Relational Teaching vs. Instrumental Teaching

Read the article written by Richard R. Skemp: Relational Understanding and Instrumental Understanding

• three things that made you "stop" as you read this piece, and why
• where you stand on the issue Skemp raises, and why.

1st stop: While reading the article, the example of instrumental understanding made me “stop”. The student asked why the area of rectangle is given by A = L x B. The teacher “explained” that the formula told to multiply the length by the breadth to get the area of rectangle. Then the student believed that he understood it because he always got the right answer. It remains me of my teaching experience as a 10th grade math teacher. The class I taught was an honour class. Students and parents very cared about the marks. So, at the beginning of my teaching, in order to make my class “efficient”, I presented the ideas straight forward, addressed the formulas, clearly showed them the procedures of problem solving, and then done some practice to master the formulas and procedures. However, by learning from my colleagues and the reflections of my work, I realized that this teaching method could lead to a short-term success on the math exams, but, there were charming beauties behind math, the logics which can have a long-term impact on the ability of thinking and problem solving. Then I tried to adjust my teaching method. I guided students to explore the concepts, formulas, and solving procedures by asking them questions. In my experience of math learning, there are a lot of amazing “tricks” that we have thought by teachers, which can help us succeed in math exam. However, it does not involve real learning and inquiry. In my opinion, it is important to encourage students to think like a mathematician rather then just throw them the formula and ask them to remember it for the exam.

2nd stop: The author mentioned the existence of a large body of teachers and of a large number of text belonging to the opposite camp. It reminds me of the textbook that I used when I was teaching 10th grade. It is the Cambridge IGCSE Additional Mathematics. A “trick” to mesmerized the signs of trigonometric functions in different quadrants was provided on the textbook, which was “ All Students Take Cambridge”. My students applied this trick to the exam very successfully. After this trick was introduced, some students gave up on understanding the concept relationally.

3rd stop: In the article, the author illustrated two kinds of mathematical mis-matches. One of them is Pupils whose goal is to understand instrumentally, taught by a teacher who wants them to understand relationally. I have a very similar experience! When I started to switch to a teaching method that had more focus on the relational understanding, students shown impatience about the complicated process of having real understanding of the concept, because they were having a type of success the other way. 

I am very happy and excited to read this article. It gives me more confidence about what I was trying to do but had a doubt with. This articles remains me of a beautiful quote from another article: A good teacher is in the business of making him or herself unnecessary, of empowering learner to learn without the teacher’s help. The aim is to enable students to get on with life under the own power and to free themselves from dependency on schools and teachers (Labaree). I think the relational teaching can benefit students’ long-term success in their life.

Labaree, D.F. (2004). Teacher ed in the present: The peculiar problems of preparing teachers. In D.F. Labaree, The trouble with ed schools (pp. 39-61). New Haven, CT: Yale University Press.