I was watching a video on youtube today, Math Education: An Inconvenient Truth and James Blackburn-Lynch’s video response to it. They debate the merit and harm of three math curriculums for 4th/5th-grade math: the traditional method and two quite modern methods.
The difference between the methods comes down to this: the traditional method focuses on getting students to master the ability of doing arithmetic (addition, subtraction, multiplication and division of large numbers) on paper. The new methods emphasize conceptually understanding how long-hand algorithms and mental arithmetic work but avoid giving students the practice of doing arithmetic on paper and instead teach calculator use. So the two warring factions are basically the anti-calculator camp and the pro-theory camp.
But there’s a subtler issue hidden beneath; the fact is that none of the teaching methods in themselves are complete. And the real problem is the same one I’ve been running up against in teaching computer programming. The goal of teaching is to lead the student to understanding. But the method of teaching is by demonstrating and challenging the student to produce results. So there is always the danger that the method of teaching will distract from the goal of teaching.
It’s difficult to wrap my thoughts and my words around this paradox of teaching, but I’ve seen it very clearly in a different domain: in swing dancing. In dancing, I’ve seen in others and experienced for myself many times the moment where understanding is suddenly reached and a new concept is finally learned. And I’ve seen and experienced the long journey leading toward understanding, where you try to follow the teacher’s instructions not knowing where it will lead and struggling to understand–sometimes falsely thinking you understand–until, as if by chance, a random thought connects ideas in your mind and the concepts suddenly become clear.
How can we teach? There must be mastery and repetition balanced with reasoning and intuition. There is synthesis and there is generalization. I suspect that for the most effective learning, you must learn the actions, as a basis for inductive reasoning; and you must learn the words that the describe the concepts, as a basis for deductive reasoning. Both are necessary because the understanding comes when the deductive and the inductive reasoning finally meet and the actions and the words suddenly make sense together.
So as I teach programming (or math, or dance), I have to remember that my method should be to create curiosity rather than to create explanation. I must guide without leading. It’s a fascinating and difficult thing. And I’m still amazed at how much gets learned even with “bad” teaching methods! So for now, I will keep trying new things and looking at learning from different angles and hopefully I will be able to teach myself to teach in the best possible way.
And to keep myself honest with where I stand,
For myself, —What did I do today? I exercised, walked on the beach, went to the farmer’s market, ate a lot of fruits and vegetables. —What do I want to have done today? Besides the above, I wish I had done 5 more hours of contract work, messaged a couple more people on OKC and done the dishes.
For my community,—What did I do today? I organized a dance practice, forwarded a useful email, and blogged about education. —What do I want to have done today? I wish I had chatted with Angela and Megan, Eva or Heather. I wish I had addressed my hesitance to call Deborah and Frank.
For others, —What did I do today? I gave some serious thought to how people learn and came up with some new ideas to try in teaching and became more aware of what I am trying to do in life. —What do I want to have done today? I wish I had bounced ideas off someone– my mom would have been ideal.