I am sure that everyone who went through high school is familiar with the quadratic formula. Not all of us have memorized this nor how the formula was derived. For most of us, we need to use this standard formula for solving quadratic equation as if there is no other way to do it. Obviously, this formula needs to be memorized exactly if it is to be of any use. Although some of us who know the formula would be able to re-create from scratch by the process of ?completing the square?, most of us would not. As educator and teachers would probably agree that the person who could derive this formula has a deeper understanding than someone who can merely reproduce the formula from memory. What do you think? Does it mean that simply memorizing the formula is not useful? According to Richard Skemp, anyone who knows and can apply this formula accurately has the so-called instrumental understanding. This is a different kind of understanding from having the knowledge where the formula comes from and how to derive it which Richard Skemp called relational understanding. So we say that both are important depending on our personal biases. Our personal perception affects which one we emphasize in the classroom. There are differences in our perceptions of the purpose of mathematics. Our aim in mind affects what aspects of mathematics we emphasize in the classroom.
Reference: Skempt, R.R. (1977). Relational understanding and instrumental understanding.?Mathematics teaching, 77, 20-26.
Source: http://love4mathed.com/2013/02/on-richard-skemps-instrumental-and-relational-understanding/
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