The Effects Of Operand Position And Superfluous Brackets On Student Performance In Math Problem-Solving - Info and Reading Options

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Early middle school students have a strong tendency to adhere to the left-to-right principle when solving math problems, which may lead them to overlook the role of brackets within math expressions (Blando et al., 1989; Gunnarsson et al., 2016). However, perceptual features, such as the spacing between symbols, can direct students’ attention to salient features of math expressions that support efficient problem-solving (Goldstone et al., 2017; Harrison et al., 2020). Similarly, superfluous brackets—brackets that do not change the meaning of notation, but can guide learners’ attention to the correct procedure—can help students achieve higher success rates in solving problems (Hoch & Dreyfus, 2004; Marchini & Papadopoulos, 2011). The current study explores how the presence of superfluous brackets and the position of higher-order operands (i.e., multiplication and division) within an expression affect student performance in an online assignment, as measured by assignment mastery speed and average response time. We will recruit at least 280 students in 6-7th grade through an online learning platform. Students will be randomly assigned to one of six conditions in this 3 (Operand position: left, center, or right) X 2 (Superfluous brackets vs. no brackets) design. Students will solve order of operation expressions that are consistent with their condition: 1) brackets-left, 2) no brackets-left, 3) brackets-center, 4) no brackets-center, 5) brackets-right, and 6) no brackets-right. We hypothesize that students who view problems with superfluous brackets will have quicker mastery speed and shorter average response time than those who don’t. We also hypothesize that students who view problems with the brackets to the furthest left will have quicker mastery speed and shorter average response time compared to students who view problems with brackets in the center or to the furthest right. We also predict that the presence of superfluous brackets may positively impact student performance on expressions with higher-order operands that are in the center or right-most position of the expression (e.g., 2+(4*3)+4 or 2+4+(4*3)) by providing perceptual cues to attend to the order of operations. We will discuss the implications of these findings for perceptual learning theory as well as instructional practice. Overall, the results from this study will further explore the roles of perceptual cues in mathematics notation in math. References: Blando, J. A., Kelly, A. E., Schneider, B. R., & Sleeman, D. (1989). Analyzing and modeling arithmetic errors. Journal for Research in Mathematics Education, 20(3), 301-308. Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. (2017). Adapting perception, action, and technology for mathematical reasoning. Current Directions in Psychological Science, 26(5), 434-441. Gunnarsson, R., Sönnerhed, W. W., & Hernell, B. (2016). Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations?. Educational Studies in Mathematics, 92(1), 91-105. Harrison, A., Smith, H., Hulse, T., & Ottmar, E. R. (2020). Spacing out! Manipulating spatial features in mathematical expressions affects performance. Journal of Numerical Cognition, 6(2), 186-203. Hoch, M., & Dreyfus, T. (2005). Structure sense in high school algebra: The effect of brackets. International Group for the Psychology of Mathematics Education. Marchini, C., & Papadopoulos, I. (2011). Are useless brackets useful tools for teaching?. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education. Aristotle University of Thessaloniki.

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