Effectiveness of problem-solving and student centred instructional strategies on students’ achievement in algebra: A systematic review

Abstract

Algebra is central to advanced mathematical reasoning and provides a foundation for participation in science, technology, engineering and mathematics. Yet students at secondary and higher education levels continue to experience difficulty with symbolic representation, algebraic language, conceptual connections and the interpretation of unfamiliar problems. This systematic review examined the effectiveness of problem-solving and student-centred instructional strategies in improving students’ achievement in algebra. The review was guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020) framework and drew on peer-reviewed empirical and review literature published between 2015 and 2025. Searches were conducted across Google Scholar, ERIC, ScienceDirect, SpringerLink, Taylor & Francis Online and relevant publisher databases using combinations of terms related to algebra achievement, problem-solving, inquiry, problem-based learning, flipped learning, blended learning, peer tutoring and active learning. Studies were retained when they addressed algebra or linear algebra instruction and reported outcomes related to achievement, conceptual understanding, engagement, mathematical thinking or problem-solving competence. A qualitative thematic synthesis identified five interconnected findings. First, structured problem-solving approaches strengthen strategic reasoning and support the translation of verbal information into algebraic representations. Second, student-centred strategies generally improve achievement and engagement when they are deliberately scaffolded. Third, many algebra difficulties are conceptual rather than merely procedural. Fourth, collaborative and active learning promote explanation, feedback and mathematical communication. Fifth, motivation, confidence, attitude and prior knowledge influence the effectiveness of instructional interventions. The review concludes that no single method is universally sufficient; effective algebra teaching requires a coherent combination of explicit guidance, purposeful exploration, collaborative activity, formative feedback and affective support. The article recommends sustained teacher professional development, curriculum alignment, improved access to learning resources and context-sensitive research on implementation quality and long-term learning outcomes.