Course Final Reflection

This course was very interesting and enjoyable. It helped me expand my view of mathematics. One of the first things I learned was that math is not primarily about numbers, as most believe, but is made up of multiple strands that are all equally important. If there is one strand of math that the rest depend on, I'd say it's pattern and relations. You can have math without numbers, for instance in symmetry, but you cannot have math without pattern. Math is a study of pattern and how to interpret it. Counting systems are made from patterns, shapes use patterns, measurement uses patterns related to shapes and numbers, data analysis is about analyzing pattern in our world.

We teach math primarily to annoy children and parents. I'm kidding. It is to help students understand the world around them. It also helps them reason and solve problems. Lessons should make the math as applicable to real life as possible and represent math in a relatable way.

I said from the beginning that true understanding of math is more than just remembering formulae. It is understanding why the formulae work as they do. This is affirmed by the new ways of teaching basic operations. We used to be taught an algorithm that unnaturally started with the last digits and was almost impossible to do mentally. Now we teach students to think about what the numbers really represent and how they relate to each other. Beginning with the first digits, the larger numbers, is a much more natural and rational way to do it.

My favourite thing about science has always been hands-on activities. I have learned that there are many ways this type of activity also make math make more sense. The best textbooks are ones that incorporate attractive visuals into the curriculum and make students want to understand what is happening.

This course taught me to think about ways math is used in the real world and what goes into a good math lesson. A lesson begins with a good discussion, involving students as much as possible so that they are participating in their own learning, an explanation of the material, sometimes a read-aloud of a relevant book, and a couple of activities that either teach things through experience or cement learning, and a discussion on what was learned.