Abstract

Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group.

Highlights

  • Word problems (WPs) are part of the school curriculum and are taught at all levels of education

  • Many children from kindergarten through adulthood have severe difficulties in solving WPs (Nesher and Teubal, 1975; Riley et al, 1983; Lewis and Mayer, 1987; Hegarty et al, 1992; Verschaffel et al, 1992). Both linguistic and numerical complexity contributes to the difficulty in solving WPs

  • Word problems: linguistic & numerical factors in the review, we extended our view of the relevant literature with systematic keyword searches in several databases (Web of Science, Ebsco, Google Scholar, ScienceDirect) including the following terms: WPs, story problems in combination with situational model, performance, consistency hypothesis, language processing, relational terminology, semantic influence, rewording, semantic cues, number size and type, working memory, text comprehension, computational errors, operations, position of unknown

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Summary

Introduction

Word problems (WPs) are part of the school curriculum and are taught at all levels of education. Many children from kindergarten through adulthood have severe difficulties in solving WPs (Nesher and Teubal, 1975; Riley et al, 1983; Lewis and Mayer, 1987; Hegarty et al, 1992; Verschaffel et al, 1992) Both linguistic and numerical complexity contributes to the difficulty in solving WPs. researchers have so far often focused on the one or the other aspect, depending on which field they come from. Different students – e.g., individuals with calculation difficulty, or WP difficulty (Powell and Fuchs, 2014) – may struggle with different types of WPs. Besides domain-general capabilities like IQ, the role of domain specific knowledge and processes were investigated to get a complete account of problem solving, basic cognitive abilities; visual, reading skills, mathematical skills, and metacognitive abilities involved in the solution process. School WPs support stereotypical thinking: WPs do not TABLE 1 | Selected linguistic, mathematical, and general factors investigated in previous studies

Mathematical factors
General factors
Linguistic Complexity and Linguistic Studies
Numerical Complexity and Numerical Studies
Required Operation
Mathematical Solution Strategies
Connecting Linguistic and Mathematical Factors
Findings
Lexical Consistency Effect
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