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.

Acknowledgments

We thank our colleagues from the IDEA and the LEAD labs who provided insight and expertise that greatly assisted the research. We thank Jay Boussier and Katarina Gvozdic for assistance with proofreading.

Additional information

Funding

This research was supported by the French Ministry of Education and Future Investment Plan under Grant CS-032-15-836-ARITHM-0; French Ministry of Education and Experimental Fund for the Youth under Grant HAP10-CRE-EXPE-S1; Regional Council of Burgundy, Paris Feder Grants under Grants 20159201AAO050S02982 and 20169201AAO050S01845.