Factors associated with children’s understanding of mathematical equivalence: An investigation across six countries

Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students’ formal understanding of equivalence has significant and long-lasting effects as it predicts arithmetic and algebra achievement throughout school years. Currently, little is known about the factors influencing students’ understanding of mathematical equivalence particularly across different countries. We have conducted the first large-scale study to explore the factors associated with primary school students’ understanding of mathematical equivalence across six countries (China, England, New Zealand, South Korea, Turkey, and the US). Participants were 2760 primary school students and their teachers (N = 108). Using multilevel structural equation modelling, we found that students’ knowledge of definitions of the equals sign relates to their equation-solving performance. We also found that while teachers’ knowledge of students’ relational strategies does relate to students’ understanding of equivalence, teachers’ knowledge of students’ operational strategies, and the format of arithmetic practice presented in the students’ current year textbooks do not. Using England as the reference country, we found that this pattern was similar across the samples from all the participating countries. Taken together, our findings have important theoretical and practical implications, providing a more complete picture of the individual and classroom-level factors associated with students’ understanding of equivalence.