Lets have a brief aside to discuss something important about mathematics.

Mathematics is *not* a fact-based subject.

That is not to say that we don’t learn true things in math, nor that facts don’t have a role to play, only that learning a mathematical idea is very different from learning a fact like “The Confederation of Canada took place on July 1st, 1867.” I have that date memorized because we have an annual celebration of it, but mostly because my Mom was a Grade 7-8 history teacher.

A mathematical idea can be memorized. For example:but that isn’t the same thing as understanding it. My current thinking is you don’t fully understand mathematics until you build it yourself. That is what I’m trying to help with in this blog.

How to derive the quadratic formula from scratch. (Assuming you remember how to complete the square, subtract fractions, and know about positive and negative square roots. Which, I’ll grant you, is asking a lot.)

But that being said there are somethings that are a pain to work out every time. Multiplication was a stumbling block for me in grade school. My fellow students learned the times table by memorization and were able to rapidly give answers to questions. Memorizing the multiplication table was very difficult for me, so I’d be stuck figuring it out each time.

Ben Orlin has two great posts on this subject: one on the evils of memorization and another on when memorization is useful. Reading them inspired me to write this post.

For further discussion: How does the memorization debate play out in your favourite subjects?

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*Related*

I am a support teacher. (And the Mom who used to teach grade 7/8 History.) When I am helping students who are struggling with Math, it becomes obvious pretty quickly whether they “know” the number facts (i.e., memorized the multiplication tables) or whether they understand the concept (i.e., why common denominators are needed to add/subtract fractions). In the first instance, I encourage using a multiplication table or a calculator, but in the latter situation, it is necessary to go back to the fundamentals to master the concept using models or drawings. Sometimes students struggle in both areas, so plenty of support is needed, usually with examples using single digit whole numbers. Students who know the number facts and understand the concepts are not sent to me for support.

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