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.

算术问题解决是数学教育的关键部分。但是，现有的解决问题理论不能完全解决算术单词问题的编码和重新编码中的语义约束。在这方面，讨论了文献中现有主要模型的局限性。然后，我们介绍语义一致（SECO）模型，这是一个理论模型，描述了世界和数学语义在算术单词问题的编码，重新编码和解决中是如何相互作用的。SECO模型解释教育心理学中的标志性结果的能力是通过六个案例研究进行审查的，这些案例研究涵盖了先前作品中观察到的广泛影响。提出了世界语义对学习者问题表示和解决策略的影响，以及表示和算法之间在语义上不一致所带来的困难。特别注意语义不一致的表示的重新编码，这是学习者努力奋斗的关键步骤。