Supporting children’s conceptual understanding of fractions with manipulatives and gesture

Fractions—their concepts, procedures, and symbolic notation—are well-known for the difficulty they present children, beginning in elementary school, and often, persisting long after. However, promoting children’s development of flexible and robust conceptual knowledge in this content area is critical for their success both in and out of school. The overarching goal of this project is to investigate the tools that support elementary school-aged children’s fraction learning by focusing on two different, yet related areas in cognitive science: physical action on objects (i.e., working with concrete manipulatives) and gesture. The first study identifies the specific mental models about fractions children develop and express through their speech and gesture. The second paper presents a comparative case study that examines how two children’s coordination of speech, gesture, and manipulatives reveals their fraction knowledge. By honing in on how children use gesture and/or manipulatives at times to their advantage and, at others, to their disadvantage, these two studies explore children’s existing knowledge to understand the nature of their fraction concepts, and ultimately, to inform the design of educational interventions that foster learning. The third, and final, study experimentally tests how variations in tools across an instructional intervention affect children’s learning of fraction notation and magnitude estimation. Preliminary results suggest that three of the four conditions—a gesture-based lesson, a manipulatives and gesture-based lesson, as well as a pencil and paper-based control, but not the manipulative-based lesson—led to learning gains from pre- to posttest on magnitude-estimation problems. None of the conditions, however, were successful at promoting transfer to problems, which included area-model estimation and fraction-magnitude comparison, beyond the intervention’s purview. Taken together, these three studies lend further insight into the affordances and constraints of using manipulatives and gesture to support the development of flexible and generalizable mathematics knowledge, concentrating specifically on a topic that challenges children as well as adults—fractions