Spacing Out! Manipulating Spatial Features in Mathematical Expressions Affects Performance

Avery Harrison, Hannah Smith, Taylyn Hulse, Erin R. Ottmar


The current study explores the effects of physical spacing within mathematical expressions on student performance. A total of 2,152 students in 5th-12th grade were randomly assigned to one of four conditions within an online problem set, with terms in algebraic expressions spaced 1) neutrally, with no spaces in the expression, 2) congruent with the order of precedence through grouping terms, 3) incongruent with the order of precedence, or 4) mixed, a combination of the previous conditions. Results show that students who viewed incongruent problems made more errors and had to solve more problems to complete the assignment than those who viewed congruent or neutrally spaced problems. Additionally, students who viewed problems with mixed spacing had to solve more problems to complete the assignment than students who viewed congruent problems. These findings suggest that viewing expressions with spacing that is incongruent with the order of precedence presents challenges for students. Overall, these results replicate prior research in perceptual learning in a natural homework environment and support the claim that physical spacing between terms does influence student performance on order of precedence problems.


perceptual learning; spatial proximity; mathematical cognition; mathematical operations

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