Exploring how understanding of the equals sign relates to additive and multiplicative equivalence performance beyond arithmetic fluency.

A strong foundation in arithmetic relies on conceptualizing the equals sign as a symbol of equivalence. However, it remains unclear whether equals sign understanding predicts equivalence performance beyond arithmetic fluency. In this preregistered study, we examined these relations in a sample of 277 pupils (Mage = 11.4, SD = 0.3; 48% girls) in their final year of primary school. Despite almost all pupils recognizing the equals sign, most interpreted it as a signal to perform a calculation or provide an answer. Some demonstrated an emerging understanding of the symbol as an equivalence relation, defining it as a link between two expressions of the same value or, less frequently, recognizing that equal expressions can be interchanged. This equal value conceptualization significantly predicted both additive and multiplicative equivalence fluency, even after controlling for arithmetic fluency and gender. Notably, this understanding explained more variance in multiplicative than additive tasks, suggesting that multiplicative equivalence may be more demanding for learners. These findings suggest that while arithmetic proficiency is important for success on equivalence problems, knowledge of the relational meaning of the equals sign also plays a role, particularly in more complex equivalence contexts. Overall, the results highlight the need for instructional approaches that extend beyond practice in solving equations by explicitly supporting pupils' reasoning about equivalence.