Latent profile analysis of eighth-grade students’ algebraic reasoning in China: What characterizes students’ algebraic reasoning at different levels

The current study aimed to develop a comprehensive framework for assessing algebraic reasoning in eighth-grade students. This framework integrated three fundamental domains: cognitive processes, content knowledge, and contexts. Within these domains, we identified specific sub-domains: cognitive processes included pattern identification, representation, and justification; content knowledge encompassed numbers and formulas, equations and inequalities, and functions; and contexts consisted of pure and non-pure mathematical situations. The framework was evaluated by administering a paper-and-pencil test to 646 eighth graders in China. Latent profile analysis revealed four distinct profiles of algebraic reasoning levels, with significant differences among them. Profiles 1 and 2 struggled with symbolic representations and using graphs for problem-solving, while Profile 4 exhibited proficiency in diverse representations. Profile 3 students showed limited reasoning skills, especially in complex situations. Our findings offered insights into students’ strengths and weaknesses in algebraic reasoning, allowing for targeted instructional interventions to improve educational quality.