Conceptual technique for comparison figures by geometric thinking in analysis level

Abstract

In underdeveloped countries, research in mathematics education has been mostly focused on students' geometry abilities based on levels, learning approaches, and textbooks. But, thinking process and level are a problem relevant to the low quality of student achievement. The process and level of students' thinking are due to the conceptual system in operating. In this study, a geometry question at the analysis level was designed to investigate conceptual systems. Students represent and compare two figures by their techniques. Data obtained from the survey and narrative study. Data were analyzed based on three components of activity: input, internal processing, and output. Students represent by copying, revising symbols, rummaging objects, and reconstructing properties. They analyze property geometry on the building block or spatial representation. Students compare through one of the two process models of think, namely: object extraction techniques to structure-property connection and inter-object connection to property extraction. The systematic paths of the two models are different. One produces a creative conceptual formulation before extracting geometry properties. Its creativity is involved in comparisons so there is a leap to a more objective point of view. Therefore, conceptual systems and construction for the conceptual formulation are two ideas for learning situations or solving problems.

Keywords

• Conceptual system
• Figural representation
• Geometric thinking

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