Relation vs. Instrumental Teaching in Mathematics

Week 2 Reflection

Is there a right way to teach math? Is there a method that allows students to learn in the best way? Instrumental or relational? Which is more realistic? These are the questions that I was left with after this week’s reading and lecture. 

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            From my experience, math has been taught to me 90% of the time in an instrumental matter, the focus was always on memorizing the information and knowing how to complete the different problems, but never why it is that way or how come that is how you complete the question. But if the focus was on how and why the rules are the rules, I think that this would make mathematics way too complex for students at the elementary and secondary school level. It was not until my last couple years of university that I myself learned by certain things are the way they are. An example I can think of is for physics (my major). All the way through high school science we were always just give the constants and formulas, never told where they come from or why they are that way. Then in higher-level university classes we would spend several lectures on deriving one single formula that was just given to us in high school and even in first year university classes. I specifically remember in my third year quantum physics class taking over two hours to show that Planck’s constant is 6.62607004×10^-34 m²kg/s and that this is a law of the universe not just some made up constant. This derivation and concept was something that I just barely understood in third year university, and would never expect a student in high school to understand or follow along with that. But I do think that a teacher can briefly explain the history and reason behind formulas, rules and constants to simply get students thinking and interested in the topics and also have something to look forward to if they continue with math and/or science after high school. There needs to be a balance, especially in secondary school, between instrumental and relational teaching methods.
            Reflecting back on my learning experiences in high school and even in university, I think I would have a better understanding of many concepts in my math classes if I had known the reason behind things or how they apply to the real world. Now that I am thinking about it, a lot of the materials that I do remember really well are things that I had a deeper meaning of, and knew why and how they were that way. There are many things that I remember being very simple at the time, but because they were just given to my in basic rules and never explained why it is that way or how they connect to the real world, that I now forget. These include simple things such as long division or multiplication with decimals (not using a calculator). Math is a subject that I tutor a lot and it is often these basic things that I have a hard time remembering, but I can usually remember how to do the more complex things such as the application problems.
            I think it is very important for math teachers to have a balance between relation and instrumental ways of teaching. Instrumental is still important because the reality with math is that there are many rules and steps that do need to sometimes be memorized. But students can still be shown or told how and why things are the way they are and also how concepts and material can be applied to real world applications. Students should have the knowledge and be able to apply it and be creative with their solutions. Math should not always be taught in a way that make students think there is only one way to get to the solution. Many problems can be done in multiple different ways and still have the same outcome or result. This is something that I did not realize until the last few years and I believe that if students were aware of this they would be more inclined to think relationally and creatively, which indicates higher-level thinking. I think more students would be successful in their math classes if more teachers establish a balance between instrumental and relational teaching strategies and are more open to explaining the same problem in different ways.

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