Algebraic Thinking and Algebraic Reasoning in School Mathematics: A Systematic Literature Review Based on the Pirie–Kieren Theory
DOI:
https://doi.org/10.15642/jrpm.2026.11.1.15-36Keywords:
Pirie–Kieren theory, Algebraic reasoning, Mathematical thinking, EducationAbstract
Algebraic thinking and algebraic reasoning are core competencies in mathematics education; however, students often exhibit procedural skills without adequate conceptual understanding. This study aims to synthesize empirical research on algebraic thinking and algebraic reasoning through the lens of the Pirie–Kieren theory of conceptual understanding. A Systematic Literature Review (SLR) was conducted using a structured and transparent protocol. Articles were collected from Google Scholar and Scopus databases using the keywords algebraic thinking and algebraic reasoning, covering publications from 2018 to 2026. From an initial pool of 400 articles, 32 empirical studies met the inclusion criteria and were analyzed using thematic coding. The findings show that algebraic thinking primarily develops in the early to intermediate layers of understanding, namely Primitive Knowing, Image Making, Image Having, and Property Noticing. In contrast, algebraic reasoning is more dominant in advanced layers, including Formalising, Observing, and Structuring. Students’ difficulties in algebra, such as errors in symbolization, limited generalization, and weak justification, reflect transitions between layers and frequently involve folding back processes. This study concludes that the Pirie–Kieren framework provides a coherent and dynamic perspective for integrating algebraic thinking and reasoning, with implications for designing algebra instruction that emphasizes conceptual growth and reflective learning.
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