Start at an Interesting Middle

A teacher I met long ago encouraged colleagues to come up with ways to start new topics “at an interesting middle.” His logic was that the beginning of many topics was not always that complicated or exciting. On the flip side, advanced aspects were out of reach for a learner new to a set of ideas. So, in the spirit of Goldilocks, teachers should identify questions and activities that are just right: rich enough to be engaging, but still accessible. A good starting lesson should require a bit of a chin up that captures students’ interest and that then motivates them to want to learn the introductory skills and concepts that support doing more work toward understanding that interesting middle. Don’t assume that all prerequisite skills have to be in place. Let the bigger picture questions make the usefulness of those skills clear and then back into foundational abilities. Many of the activities and projects in the Making Math site follow this advice. John Dewey noted that we don’t learn basic skills simply by repeating them, but by engaging in rich tasks that require them. This way they are learned in the context of connections between those skills, prior learning, and the new setting that makes them more accessible, better understood, and more readily applied. Think of math less as a ladder of topics and more as a web with many possible interesting entry points and paths through the ideas and skills. Don’t require mastery before a project; let it develop during the project.