Abstract
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.
Highlights
The current study explores the effects of physical spacing within mathematical expressions on student performance
Learning mathematics is difficult for many students, in part because of the requirement to learn and execute abstract rules as they apply to mathematical notation
To extend prior research on perceptual learning as it pertains to mathematics performance, we present a randomized controlled trial with upper elementary, middle, and high school students in ASSISTments, an online tutoring system
Summary
The current study explores the effects of physical spacing within mathematical expressions on student performance. 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. Smith, Hulse, & Ottmar proximity, a Gestalt law that posits that individuals perceive objects in close proximity to be a group, has been shown to bias mathematical reasoning This phenomenon in mathematics supports the notion that people rely on perceptual cues to process symbolic notations and are heavily influenced by spatial properties of notation (Goldstone et al, 2017; Wagemans et al, 2012). Regardless of conceptual knowledge, the tendency to use perceptual cues and groupings in mathematics notation is somewhat automatic and has implications for the ways in which individuals interpret, compute, and produce mathematics notation
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