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Depending on the textbook or the teacher, children may learn to multiply and divide in different ways. These varying approaches seem new to many adults, but are actually several hundred years old.

Over the past several decades, alternatives to standard multiplication and long division have been re-introduced into the U.S. curriculum. Unfortunately, there is little research on which approaches help students, and which should be left out of the classroom. Professor Karl Kosko, Ph.D., from the School of Teaching, Learning and Curriculum Studies, is seeking answers.

The professor recently secured a grant from the National Science Foundation to examine the reasoning and level of success associated with children using different strategies and algorithms for 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.

"I hope to provide empirical evidence for which algorithms for multiplication and division are most supportive of children's reasoning," said Kosko. "The goal is to help inform which approaches to multiplication and division are most beneficial for students to be exposed to in the classroom." 

This three-year, exploratory, learning strand project will focus on studying over 2,500 children’s multiplicative reasoning in the context of multi-digit multiplication and division. Kosko will study the statistical effect of exposure to different algorithms and visual models taught in schools on how children solve and reason about multi-digit multiplication and division. Additionally, children will be interviewed to better understand how they use and reason with different algorithms for multiplication and division across grades 4-6.

This exploratory project 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 attempt to accomplish several things:

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
3. Explore how eye-tracking data and gesture is associated with children’s strategies when solving multiplication and division tasks.

Fulfillment of these objectives will result in specific activities and products over the funding period of the project.

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 and division interact with their reasoning and problem solving. 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 professional development of teachers.

“Not only will this project help us understand students’ multiplicative reasoning, it will also provide resources for helping teachers, including released videos of students and examples of written work, among other things.”

Kosko also serves as the principle investigator of the , which develops immersive educational experiences in the realm of extended reality.