The interaction of linguistic and arithmetic factors affects adult performance on arithmetic word problems

Performance on word problems is influenced by linguistic and arithmetic factors, and by their interaction. To study these factors and interactions, we manipulated linguistic and arithmetic factors independently in a within-participant design that included complexity parameters (a) in the domain of arithmetic: carry/borrow (no-carry/borrow vs. carry/borrow), operation (addition vs. subtraction), (b) in the domain of linguistics: nominalization (nominalized vs. verbalized form), and (c) linking the two domains: lexical consistency (linguistic predicate locally consistent vs. inconsistent with mathematical operation). Response times of 25 students solving 320 one-step word problems were measured. All four factors showed a main effect on response times, and interactions between linguistic and arithmetic factors affected response times. These interactions were observed when the linguistic and arithmetic factors were conceptually linked. Our results highlight that not only the linguistic and arithmetic complexities of an item contribute to the difficulty of a word problem, but linguistic and arithmetic factors interact. We discuss the theoretical implications for the numerical and the linguistic domain as well as the possible impact of domain-general characteristics, such as working memory limitations as a potential reason for the observed interactions between numerical and linguistic attributes.