Epistemological, ontogenic, and didactical learning obstacles in the Pythagorean Theorem: A systematic literature review

Source abstract

Background: Geometry is a fundamental branch of mathematics that develops students’ spatial reasoning, logical thinking, and problem-solving abilities. One important topic in geometry is the Pythagorean Theorem, which remains challenging for many students due to persistent conceptual and procedural difficulties in solving related problems. Aims: This study aimed to identify and analyze students’ learning obstacles in the Pythagorean Theorem from epistemological, ontogenic, and didactical perspectives through a systematic literature review. Method: This study employed a qualitative approach using a Systematic Literature Review (SLR) following the PRISMA protocol. Twenty articles published between 2019 and 2025 from 14 academic journals were selected based on predefined inclusion and exclusion criteria. The collected studies were analyzed qualitatively to identify patterns of learning obstacles and instructional challenges in learning the Pythagorean Theorem. Results: The findings revealed that students’ difficulties were predominantly associated with epistemological obstacles, including fragmented understanding of powers and roots, misconceptions regarding side relationships in right triangles, reliance on trial-and-error strategies when using Pythagorean triples, and inability to interpret the theorem as a meaningful geometric relationship. These difficulties were further reinforced by ontogenic obstacles such as limited prerequisite knowledge, weak visual–spatial reasoning, and poor problem-modeling ability. In addition, didactical obstacles emerged from instructional practices emphasizing formula memorization and procedural computation rather than conceptual reasoning, visualization, and proof. Conclusion: This study concludes that learning obstacles in the Pythagorean Theorem are multidimensional and interconnected across epistemological, ontogenic, and didactical domains. Therefore, mathematics instruction should integrate conceptual understanding, visual representation, and contextual problem-solving activities to support meaningful learning of the Pythagorean Theorem.