The Profile of Structure Sense in Abstract Algebra Instruction in an Indonesian Mathematics Education
Junarti , Y. L. Sukestiyarno , Mulyono , Nur Karomah Dwidayati
The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at build.
- Pub. date: October 15, 2019
- Pages: 1081-1091
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The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of abstract algebra course from two individual assignments given to the students. The students who could provide the best answers from the first and second individual assignments were chosen to be the respondents. The data from the second assignment, then, was analyzed through presentation, interpretation, coding, making a pattern, leveling and continued with clarification through an interview. The results of the study show that there were six patterns of structure sense answers and five levels of structure senses made by the students as the profile of structure sense. The conclusion is the inability to recognize the structure of the set elements, operation notations, and binary operation properties is one of the causes of the constraints in structuring the proof construction of the group. Thus, a thinking of mathematics connection is needed in structure understanding as a connection between symbol in learning and the symbol of abstract.
Keywords: Structure sense, group property, element structure.
References
Basturk, S. (2010). School experience group lessons and prospective teachers according to practice teachers. Gazi University Journal of Turkish Educational Sciences, 8(4), 869-894.
Collins, A. G. E., & Frank, M. J. (2013). Cognitive control over learning: Creating, clustering, and generalizing assignment set structure. American Psychological Association, 120(1), 190-229. https:/doi.org/10.1037/a0030852
Dreyfus, T., & Eisenberg, T. (1996). On different facets of mathematical thinking. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 253-284). Mahwah, NJ: Lawrence Erlbaum Associates.
Durand-Guerrier, V., Hausberger, T., & Spitalas, C. (2015). D´efinitions et examples: Pr´erequis pour l’apprentissage de l’alg`ebre modern [Definitions and examples: Prerequisites for learning modern algebra]. Annals of Didactics and Cognitive Science/ Annales de Didactique et de Sciences Cognitives, 20(1), 101–148.
Hausberger, T. (2015). Abstract algebra, mathematical structuralism, and semiotics. In K. Krainer & N. Vondrova (Eds.), Proceedings of the NinthCongress of the EuropeanSociety for Research inMathematics Education (pp. 2145-2151). Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME.
Hausberger, T. (2017). Structuralist praxeologies as a research program on the teaching and learning of abstract algebra. International Journal of Research in Undergraduate Mathematics Education, 4(1), 74-93, https://doi.org/10.1007/s40753-017-0063-4
Hoch, M., & Dreyfus, T. (2004). Structure sense in high school algebra: The effect of brackets. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 49-56). Bergen, Norway: PME.
Hoch, M., & Dreyfus, T. (2005). Students’ difficulties with applying a familiar formula in an unfamiliar context. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 145-152). Melbourne, Australia: PME.
Hoch, M., & Dreyfus, T. (2006). Structure sense in high school algebra: the effect of brackets. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 49–56). Bergen, Norway: Bergen University College.
Hoffman, A. J. (2017). Abstract algebra for teachers: An evaluative case study (Doctoral Dissertation, Purdue University). Retrieved from https://eric.ed.gov/?id=ED579693
Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358–390.
Miyazaki, M., Fujita, T., & Jones, K. (2017). Students' understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239. https://doi.org/10.1007/s10649-016-9720-9
Novotna, J., Stehlikova, N., & Hoch, M. (2006). Structure sense for university algebra. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 249-256). Prague, Czech Republic: PME.
Novotna, J., & Hoch, M. (2008). How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra. Mathematics Education Research Journal, 20(2), 93-104.
Oktac, A. (2016). Abstract algebra learning: Mental structures, definitions, examples, proofs and structure sense. Annals of Didactics and Cognitive Science/ Annales De Didactique Et De Sciences Cognitives, 21(1), 297 -316.
Schuler-Meyer, A. (2017). Students’ development of structure sense for the distributive law. Educational Studies in Mathematics, 96(1), 17-32. https://doi.org/10.1007/s10649-017-9765-4
Simpson, A., & Stehlikova, N. (2006). Apprehending mathematical structure: a case study of coming to understand a commutative ring. Educational Studies in Mathematics, 61(3), 347-371. https://doi.org/10.1007/s10649-006-1300-y
Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72, 237–253. https://doi.org/10.1007/s10649-009-9191-3
Stylianou D., Chae N., & Blanton, M. (2006). Students’ proof schemes: A closer look at what characterizes students’ proof conceptions. In S. Alatorre, J.L. Cortina, M. Saiz & Mendez, A. (Eds), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 54-60). Merida, Mexico: Universidad Pedagogica Nacional.
Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate students’ understanding of proof: Relationships between proof conceptions, beliefs, and classroom experiences with learning proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91–134.
Wasserman, N. H. (2014). Introducing algebraic structures through solving equations: Vertical content knowledge for K-12 Mathematics teachers. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 24(3), 191-214. https://doi.org/10.1080/10511970.2013.857374
Wasserman, N. H. (2016) Abstract algebra for algebra teaching: influencing school mathematics instruction. Canadian Journal of Science, Mathematics and Technology Education, 16(1), 28-47. https://doi.org/10.1080/14926156.2015.1093200
Wasserman, N. H. (2017). Exploring how understandings from abstract algebra can influence the teaching of structure in early algebra. Mathematics Teacher Education and Development, 19(20), 81 – 103