RE: Skemp on Two Approaches to Teaching and Learning Mathematics
Three STOPS I had while reading this article were 1) when I took a guess of what distinguishes instrumental teaching from relational teaching and whether such distinction matches that of Skemp's own. I have gotten the idea of instrumental teaching from my experience of tutoring children of age 9 to 12. Whenever I taught them how to do 1 digit multiplication, sometimes I tell students that the result is just what it is (i.e. 8*8=64) but I know that the ideal explanation of such result would be by demonstrating the relation between addition and multiplication (that is, multiplication is adding a number by multiple times). 2) As I tried to reflect on my experience of instrumental teaching and relational teaching: I wondered if I focused too much on teaching students what to think instead of how to think 3) When I thought of the possibilities that not-so-well-thought-out relational teaching strategy might exhaust students' brain powers: I realized how important it is to teach students the relational mathematics well to have them acquire relational understanding of mathematical concepts that they are learning.
The issue that can be raised in the Skemp's take on relational learning is that it overlooks the essentials and the importance of instrumental teaching. As a teacher whose English is not his/her primary language, this would sound much as an excuse but there are certain aspects of instrumental teaching that help students develop relational understanding of mathematics. For example, even with teachers explaining the relations and principles so well, students still may find the concepts very hard to understand. Yet, some students would instantly see the 'big picture' after seeing photos/drawings that are used as examples to demonstrate the main concept. Hence, it is justifiable to let students figure the relations themselves with teachers' aid of providing examples, instead of having to point out every detail of the relations between the objects of study.
The issue that can be raised in the Skemp's take on relational learning is that it overlooks the essentials and the importance of instrumental teaching. As a teacher whose English is not his/her primary language, this would sound much as an excuse but there are certain aspects of instrumental teaching that help students develop relational understanding of mathematics. For example, even with teachers explaining the relations and principles so well, students still may find the concepts very hard to understand. Yet, some students would instantly see the 'big picture' after seeing photos/drawings that are used as examples to demonstrate the main concept. Hence, it is justifiable to let students figure the relations themselves with teachers' aid of providing examples, instead of having to point out every detail of the relations between the objects of study.
Fascinating, especially #2!
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