Playing with half a balloon? How different considerations and problem characteristics affect problematic word problem solving

Abstract Providing realistic solutions for word problems proves to be challenging. A possible explanation is the influence of individual’s expectations and beliefs about word problems. This explanation was tested in the present study in an out-of-school context. Specifically, the study assessed effects of (1) prompting participants to make realistic considerations, (2) activating individual’s expectations and beliefs about mathematical problems by prompting participants to consider mathematical operations, and (3) problems where the exact mathematical result had varying degrees of applicability in reality, on the number of realistic responses in division-with-remainder problems. An experiment was conducted ( N = 131, 14–61 years), factor 1 “realistic considerations” (with vs. without), factor 2 “mathematical operations” (with vs. without), and factor 3 “problem characteristics” (exact result pointless vs. exact result impractical). There was no significant main effect “realistic considerations,” F (1, 119) = 0.06, p = .801, and η p 2 = .001. Addressing mathematical operations significantly reduced realistic solutions (main effect “mathematical operations”: F (1, 119) = 4.20, p = .043, and η p 2 = .034). Realistic solutions occurred significantly more often with problems where the application of the exact mathematical result would be pointless in reality (main effect “problem characteristics”: F (1, 119) = 4.73, p = .032, and η p 2 = .038). The main effect “age” was significant; F (1, 119) = 3.94, p = .049, and η p 2 = .032. All two-way interactions and the three-way interaction between the three factors were not significant. The results indicate that activating individual’s expectations and beliefs about word problems and problem characteristics significantly influence the generation of realistic solutions.