Our class discussion raised some interesting points regarding the different types of learning. I had been quite convinced that relational learning was the better method, especially after reading Skemp's article. I was quite surprised to see so many students arguing the opposite theory. I would now think that firstly: instrumental learning is better when you simply want to learn how to solve a problem and relational learning is better when you want to build a foundation for more learning. If I were to separate my math students into essential (the ones who simply want to learn the bare minimum) and advanced (the ones who plan to take higher level math) class, I think that I would emphasize relation learning to the latter group.
I feel that to incorporate fluency of the material, it is essential to use relational learning. If I am teaching students how to find the area of a rectangle and I tell them to just memorize " A = a*b ", they will be able to solve that question, but that is all. If I give them graph paper and explain that area is the amount of space inside the rectangle, they will be able to build the formula themselves and, more importantly, they will have an idea of how to find the area of different shapes. However, if I wanted to teach them how to find the area of a circle, it is much easier to simply give them the formula, as they won't have the ability yet to have a relational understanding of the solution. Therefore, I feel that it is not simply a matter of which method to use, but a larger problem of which ideas of math to teach them first.
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