November’s “Teaching Children Mathematics” has an article I’ve been reflecting on for quite some time now. The author, Kelly McCormick, teaches preservice elementary teachers (PSTs) and describes her unit on fractions. She makes use of actual fourth grade classroom videos and also has the PSTs solve similar math problems. Both the teacher and student lessons feature two important components of effective instruction: authentic problem solving and the opportunity to deepen conceptual understanding of fractions. The PSTs, divided into three groups, use different methods of modeling their solutions. One of the three groups went off the rails, but a group discussion revealed their misunderstanding (that fractions must be derived from the same whole in order to compare them).
As a special ed teacher, I appreciate the emphasis on taking adequate time, using hands-on activities and authentic problems, to support student learning. My concern is that by fourth grade, kids with a math disability, attention problems, language issues, and social weaknesses, are just not comparable to these PSTs or a classroom of typical learners. The kids I teach are going to struggle to keep up with the work of those who can draw models and talk through their reasoning. My math-disabled students already have far too many misconceptions about fractions. And their class is not going to take the time needed for them to catch up. The class will speed on by, leaving some kiddos in the dust. I’ve seen that happen repeatedly.
Based on her PST feedback, this class was a turning point for many of these preservice teachers. One of them even commented that she understood fractions for the first time. All of that is terrific. Now how do we shape the reality of school so that our fragile learners understand fractions for the first time? More thoughts tomorrow.