A Gifted High School Student’s Abstraction Process of Divisibility Rules
Abstract
Purpose: Gifted students are often motivated by complex mathematical tasks. Mathematical abstraction allows access to gifted students’ cognitive processes in knowledge construction. The question “How and why do the divisibility rules work?” evokes in them an intellectual need for constructing the working principle of a divisibility rule. Hence, this research focused on a gifted high school student’s abstraction process of divisibility rules. By examining mathematical abstraction through observable actions, this study presents a deeper insight into the gifted student’s thoughts, difficulties, and strategies regarding the working principle of divisibility rules.
Design/Methodology/Approach: The data was obtained from a 9th-grade gifted high school student through clinical interviews in a case study research design. The data were analyzed using the RBC+C abstraction theoretical framework's epistemic actions: Recognizing, Building-with, Constructing, and Consolidating.
Findings: The gifted student could recognize and use the necessary prior knowledge about divisibility to abstract the divisibility rules. In the construction process, the student explored the complex divisibility rules based on the place values of numbers with different digits.
Highlights: The student needed guidance in the process of creating more complex divisibility rules. With the researcher's help, the student could understand even more complicated divisibility rules and consolidate the cognitive way.
Keywords
Divisibility, Gifted student, Mathematical abstraction, RBC+C, Qualitative study
Ethical Statement
Ethical approval for the current study was taken from the Social Sciences & Humanities Ethics Committee at the University of Kastamonu (02/02/2022).
References
- Altun, M. & Durmaz, B. (2013). A case study of process in generating knowledge of linear relationship. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 26(2), 423–438.
- Altun, M. & Yılmaz, A. (2010). High school students’ processes of constructing and reinforcing piecewise function knowledge. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 23(1), 311–337.
- Aydemir-Özdemir, D., & Işıksal-Bostan, M. (2021). Mathematically gifted students’ differentiated needs: What kind of support do they need? International Journal of Mathematical Education in Science and Technology. 52(1), 65–83.
- Baykoç, N., Aydemir, D., & Uyaroğlu, B. (2014). Inequality in educational opportunities of gifted and talented children in Türkiye. Procedia-Social and Behavioral Sciences, 143, 1133-1138.
- Bogdan, R. C. & Biklen, S. K. (2003). Qualitative research for education: An introduction to theory and methods (3rd ed.). Boston: Allyn & Bacon.
- Bozkurt, A. & Polat, S. (2018). An examination of the teacher’s questions for revealing students’ mathematical thinking. Turkish Journal of Computer and Mathematics Education, 9(1), 72–96.
- Brigandi, C. B., Gilson, C. M., & Miller, M. (2019). Professional development and differentiated instruction in an elementary school pullout program: A gifted education case study. Journal for the Education of the Gifted, 42(4), 362-395.
- Brousseau, G. (1997). Theory of didactical situations in mathematics. Kluwer Academic.
- Butuner, N., & Ipek, J. (2023). Examination of the Abstraction Process of Parallelogram by Sixth-Grade Students According to RBC+ C Model: A Teaching Experiment. European Journal of Educational Sciences, 10(2), 101-125.
- Chakraborty, S. (2007). Divisibility by 4 and 8 for smaller natural numbers. International Journal of Mathematical Education in Science and Technology, 38(5), 699–701.