LINKING A TWO-STAGE CONSTRUCTIVIST FRAMEWORK OF LEARNING ABILITIES WITH BRAIN ACTIVATION: ILLUSTRATIONS FROM FMRI STUDY (FRACTIONS) Ron Tzur School of Education and Human Development University of Colorado Denver

Abstract: In this presentation, Dr. Ron Tzur will address the problem of how task design, rooted in a constructivist framework of learning abilities—reflection on activity-effect relationship—may contribute to studying (mathematical) processes in the brain. Specifically, he will propose linking two stages identified in the learning of a new concept, prompt dependent (participatory) and prompt independent (anticipatory), with measuring brain activation via breaking apart task components. He will illustrate this linkage with analysis of behavioral and fMRI data from participants’ (N=20, ages 22-38) comparisons of whole numbers or of unit fractions. This analysis confirmed a hypothesis that inversion needed for comparing unit fractions would recruit different circuitry than those needed for directly comparing whole numbers (e.g., 1/5>1/7 though 7>5). It also revealed a startling finding of reversal in the five-decade old Distance Effect due to different sequencing of task components—cuing (prompting) first by a number or by an operation. Finally, he will discuss implications of the proposed theoretical linkage (and illustrative findings), particularly the key role that conceptual analysis of learning abilities can play in the design and interpretation of cognitive neuroscience studies.