Once I understood the meanings of both relational and instrumental, I stopped to notice that I incorporate instrumental teaching into my explanations into my tutoring, for the same beneficial reason Skemp described. I use it to help my student experience the satisfaction and enjoyment of solving problems on his own, since he was not confident in math. This approach boosted his confidence, but I need to continue reminding him how to apply these skills to questions worded or formatted differently, while also mixing in relational teaching. Another point that stood out to me is that relational understanders also use instrumental understanding. With relational understanding as a foundation, using memorization techniques are not an issue, since students can distinguish when it is appropriate to apply them. Finally, I found it striking that instrumental understanding is often favoured over relational understanding to get good grades in tests. Thinking about this in terms of short-term versus long-term goals, instrumental understanding may help students succeed immediately but with some degree of limitation, while relational understanding could take time for knowledge to sink in but can be well-ingrained in our brain.
I agree with Skemp's point that, to understand mathematics, we need relational understanding of it. Instrumental understanding could be perceived as a memorization method, limited in its application. In the teaching position, if we are asked why anything to the power of zero must equal 1 works as a rule, we must prove and explain through relational math. As a teacher I would want to accommodate the students to get a deep understanding of the whys and hows in math if they wonder and wish to know, even if it’s just one student. As I mentioned earlier, looking at short-term memory and long-term memory, understanding the core of math (and any other subject) will definitely develop into a memory that is hard to forget or easy to bring back, because you already learned the skeleton of it.
This is a thoughtful response. I liked how you brought in your tutoring experience to show both the benefits and limits of instrumental teaching, and your point about short-term vs. long-term memory gave the discussion extra depth. The power of zero example was also a clear way to show why relational understanding matters. To go further, you could challenge Skemp’s framework, for example, are there cases where instrumental isn’t just a shortcut but the most appropriate approach? Still, this is a strong and reflective post.
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