TITLE: Typos and Uncertainty AUTHOR: Eugene Wallingford DATE: February 21, 2010 7:32 PM DESC: ----- BODY: Last week, a student asked me why one of my examples in the programming assignment said this:
     > (insertion-sort > '(1 4 2 5 3 6 4 7))
     (1 2 3 4 4 5 6 7)
Shouldn't the answer be (7 6 5 4 4 3 2 1)? Or was there something that he didn't understand? At first, I thought his question was a polite way of pointing out my typo, but as we talked it became clear that he felt some real uncertainty about the answer. How? Surely it was obvious that sorting the list in descending order should produce the second list. This seemed all the more obvious because the previous example on the same page sorted the same input with < and had the correct output! What could he be thinking? Sometimes, I ask myself such things rhetorically, out of wonder or frustration. Over the years, though, I have learned to take these questions seriously, because they are the key to understanding what's going on with my students. In the Case of the Backward Bracket, I recognize a lesson I have learned before: Even the smallest error or inconsistency can create major doubt in the mind of a novice. Originally, I wrote "fragile novice", and it's true that some novices are more fragile than others. But to be a beginner is by its nature to be fragile. Our minds are still learning to see, so when they see something that is wrong we are willing to believe that something is wrong with with us. Learning functional programming and Scheme puts my students in the position of facing problems they feel confident solving -- if only they could use their favorite programming style and language. Right now, though, they struggle with a new way of seeing, and this creates uncertainty for them. It makes them tentative, maybe even scared. They see my typo and wonder what it is they don't get. This lesson means at least two things to me as a teacher. First, I need to be extra careful to weed out mistakes in what I tell, show, and ask them. I want them to be able to focus as much as possible on the necessary complexity in the problems, not on distractions that result from my fingerfehlers. Second, I need to keep my eyes open for moments when this kind of uncertainty and fear begin to dominate my students' minds, whether in class or working on their own. By recognizing the situation early enough and intervening, carefully, I may be able to help them stay on a productive path toward understanding. -----