Instrumental vs. Relational

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Richard Skemp describes instrumental understanding as 'rules without reason'. When he was giving such examples in math, it made me think of my time as a student in high school. I remember learning trigonometric identities and using them to solve problems, but I didn't understand what they truly meant. I did not understand where they came from and why we used them, I only understood how to apply them. This is the main difference between what Skemp describes as relational vs. instrumental understanding. Relational understanding answers why, whereas instrumental only answers how.

Skemp tells us of these mathematical mis-matches, where the student's goal is to understand instrumentally, while being taught by a teacher wants them to understand relationally. Up until grade 10, I was one of these students who only had a instrumental understanding of mathematics. I had an amazing teacher who taught us in this relational way of understanding. This teacher helped me see the details and intricacies of mathematics, and that it wasn't just all about following a recipe or set of instructions.

On page 14, Skemp presents the idea of walking from A to B (arbitrary locations). There were 2 different goals, the first was to get to B, and the second was to create a mental map of the town. This reminded me of the somewhat overused saying, "It's not about the destination, it's about the journey". This quote holds true for many aspects as life, and not surprisingly, also in mathematics. Despite being cliché, this saying bears some truth, and resonates with what Skemp is speaking about.

I agree with Skemp, I do favour a relational understanding of mathematics. That being said, I am a realist and I understand that teachers can get very busy and overwhelmed. Sometimes we are constrained by time and deadlines such that we cannot always explain the finer details. Of course we should always strive for the goal of relational understanding, but in reality this will not always be possible. I do believe that instrumental learning has its time and place and should not be seen as overtly negative. I feel that a correct mixture of both relational and instrumental understanding is the most practical and efficient.



Comments

  1. Susan GerofskySeptember 11, 2019 at 11:51 AM

    Good work, Hugo! I like your balanced approach, and the metaphor of wayfinding/ maps in Skemp is one I really like too.

    ReplyDelete

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