Construction Of Mathematics Problem-Based On APOS Theory To Encourage Reflective Abstraction Viewed From Students’ Creative Thinking Profile

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Puput Suriyah , S.T. Budi Waluya, Dwijanto, Isnaini Rosyida


The highest category within the cognitive process category is 'to create,' which refers to the creative process. The term 'create' is linked to three cognitive processes: generating, planning, and producing. This conforms to the framework of abstraction-reflective knowledge construction mechanisms theory. In order to generate new scientific knowledge, students must engage in reflective abstraction. This study aims to describe the seven processes of reflective abstraction construction based on the student's APOS theory in constructing mathematical problems, namely in the basic introductory mathematics concepts. This study involved sixty students as the research participants/subjects. Everyone was given a test question regarding the introduction of complex numbers. Based on these answers, four students were chosen according to their level of creative thinking: first, second, third, and fourth. An interview was conducted based on the test results for each level of creative thinking. To confirm the validity and reliability of the research, triangulation was accomplished by displaying data from video interview results and comparing them to students’ written test results. Students at the fourth level of creative thinking demonstrated seven steps of reflective abstraction construction based on APOS theory, i.e., interiorization, coordination, reversal, encapsulation, de-encapsulation, generalization, and specialization. The findings demonstrated that students at the first level of creative thinking with a high level of thinking ability could perform a specialization process, that is, infer solutions from the roots of quadratic equations that can be solved using a complex number system. Therefore, it can be stated that students can produce accurate descriptions when applying the scheme to a larger collection of phenomena.

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