When my son first looked at a figure matrix, where the child is invited to identify the transformation on the top row and apply the transformation on the first shape in the bottom row to derive the answer, he totally didn't get it.

We started too early, and he was missing a few tools from the tool shed, like all of them.

My abnormal response to a situation like this is to try harder. I should probably take medication or go to therapy for this, but instead, I reach into problem solving skills. The most important problem solving skill of all is to do something similar, but easier. All top mathematicians do this routinely while exploring new material or new problems. When they see complicated equations and big numbers, they start with a simple equation and small numbers until they get it, then move on to the harder problem. The second most important skill is just to do part of the problem. This is formally known as problem decomposition, but for 4 year olds, I modified this a bit by removing all the parts but one.

In the case of the figure matrix, I just put a piece of paper over the bottom row and the answers and asked what is going on with the top row. There's a square, and it took a growth serum and got bigger. No, it didn't get bigger, it got taller. For the quantitative matrices, we usually have a before and after at a party. Before, there were 2 circles and a square, and then another square showed up late, and now there are 4 people at the party.

Once we worked our way up to the full matrix problem, I came back to this technique under the heading of "read the question first", because my son developed the habit of picking the first answer and then guessing his way through the next 3 answers until he got it right. I covered everything but the top row and told him to tell me what was happening. After a few weeks of this, we started doing the whole problem, but only ones he hadn't seen before.

Fast forward 4 years to the next skill level. We're working through complicated problems that require doing an earlier version first. I'm determined to ingrain this skill, because once kids start to "get it" with math, they stop using it. I announced that we are going to work with this one skill for an entire month before moving on.

Fast forward another 4 years to the third skill level. The older one is doing power series and the power formulas. He has a new sixth grade teacher. She formerly taught 7th grade math in a GAT program and just handed them ridiculously convoluted exponential equations instead of teaching them anything and let the kids sort them out.

Take xaxb = xa+b and the 57 variants of this equation. The only way for a 6th grader to know how these equations behave is to substitute small numbers like 2, 3, and 4 and find out what happens. It's easy and it requires far less thinking.

The problem I've been having for the last 8 years is that no one ever wants to use this technique. It's much easier for them to do things the long hard way on the way to an incorrect answer and no understanding. It's easier to spend 2 minutes reading the question and 30 minutes being unable to answer it than spending 15 minutes reading the question and 2 minutes getting the correct answer. These are the habits that I want to change.

There are some children who develop this approach on their own at a young age, and it works for them, so they use it. These children own the term "gifted and talented". There will be at least 2 children who I force to use this approach, and they will be renting the term "gifted and talented" with an option to buy. I don't care. I'm working with what I've got.

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