STRATEGIES OF REDUCTION OF ABSTRACTION IN ABSTRACT ALGEBRA

Authors

  • Ruma Manandhar (PhD) Assistant Professor, Nepal Open University, Nepal https://orcid.org/0000-0002-1828-1619
  • Prof. Lekhnath Sharma (PhD) Nepal Open University, Nepal

DOI:

https://doi.org/10.29121/granthaalayah.v8.i11.2020.2446

Keywords:

Abstract Algebra, Ethnography, Mathematics, Process-Object Duality, Reduction, Strategies

Abstract

This article is based on the study, which tries to unpack strategies of reduction of abstraction in learning abstract algebra from learners’ perspective. Ethnography was used to collect the required information. The study found the strategies of reduction of abstraction in abstract algebra are: making sense and meaning through previous experiences and existing knowledge an analogical creation of mental image, using first person language in course of doing mathematics by students as teachers do in the classroom for logical arguments, focusing on “symbol” or some mathematical entity to manage abstraction for their idiosyncratic understandings of abstract mathematical structure rather than the reflective thinking, using students own idiosyncratic figures to reduce the degrees of complexity of mathematical concepts. This study can lead teachers of abstract algebra to a new awareness of their teaching strategies and their practices.

Downloads

Download data is not yet available.

References

Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E.,Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. In J. Kaput, A. H. Schoenfeld, & E. Dubinsky (Eds.), Research in Collegiate mathematics education, II (pp. 1-32). Providence, RI: American Mathematical Society.

Asiala, M., Dubinsky, E., Mathews, D.M., Morics, S., & Oktac, A. (1997). Development of students‟ understanding of cosets, normality, and quotient groups. Journal of Mathematical Behavior, 16, 241-309 DOI: https://doi.org/10.1016/S0732-3123(97)90029-8

Beth, E. W. and Piaget, J. (1996). Mathematical Epistemology and Psychology. Dordrecht, The Netherlands: D. Reidel Publishing Company

Brown, A., DeVries, D.J., Dubinsky, E., & Thomas, K. (1997). Learning binary operations, groups and subgroups. Journal of Mathematical Behavior, 16, 187-239. DOI: https://doi.org/10.1016/S0732-3123(97)90028-6

Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.),

Advanced Mathematical Thinking, Kluwer Academic Press, pp. 95-123

Dubinsky, E., Dautermann, J., Leron, U., & Zazkis, R. (1994). On learning fundamental concepts of group theory. Educational Studies in Mathematics, 27(3), 267-305. DOI: https://doi.org/10.1007/BF01273732

Dubinsky, E.,& Leron, U.(1994). Learning abstract algebra with ISETL. New York: Springer-Verlag DOI: https://doi.org/10.1007/978-1-4612-2602-4

Edwards, T. & Brenton, L. (1999). An attempt to foster students' construction of knowledgduring a semester course in abstract algebra. The College Mathematics Journal, 30, 120-128 DOI: https://doi.org/10.1080/07468342.1999.11974043

Findell, B. (2001). Learning and understanding in abstract algebra. Unpublished Doctoral Dissertation, The University of New Hampshire Association of America

Fukawa-Connelly, T. (2007). A tale of two courses: Teaching and learning undergraduate abstract algebra. Unpublished Doctoral Dissertation, The University of Maryland College ParkHirsch, J. (2008). Tracking changes in teaching and learning abstract algebra; Beliefs and ability to abstract. Unpublished Doctoral Dissertation, Columbia University USA

Hazzan, O. (1999). Reducing abstraction level when learning abstract algebra concepts.

Educational Studies in Mathematics, 40, 71-90.

Hirsch, J. (2008). Tracking changes in teaching and learning abstract algebra; Beliefs and ability to abstract. Unpublished Doctoral Dissertation, Columbia University USA

Leron, U., & Hazzan, O. (1997). The world according to Johnny: A coping perspective in mathematics education. Educational Studies in Mathematics, 32(3), 265-292. DOI: https://doi.org/10.1023/A:1002908608251

Mingus, T. (2001). A case study of spiraling content and pedagogy through core courses for pre-service secondary mathematics teachers. In M. Ahmadi (Ed.), Reading in innovative ideas in teaching collegiate mathematics (pp. 191-213). Lanham, MD: University Press of America.

Mitchel, M.C., & White, P. (2007). Abstraction in Mathematics. Mathematics Education Research Journal, Vol 19, No 2, 20-9.

Nardi, E. (1996). The Novice Mathematician’s Encounter with Mathematical Abstraction: Tensions in Concept Images Construction and Formalization. Unpublished Doctoral Dissertation, University of Oxford. Linacre College.

Nardi, E. (2008). Amongst Mathematicians: Teaching and learning Mathematics at University level. New York: Springer. DOI: https://doi.org/10.1007/978-0-387-37143-6

Novotna, J., & Hoch, M. (2008). How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra. Mathematics Education Research DOI: https://doi.org/10.1007/BF03217479

Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification- The case of function. In E. Dubinsky and G.Harel (eds.), The Concepts of Function-Aspects of Epistemology and Pedagogy, MAA Notes.

Thompson, P.W. (1985). Experience, problem solving, and learning mathematics:

Considerations in developing mathematics curricula, in E.A. Silver (ed.), Teaching and Learning Mathematical Problem Solving: Multiple Research Perspective, Hillsdale, NJ, pp. 189-236.

Downloads

Published

2020-12-09

How to Cite

Manandhar, R., & Sharma, L. . (2020). STRATEGIES OF REDUCTION OF ABSTRACTION IN ABSTRACT ALGEBRA. International Journal of Research -GRANTHAALAYAH, 8(11), 245–250. https://doi.org/10.29121/granthaalayah.v8.i11.2020.2446