Exploratory Study of Children's Multi-Digit Multiplication and Division

Despite the significant role of multiplicative reasoning in facilitating students’ mathematical learning, there is little research on children’s use of and reasoning with different approaches to multiply or divide multi-digit numbers. In addition, many students finish fifth grade with a lack of multiplicative reasoning strategies. This project will improve STEM education by studying the various strategies taught to and used by students for solving multi-digit multiplication and division to develop a more cohesive understanding of children's multiplicative reasoning. The work will also support teachers’ ability to better support students’ multiplicative reasoning strategies via professional development videos that help them learn about students’ strategies.

This three-year, exploratory, learning strand project focuses on studying 4th-6th grade students’ multiplicative reasoning in the context of multi-digit multiplication and division. This project utilizes a mixed-methods approach and will collect large-scale data with paper-based measures, followed by interviews to integrate empirical data from psychological (observational data, assessment scores) and embodied perspectives (eye-tracking, gesture). This approach will allow for triangulation of psychological measures of multiplicative reasoning, children’s video-recorded actions in problem solving, and analysis of children’s written and spoken discourse. Thus, the project will: 1) examine and document the range of strategies children use to solve multi-digit multiplication and division tasks; 2) examine students’ exposure to and teachers’ use of different approaches to multi-digit multiplication and division, as well as the effect of such approaches on children’s mathematics; and 3) explore how eye-tracking data and gesture is associated with children’s strategies when solving multiplication/division tasks. Fulfillment of these objectives will result in specific activities and products over the funding period of the project. First, findings will allow for an improved understanding of how children solve multi-digit multiplication and division tasks. This includes how exposure to different approaches to multi-digit multiplication/division interact with their reasoning and problem solving. Second, recorded videos and images of student work will allow for creation of a publicly available repository of children’s strategies. This repository will be available to teacher educators for use in the professional development of teachers.