Algebraic Thinking and Habits of Mind: A Systematic Review of Conceptual Foundations and Pedagogical Challenges

Abstract

Algebraic thinking, a cornerstone of mathematical literacy, supports learners in recognizing patterns, articulating relationships, and forming generalizations across representations. However, persistent challenges—particularly in understanding variables, equivalence, and structural relationships—reveal that its development requires more than procedural fluency. Emerging research highlights the role of algebraic habits of mind—cognitive dispositions such as doing and undoing, building rules to represent functions, and abstracting from computation—in fostering flexible reasoning about mathematical structures. This study presents a systematic review conducted within the TÜBİTAK 1001 Project (No. 223K317), synthesizing 41 empirical and theoretical studies published between 1990 and 2024. Following the updated PRISMA 2020 guidelines, the review addresses three objectives: (1) identifying the conceptual components of algebraic thinking, (2) examining recurring cognitive and pedagogical challenges in developing algebraic habits of mind, and (3) deriving implications for instructional design that cultivates structural reasoning and representational fluency. Findings indicate that difficulties often stem from fragmented representational understanding, limited structural awareness, and procedural teaching orientations. The review underscores the importance of integrating multiple representations, scaffolding generalization and justification, and aligning instruction with reasoning-centered practices. These insights inform the design of evidence-based professional learning programs aimed at supporting teachers in cultivating algebraic thinking and algebraic habits of mind.