Promoting Discriminative and Generative Learning: Transfer in Arithmetic Problem Solving

Our goal is to understand some of the conditions that affect transfer in mathematic learning. We present an account of memory models, representations that students form as they practice solving problems. We contrast item-specific, prototype, discriminative, and generative
models in terms of the transfer they support. We test malleable factors of practice that may lead students to form different kinds of memory models. We also study tradeoffs between fluency and generality in learning memory models.

The project focuses on early elementary arithmetic (e.g., 15+8=__), though the malleable factors and memory models are broadly applicable across the curriculum. We propose a parallel line of research with adults learning a novel mathematical relation (base-8 addition with alphabetical symbols).

This project will result in better appreciation of the ways that different forms of instruction (problem solving practice) can achieve particular learning goals (fluency and transfer).