THE NATURE OF LOWER SECONDARY STUDENTS’ PROOF COMPREHENSION IN GEOMETRY
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Abstract
This study investigates the nature of lower secondary school students' proof comprehension in geometry. This qualitative inquiry was grounded in a theoretical model of reading comprehension in geometry proofs. The participants were six Grade 9 students who had previously studied geometric proofs, selected through purposive sampling. The research instruments consisted of:
1) Task: geometry proof comprehension, and 2) Task-based interview questions. Data were collected by asking participants to read a given proof and respond to questions to assess their comprehension, followed by task-based interviews. Data analysis was conducted using content analysis alongside transcript coding via the ATLAS.ti program. The findings revealed that most could understand the meaning of terms, symbols, figures, and proof statements. They could identify the logical status of statements, the applied properties, and the logical relationships among those statements. However, only a few participants successfully identified key premises, recognized necessary conditions for concluding, and summarized the main ideas of the proof. A subset of participants evaluated
the reasonableness of the proof's details to determine its correctness, while others accepted the proof as correct without verification. Most participants struggled to apply the ideas gained from reading to constructing more complex proofs. Therefore, the nature of students' proof comprehension in geometry reflects a clear understanding of fundamental concepts, but a lack of holistic understanding and an inability to apply those concepts to more complex situations.
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References
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