Your Students Crave Moral Simplicity. Resist.
Lyell Asher, an Associate Professor of English at Lewis & Clark College, has written a very fine piece, "Your Students Crave Moral Simplicity. Resist." in The Chronicle of Higher Education, 10 February 2017 issue, pp. B3-B5.
The theme of the article surrounds his assignment for his students to read Tolstoy's 800 page tome, Anna Karenina. We find the literary issues he raises to be very interesting. We almost double majored in literature and loved Tolstoy's meanderings. Tolstoy may not have thought of them as meanderings, but with books at 800 pages a pop it appeared to be meandering to me when I was a student. Now let's see where was I? It is the not-necessarily-literary message Asher offers that got to us and got us thinking.
Asher says, "We rarely understand what people mean until we ask them. Moreover, they may not know themselves what they mean until they're asked. This is why, on subjects of any depth and complexity, the dialogue, rather than the sermon, is the model for intellectual engagement."
So here comes the sermon on why we should dialogue more and engage in conversation.
We have, as a profession of college educators, been moving to active learning of some sort or another, whether or not we realize it. We engage students more than we did in the past. We ask them questions and then WE LISTEN to their responses. The days of pulling out the tattered lecture notes from previous years and droning on through them are gone for most, dare I say almost all in the measure theory sense; at least most of us reading this blog post. Moreover, if you embrace what we are offering in SIMIODE you are most likely using the discovery approach of modeling to teach differential equations or other mathematics course of the moment.
Think about the sentence, "We rarely understand what people mean until we ask them." And think about (here I am paraphrasing), "We may not know what we mean until we're asked." These are the assumptions of active and engaged learning. They form the basis of modeling, for we are having inner conversations with ourselves all the time as we pose some term, make some assumption, tweak an expression, throw away a bad start, check an advance or solution looking at us longingly for approval, etc.
So go out and have conversations with yourself, first in building models and then engage with your students to continue these conversations. You will all grow in understanding and your students will learn and grow in appreciation of the mathematics emerging before their very eyes.