TITLE: Teachers Need Relational Understanding AUTHOR: Eugene Wallingford DATE: October 10, 2010 10:55 AM DESC: ----- BODY: Last week I was pointed in the direction of Richard Skemp's 1976 article, Relational Understanding and Instrumental Understanding, on how peoples' different senses of the word "understanding" can create dissonance in learning. Relational understanding is what most of us usually mean by understanding: knowing how to solve a problem and knowing on a deeper level why that works and how it relates to the fundamental ideas of the domain. Sometimes, though, we settle for instrumental understanding, simply knowing the rules that enable us to solve a problem. Skemp describes the cognitive mismatch that occurs when a teacher is thinking in terms of one kind of understanding and the student in terms of the other. Throw in a textbook that aims at one or the other, and it's no wonder that teachers and students sometimes have a difficult time working together. The paper is a little long for its message, but Skemp does try to cover a lot of ground in his own slow realization that teachers need to see this dissonance as a concrete challenge to their efforts to help students learn. He even considers the sort of situations in which a teacher may have to settle for giving students an instrumental understanding of a topic. But one thing is clear:
... nothing else but relational understanding can ever be adequate for a teacher.
I know that when I am weakest as a teacher, it is either because I am underprepared for a particular lesson or because my understanding of a topic is instrumental at best. I often hear teachers at all levels talk about teaching a new course by staying one chapter ahead of the students in the textbook. While there may situations in which this approach is unavoidable, it is always less than ideal, and any teacher who does it is almost necessarily shortchanges the students. Teaching is so much more than presenting facts, and if all the teacher knows today is the facts his or her students will be seeing a week or so hence, there is no way that student learning can tie ideas together or push beyond 'how' to 'why'. When I think about teaching computer science and especially programming, I think of three levels of activity that give me different levels of understanding:
  1. reading about something, even extensively
  2. doing something, applying knowledge in practice
  3. understanding something at a deeper level
At the third level, I know not only how to solve problems, but when and how to break the rules, and when and how to reason from first principles to create a new method of attack. When I am at my best as a teacher, I feel fluid in the classroom, knowing that my deep understanding of an area has prepared me for nearly any situation I might encounter. I'll close with this quote from Skemp, which alone was worth reading the paper for:
... there are two kinds of simplicity: that of naivety; and that which, by penetrating beyond superficial differences, brings simplicity by unifying.
Many people talk about the virtue of simplicity, but this sentence captures in fewer than two dozen words two very different senses of the word and expresses that the best kind of simplicity both grasps differences and unifies over them. That is what relational understanding is about. -----