Different complex word problems require different combinations of cognitive skills

Anselm R Strohmaier,Sarah Hofer,Michal Berkowitz,Birgit Vogel-Heuser,Frank Reinhold,Kristina Reiss

doi:10.1007/s10649-021-10079-4

Abstract

Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.

Highlights

Word problems have been a focus of research in mathematics education for the past 50 years (Verschaffel et al, 2000)
We investigated the role of predictors of word problem solving by comparing the effects of arithmetic skills, verbal skills, spatial skills, and general reasoning skills on word problem solving performance (Reinhold et al, 2020)
We found that arithmetic skills positively affect the solution probability of Programme for International Student Assessment (PISA) items in adults, this effect was smallest than the influence found for verbal, spatial, and general reasoning skills (Reinhold et al, 2020)

Summary

Introduction

Word problems have been a focus of research in mathematics education for the past 50 years (Verschaffel et al, 2000). Mathematical word problems are considered mathematical tasks in which relevant information is presented as text rather than in mathematical notation (Boonen et al, 2016; Daroczy et al, 2015; Verschaffel et al, 2020). They exist in various forms, ranging from a simple verbal description of a basic mathematical operation (e.g., de Koning et al, 2017) to Extended author information available on the last page of the article advanced modeling problems (e.g., Leiss et al, 2019; Vorhölter et al, 2019). They may be contextualized, but unlike complex word problems, the context is not of functional importance for solving the problem (Strohmaier, 2020)

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