Can our knowledge about apples, cars, or smurfs hinder our ability to solve mathematical problems involving these entities? We argue that such daily-life knowledge interferes with arithmetic word problem solving, to the extent that experts can be led to failure in problems involving trivial mathematical notions. We created problems evoking different aspects of our non-mathematical, general knowledge. They were solvable by one single subtraction involving small quantities, such as 14-2 = 12. A first experiment studied how university-educated adults dealt with seemingly simple arithmetic problems evoking knowledge that was either congruent or incongruent with the problems' solving procedure. Results showed that in the latter case, the proportion of participants incorrectly deeming the problems "unsolvable" increased significantly, as did response times for correct answers. A second experiment showed that expert mathematicians were also subject to this bias. These results demonstrate that irrelevant non-mathematical knowledge interferes with the identification of basic, single-step solutions to arithmetic word problems, even among experts who have supposedly mastered abstract, context-independent reasoning.
Arithmetic problem solving is a crucial part of mathematics education. However, existing problem solving theories do not fully account for the semantic constraints partaking in the encoding and recoding of arithmetic word problems. In this respect, the limitations of the main existing models in the literature are discussed. We then introduce the Semantic Congruence (SECO) model, a theoretical model depicting how world and mathematical semantics interact in the encoding, recoding and solving of arithmetic word problems. The SECO model's ability to account for emblematic results in educational psychology is scrutinized through six case studies encompassing a wide range of effects observed in previous works. The influence of world semantics on learners' problem representations and solving strategies is put forward, as well as the difficulties arising from semantic incongruence between representations and algorithms. Special attention is given to the recoding of semantically incongruent representations, a crucial step that learners struggle with.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.