Harvesting Prior Knowledge in Math Classrooms, or, “Everybody Knows Something About Something”

Children have interesting conceptions of infinity.

Proposed: There is more ambient mathematics knowledge in the world than ever before. Knowledge will (never again?) solely reside in libraries. There are more “loose knowledge bits” about math floating around that teachers can use as entry points to interesting lessons about mathematics.

It has been the work of a career to properly value student prior knowledge, and use it as “fuel” for lessons. Consider a set pathway through a topic in which we proceed from a section of a textbook or other published resource. The resource tells us where to begin, what to say, and how to begin to unfold the topic. The resource will lead you through a linear pathway from knowing little, to knowing lots more, about a subject. This is a traditional starting point for teaching and learning.

I offer you another starting point. Years ago, I realized that I could save lots of time by gathering prior knowledge in the room. I came up with the phrase “harvest the prior knowledge.” Harvest your students’ prior knowledge, and use that as your starting point. You might find that your students know more than you think. Having taught hundreds of students math and many other subjects, I have enough of a sample to very nearly certainly say that you will have more to work with, and a more…