In this reflection I will be taking a look at the assigned reading for this week and give my thoughts on a particular section of the reading based on my feelings and personal experiences. This reading is from the textbook teaching Mathematics through Problem Solving Grades 6-12 written by Harold Schoen and Randall Charles.
In the first chapter, it gives two reasons why understanding math is important. The first one is: “[…] understanding a topic ensures that everything one knows about the topic will be useful. One will remember things when one needs them and will use them flexibly to handle new situations.” I agree completely with that statement. For instance, different concepts that are learnt in math one year can come up again many years later. For instance, in grade four I learnt how to do long division. We did enough examples that I understood the concept and even though I could use a calculator for long division for most grades after that, I still knew how to do it. Then, in my first year of university long division came up again but instead of just numbers, there were polynomials. So, I remembered how to do long division but I had to put my prior knowledge to use in a new situation. This example demonstrates what the first reason of why understanding math is important. That is just one example though, the book gives a different one but there are many more than just those.
The second reason is the following: “[…] to set understanding as a central goal.” I agree with the second reason because I understand how it feels to actually understand something compared to just memorizing a concept or barely getting by on a concept. When I am learning a new difficult math topic and having troubles with some of the questions from the new topic, it is frustrating. But then, when I work through the questions and finally come to understand the questions and topic, it is very satisfying. I have been in situations in Chemistry or Physics though when, in some cases, I have just memorized what to do without really understanding the concept. It is nowhere near as satisfying then understanding a concept. In general, it feels a lot better when I can talk confidently and fully understand different concepts than just memorize what to do and keep being frustrated. Therefore I agree why this is the second reason they give in why understanding math is important.
This was part of the reading really stood out to me because I could recall on my own previous experiences and make connections to what the main points they were trying to get across.