Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

Abstract

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals’ ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.