I believe that both instrumental and relational understanding should be the goal of the teachers and the students in a mathematics classroom. The first involves knowing the “how” and the second involves knowing the “why”. As long as marks take part in students’ assessment, and as long as we are bounded with time and the curriculum, instrumental understanding approach to teaching and learning will always be present in mathematics classrooms.
I was a teacher myself and my goal was relational understanding as well as instrumental understanding. I was teaching my students rules about how to solve a problem quickly to get to the right answer but at the same time I tried to relate the concept to other concepts in mathematics, to other subject matters and also to their daily life.
I see that teaching for relational understanding might be time consuming but I do agree with Skemp that it would save time on the long run because students will be able to understand new concepts quickly by relating it to previously learned concepts. They will also make sense of the new concept and will have an in-depth understanding of it when they can relate it to something they experienced in another course or everyday life.
The question I raise here is about the relation between the different way of teaching/learning mathematics and how students look at mathematics and at themselves as mathematics learners?
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