the kid to discuss 3 x 31. It took us an hour. She's barely mastered single digit addition.

I would love to get one of these kids an mom or dad in a video to show you how this works, but it would be embarrassing for all involved. Therefore, I'll offer a rough transcript. I'm going to demonstrate the crutches I use to distract me from yelling at my own kids. There are 3 categories of crutches:

- I stay focused on learning. Learning is a priceless skill. Multiplying 3 x 31 is a useless skill. If knowing 3 x 31 was important, I would just tell them it's 93. While they struggle to make sense of what 31 is, I can see learning.
- I can see what is happening as we go through the process, and I have already seen the result in 1 or 2 years with kids who do this. The pay off is huge.
- I've replaced scaffolding with advanced problem solving techniques. The kids never adopt these until high school. Until then, the parent has to suggest them. On the bright side, it gives me an alternative to frustration and yelling. That's why I'm so chipper when I coach.

I want to start with an easier problem and then we'll work our way up from there. Here's how it went:

First, we started with 1 x 30, 2 x 30 , 3 x 30. This didn't go well.

Next we went to this list.

- 2 x 3 = ?, 2 x 30 = ?
- 3 x 3 = ?, 3 x 30 = ?
- 3 x 4 = ?, 3 x 40 = ?
- 3 x 5 = ?, 3 x 50 = ?

I was pleased to find that every time I asked 3 x 4 = ? the child had to think for about a minute to answer the question. I asked 8 times. I got 8 blank looks. A child who does not learn their math facts is slowly building number sense. Eventually, probably in 3rd grade, she'll know that 3 x 4 = 12, but she will really know it intuitively, and this will pay off during pre-algebra.

We were so close to taking the leap to 3 x 31 or 3 x 35, but we ran out of time. With my kids, we repeated this exercise once a week for 3 weeks, and then 82 x 5 was totally doable. 116 x 56 in school a few years later required no mental effort or parental involvement.

What's really cool is when a child sees 48 x 4 and their eyes get wide, and they totally understand it. I don't exactly know what they are thinking, but they can tear apart more complicated arithmetic problems with whatever they discovered, except when they get 4 x 4 = 18, which they get a lot, because I won't let them memorize math facts.

Could you as a parent sit with your child for 60 minutes working through problems in the vicinity of 3 x 31? What happens when the child can't remember what 3 x 4 is even though you've asked the same question 8 times? Of course you can't, no sane parent can.

We did just that, week after week, year after year. We're still doing it. I'm in charge of finding unsuitable problems that take at least 25 minutes of struggling each, and each child is in charge of doing something at school that may involve math but I've never seen it.

I'm struggling with something. I'm a huge fan of your blog and understand the underlying theme of persistence and continuing to work on a problem even if you come up with the wrong answer because that's how you 'learn'. However I'm struggling with the fact that it's been years since I've done advanced math myself and I don't know how to encourage my middle school son to keep working on an algebra or trig problem that I have no idea how to solve myself. I'm trying to apply perseverance concepts that I've learned through your writing, but what would be your advice for parents whose kids are working on material that they don't know how to teach/solve themselves?

ReplyDeleteWhen I started out, I didn't know anything about teaching, coaching, or even parenting. But if it's important, sometimes you have to join the team and start learning. Every problem is solvable on Khan or somewhere, but having that will just undermine learning. I'm in the process addressing this issue on my other blog. Here's a tip. There are only 4 operations in algebra (at this level). There are only 4 equations in trig. Try them all. One will lead toward the solution and 3 won't. Then repeat. It's solving a puzzle, and sometimes trying 10 steps to see which one will work. Then look at the one that worked and ask why. Then say 'beats me' and keep going. Send me the problem and I will demonstrate how to solve it.

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