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http://dx.doi.org/10.7468/mathedu.2013.52.3.271

A Qualitative analysis of students' factorization of xn-1 using a CAS application  

Cho, Yeong Ju (Kyesan Girl's High School)
Kim, Kyung Mi (Center for Curriculum and Instruction studies, Korea University)
Whang, Woo Hyung (Dept. of Math. Education, Korea University)
Publication Information
The Mathematical Education / v.52, no.3, 2013 , pp. 271-301 More about this Journal
Abstract
The purpose of the study was to investigate how students generalize and prove the factoring of $x^n-1$ using a Computer Algebra System application and the role of CAS in this process. The theoretical framework consists of the anthropological and the instrumental approach. In particular, the basis of the Task-Technique-Theorization(T-T-T) frame adapted form Chevallard's anthropological approach of Didactics is utilized. We found that Technique-Theorization emerges in mutual interaction between paper-and-pencil techniques and computer algebra techniques. And this interaction led to the students' theoretical reflection and conceptual understanding. In this process, we could identify three epistemic role of CAS : the role of checking the result, the role of cognitive stimulation and the role of extending thinking. Therefore CAS plays on a epistemic role of checking the result of a task, stimulating the student' cognition and extending their thinking as well as pragmatic role of producing the result of a input.
Keywords
Computer Algebra System; CAS application; Task-Technique-Theorization;
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