Perceptual and Number Effects on Students’ Initial Solution Strategies in an Interactive Online Mathematics Game

Abstract

This study investigated the effects of 1) proximal grouping of numbers, 2) problem-solving goals to make 100, and 3) prior knowledge on students’ initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state. We recorded students’ solution strategies and focused on the productivity of their first steps—whether their initial action led them closer to the goal. We analyzed log data within the game from 227 middle-school students solving four addition problems and four multiplication problems consisting of a total of 1,816 problem-level data points. Logistic regression modeling showed that students were more likely to use productive initial solution strategies to solve addition and multiplication problems when 1) proximity supported number grouping, 2) 100 was the problem-solving goal, and 3) students had higher prior knowledge in mathematics. Furthermore, when problem-solving goals were non-100s, students with lower prior knowledge were less likely to use productive initial solution strategies than students with higher prior knowledge. The findings of the study demonstrated that perceptual and number features influenced students’ initial solution strategies, and the effect of number features on initial solution strategies varied by students’ prior knowledge. Results yield important implications for designing instructional activities that support mathematics learning and problem-solving.

Keywords

• mathematical strategies
• perceptual grouping
• individual differences
• mathematical structure
• algebraic knowledge