Progressing from additive to multiplicative thinking is a key outcome of school mathematics, making ratios an essential topic of study in junior secondary. In this study, 15 Australian Year 8 students were administered a ratio test followed by semi-structured interviews to explore their conceptions of ratio prior to formal instruction. In this…

This study aims to investigate the obstacles in eighth-grade students' understanding of integer exponents using a mixed method research design. A total of 165 eighth-grade students were given a paper-pencil task and clinical interviews were conducted with 12 students. The findings indicated that achievement of the participants was low, especially…

After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…