Semantic congruence in arithmetic: A new conceptual model for word problem solving

Abstract

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.

What we count dictates how we count: A tale of two encodings

“…Thus, the schema theory and the Situation-Problem-Solver model both struggle to account for the results of our six experiments. On the other hand, those results are well within the scope of the new Semantic Congruence (SECO) model, which provides a conceptual framework for arithmetic word problem solving (Gros et al, 2020).…”

“…When no relevant solving algorithm can be specified from the interpreted structure, then solvers may attempt to engage in semantic recoding by using mathematical knowledge to construct a new representation of the problem at hand. When performed successfully, this semantic recoding makes it possible to use different solving algorithms compatible with the new constructed representation (Gros et al, 2020). Fig.…”

“…Yet, it has been argued that by relying on the notion of situation model, the Situation-Problem-Solver approach neglects some interpretative effects at play in mathematical word problem solving. Indeed, this model does not directly include the idea that different models of a given problem statement can be built, depending on the solver's viewpoint (Gros, Thibaut, & Sander, 2020).…”

“…9: Structure of the SECO model. Reprinted from "Semantic congruence in arithmetic: A new model for word problem solving," by H. Gros, J.-P. Thibaut, & E. Sander, 2020, Educational Psychologist, 55, pp. 0046-1520 For instance, in the case of the problems used in this study, SECO would predict that a cardinal problem featuring marbles will activate the solver's world knowledge about marbles (e.g.…”

The cognitive cost of semantic recoding: An eye-tracking study on arithmetic word problem solving

“…It has also been suggested that general semantic knowledge about the entities featured in a problem interfere with its solving process, by means of an interpreted structure describing one's interpretation of the situation depicted in the problem (Bassok, 2001). More recently, the SECO framework (Gros, Thibaut, & Sander, 2020a), suggested that an initial semantic representation is encoded based on the problem statement and on the solver's general, non-mathematical knowledge about the entities it features. This approach notably predicts that an inappropriate encoding of a given problem statement may sometimes be semantically recoded into a new representation, in an attempt to overcome a dead end and find the solution to an arduous problem.…”