Our group had a heated discussion and we all shared our experiences related to the topic. There are two most important questions.
First question regarding whether the two kinds of understanding are distinct or separable. Our answer is they complete each other. Learning math is a fluid process where different parts of the brains are engaged. A student will need the logical side to do computations, whereas areas like geometry require visual imagination, and that is when the artistic part of the brain gets fired up. According to the article, learning that involves using a “mental map” could be considered as relational understanding, and that is equivalent to picturing different dimensions of an object in our example. In UBC course MATH 200, students extensively studied taking derivatives in multidimensional spaces. I found it amazing that calculus and geometry, when used together, is the perfect marriage for solving special problems.
Our group also talked about the kinds of activities that promote each kind of understanding. Academic institutions such as Kumon, Math drills and Time drills are examples. Their goal is to help students succeed in math by practicing a lot of questions, focusing on quantity over quality. Students get exceptionally skilled at doing math by memory instead of actually understanding the concepts. On the other hand, relational understanding happens when a teacher explains a deeper connection, when the students seek out to understand a math topic independently before learning it in-depth, and many other examples.
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