Instrumental ways of understanding Mathematics works for some students and in some situations but it is not the best way to understand a concept or have it be applicable to other fields. Something that excites me about Math education is that it develops critical thinking skills and is connected to many different areas. However, if it is taught purely instrumentally, that application may not be as accessible to students. Reading this reminded me of the times I was in courses at university and started making connections about things I was taught in high school. I was finally able to make relational connections as my understanding grew. I don't think students should have to go into University Math to have a relational understanding of Math. I also reflected on the general dislike of Math I have seen in many students and I wonder if that is because they were taught instrumental knowledge and it seems irrelevant and hard to grasp. Students desire there to be meaning and purpose in what they are doing. I appreciate the map example (page 14) presented by Skemp; students who have an understanding of where a certain skill fits in a bigger picture will be able to connect the skill to different concepts and fields.
I generally agree with Skemp; relational understanding is deeper knowing and therefore more adaptable and long-lasting. However, sometimes learning instrumentally first makes the relational connections easier to present. Overall, I think having a goal of communicating meaning and connections in Mathematics should be a primary goal in Math education, not just teaching a certain skill.
Hi Christine, it is interesting to note your perspective that instrumental learning can sometimes pave the way for easier relational connections. Could you provide an example or specific scenario where starting with instrumental learning actually enhanced the later development of relational understanding in mathematics?
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