"The principle is called the power principle or "what comes first, using it or 'getting it'?" The natural mode of acquiring most knowledge is through use leading to progressively deepening understanding. Only in school, and especially in SME is this order systematically inverted. The power principle re-inverts the inversion."
-Seymour Papert, An Exploration in the Space of Mathematics EducationA phrase I often hear is "teaching for understanding", which is a personal goal of mine. I don't just want my students to be able to do, I would like them to understand. So I try to introduce new material with exploratory activities where they wrestle with the material, apply what they already know, and try to create something new. My success varies, and I'm sometimes at a loss for why.
It might be something as simple as this: I'm asking to students to understand something before they know what it is. I would imagine this is difficult indeed.
I really think this is true, especially when the knowledge has use. Much of abstract mathematics has no apparent use though, especially in the lives of our students, but we are still expected to teach it. Seymour's point that we have chosen much of the math we teach in schools based on how easily we can do the calculations on paper is appropriate here, I think.
ReplyDeleteAgreed, the current curriculum can make the power principle difficult to put into practice. For me, the takeaway is the question I will try to more consistently ask myself when planning - "what experience can I give my students with [insert topic] ?" This should give students a better foundation upon which they can develop an understanding.
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