The Mechanism of Didactical Obstacles in the Pythagorean Theorem: From Visual Rigidity to Procedural Failure
), Seth Junior Nti(4)
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Country:
(1) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia
(2) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia
(3) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia
(4) Department of Mathematics and Statistics, Stephen F. Austin State University, United States
Corresponding Author
Learning the Pythagorean theorem is a significant challenge at the junior high school level because students often struggle to understand concepts, connect geometric and algebraic representations, and solve contextual problems. Based on previous studies, students' difficulties indicate the presence of learning obstacles. Existing research has addressed students' difficulties, errors, and epistemological obstacles in solving Pythagorean theorem problems and has presented applications of the Pythagorean theorem. Therefore, this study aims to analyze students' didactic learning obstacles to the Pythagorean theorem topic. To achieve this goal, a qualitative case study was conducted. Data was collected through data triangulation: written tests, interviews, and document studies. At the data-collection stage, 30 students and two teachers participated. Based on the written test results, the answers exhibit various characteristics. At the analysis stage, it is performed using ATLAS.ti software. The results show that there is a form of didactic learning obstacles consisting of visual orientation obstacles and formula procedural obstacles. The Visual orientation obstacles include students' lack of understanding of triangle concepts. The procedural obstacles include students' incomprehension of algebraic representations, understanding of problem-solving, understanding of procedures beyond integers, and application of Puythagos' theorem formulas. Visual orientation obstacles cause formula procedural obstacles. The didactic factor that creates obstacles is the way the topic is presented and the teacher's approach to designing learning. Didactic obstacles analysis is an important step in formulating a hypothesis about how a concept should be taught. By knowing the didactic obstacles, teachers or researchers can develop a more accurate Hypothetical Learning Trajectory (HLT). This will lead to the design of learning activities that anticipate common mistakes and misconceptions.
Keywords: didactical obstacle, learning obstacle, topic presentation analysis, textbooks, pythagorean theorem.
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