We know that children do not learn simply because we have given them information that we find to be important. And I hope that we know that just because we list the objectives on the board, cover each one with diligence, and check it off doesn’t mean that we have taught the objective. So what does it mean for a child to learn? What has to take place in order for a child to learn? How do we encourage our students to learn?
While there are many formal definitions and theories about learning, at the heart of each is that the knowledge has to belong to the individual. At the AIMS Center we make it our work to deeply understand how children “come to know.” The teams that I work with are specifically looking at children’s mathematics. Children’s mathematics refers to the understandings that children have constructed from previous experiences.
I have been reading a lot of writings by Ernst von Glasersfeld and Les Steffe. They both discuss the ideas of disequilibrium and reflection. Disequilibrium is that state of being when suddenly something feels wrong, doesn’t meet with expectations or simply leaves one bewildered. It relates to the feeling that one has when, after performing an action for which you have some expectation, there is a different result from the one expected. For me it might be the time that I made cookies that were supposed to be very crunchy, but they turned out super soft. Or, when I read research and stumbled across a word that felt familiar, but it did not seem to have the meaning that I attributed to it. The word was perturb.
In both cases I was put into disequilibrium because what I thought would be the outcome was not. I felt bothered by the outcomes and could not help but ponder, reflect, and muse about resolving the perceived problem. In the case of the cookies, I had to examine my treatment of the sugar in the dough; did I bring it to a roaring boil? Had I stored the cookies with anything that would soften them? In the case of the disconcerting vocabulary, I had to look it up and read it in more contexts. It turns out that I probably didn’t boil the sugar mixture long enough and that perturb can mean ‘upset’ like it is commonly used, but it can also be interpreted as meaning to “make one unsettled,” which is what was meant in the context of my reading. In fact, I could have described both of these situations as having perturbed me, rather than as having caused me some disequilibrium.
What are some situations that you have encountered in which the result was an unexpected one? Did it perturb you? If so, how did you resolve the perturbation?
If you are curious about how this applies to mathematics students, read Brook’s blog post on January 17, 2017.