I recently rediscovered a story from my teaching career decades ago. It was recalled in a paper written in the after 1990s while working on my master’s degree. The course was “Reading and Writing in the Content Areas,” and I was describing a situation in my grade 7 math classroom.
“Today in class, we started talking about triangles. I put on the board, “the sum of the interior angles is 180 degrees” and I asked them what it means. They honestly did not know. They could read the works perfectly well, but it was something they could not understand. They could not understand it until we started cutting out angles and arranging them to form straight lines, then they could see it and they understood the idea. As I see it, ideas are big and words are small. We can read the words, but we don’t necessarily understand the ideas.”
I am not sure what I meant by my choice of words to describe ideas as big and words as small. In the decades since I wrote this, I have become even more sure of the last sentence. In so much education, we define “things” before we understand them.
It seems to make perfect sense. The lesson proceeds in this way: “hear is something new, and this is what it is.” Once students know what it is, we can explore it in more detail (well maybe, too often we move on once students define it).
In my experience, there are some ideas that students must experience first. Once they know (from experience) that placing the angles (in any order) will result in a straight line which is 180 degrees, then we can define it. I have called this approach to teaching “moving from known to new.” Once students know the idea, then we can give them words to define it.
This seems contrary to common sense but try it and you will find it works.