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.