“It has the same numbers, just in a different order”: middle school students noticing algebraic structures within equivalent equations

<p>In this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed algebraic structures in a task using equivalent equations. Findings indicate that students were able to recognise equation pairs that drew on both the associative and distributive properties. A limited number of students were able to notice the general structure and draw on number properties to support their claims, moving beyond using algorithmic thinking. </p>