Blog 2: Personal Reflection on Instrumental vs. Relational Learning

The choice of having an instrumental or relational understanding for students is very subjective among teachers, and I think it really depends on students' learning abilities to see which choice of learning is the best or preferable. In our debate, I think many of us teachers candidates used our learning strategies when we were students and how we think should be a good learning method for our future students. In my opinion, depending on the grades we teach, the overview of math concepts should be introduced first. For example, teachers should introduce the signs of addition (+) or subtraction (-), multiplication, and division. Once it is introduced, or it has been taught "instrumentally", students can then dwell deep into why addition exists, or why division exists, and how these concepts are practical in real life. Provided with these questions, teachers can then explain things such as "When you are at a supermarket, you may want to calculate the cost of each apple, and see which one is the cheapest!", for instance. Teaching students the concept of the order of operations is another example. We first introduce the concepts to students "instrumentally", then we can explain to them why this order of operation, BEDMAS, is important in real life, "relationally".

Furthermore, as we go on to teach at higher grades, complex math concepts such as the Pythagorean Theorem or the vertex form of a quadratic equation, in my opinion, should be taught first "instrumentally" as well. Once students understand fully these concepts and are able to, fluently and correctly, solve questions using the concepts as tools, we can further let them question why and how certain theorems work that way. Of course, the real meaning behind these formulas, proofs and theories is the foundation to a better understanding, but It doesn't necessarily mean that students with instrumental way of learning is wrong or are less knowledgeable than students with relational way of learning. It just means that they both understand the same concepts and that they both know how to apply those concepts as a tool to manipulate them in order to fit their learning framework. In all, I think students have various preferred learning strategies, and it is how they choose to learn that are ultimately important to our math teaching.