Concrete Learning Materials

We are exploring effective ways to use concrete objects (e.g., blocks, balance scales, counters) as learning tools in mathematics. In particular, we are investigating a method called “concreteness fading” in which you begin with an actual physical object and gradually fade to a more abstract or generic representation. For example, to learn about equality, one might start with a physical balance scale, move to a pictorial worksheet of a balance scale with an equal sign, and end with a traditional, symbolic equation. We are conducting a series of tutoring studies with young children to figure out the best ways to implement concreteness fading and to compare it to other techniques.