Exploring the Impact of Symbol Spacing and Problem Sequencing on Arithmetic Performance: An Educational Data Mining Approach

Experimental research on perception and cognition has shown that inherent and manipulated visual features of mathematics problems impact individuals' problem-solving behavior and performance. In a recent study, we manipulated the spacing between symbols in arithmetic expressions to examine its effect on 174 undergraduate students' arithmetic performance but found results that were contradictory to most of the literature (Closser et al., 2023). Here, we applied educational data mining (EDM) methods to that dataset at the problem level to investigate whether inherent features of the 32 experimental problems (i.e., problem composition, problem order) may have caused unintended effects on students' performance. We found that students were consistently faster to correctly simplify expressions with the higher-order operator on the left, rather than right, side of the expression. Furthermore, average response times varied based on the symbol spacing of the current and preceding problems, suggesting that problem sequencing matters. However, including or excluding problem identifiers in analyses changed the interpretation of results, suggesting that the effect of sequencing may be impacted by other, undefined problem-level factors. These results advance cognitive theories on perceptual learning and provide implications for educational researchers: online experiments designed to investigate students' performance on mathematics problems should include a variety of problems, systematically examine the effects of problem order, and consider applying different analytical approaches to detect effects of inherent problem features. Moreover, EDM methods can be a tool to identify nuanced effects on behavior and performance as observed through data from online platforms.