Students depend on the Pythagorean theorem: Analysis by the three parallel design of abstraction thinking problem

Abstract

Based on students’ geometry knowledge, there are contrast and less relevant skills goals being prepared for the students. Students are more dominant in learning how to apply procedural knowledge so there is a need for students to use the Pythagorean theorem when facing a triangle properties problem. Therefore, this case study aims to analyze how students’ conceptual knowledge depends on the Pythagorean theorem. The analysis uses a cognitive diagnostic assessment framework through the three parallel design of abstraction problem. This study was conducted for students at the senior high school. The findings are the Pythagorean theorem as a result of thinking abstraction at least two of the three design problem formations, including for the effect of claims and metacognitive knowledge them. There is a disconnected conceptual system between the products of thought and the claims elicited so that abstraction is not optimal. Development for in-depth understanding of conceptual experience is needed in the instructional intervention so that more adequate reasoning.