An emerging methodology for studying mathematics concept learning and instructional design

Our microgenetic research methodology was developed for two purposes: 1) to develop greater understanding of conceptual learning and instructional design that promotes conceptual learning and 2) to develop empirically-based hypothetical learning trajectories for particular mathematical concepts. The challenge in developing the methodology was to afford analysis of the learning process (e.g., the transition), not just identification of conceptual steps through which learners progress. The methodology, developed by the Learning Through Activity research program, was based on constructivist teaching experiment methodology. Modifications were made to data collection for the purposes outlined and a multi-level retrospective analysis was developed.