Pseudo Folding Back When Students Solve Real Analysis Problems

Main Article Content

Edi Purwanto
Makmun Solehudin

Abstract

Folding back is an important element of Pirie-Kieren's theory of growth in mathematical understanding. Students do folding back to the inner level of understanding, when facing problems at a certain level of understanding. The main focus of the folding back is the thicker understanding of the deeper components. Susiswo (2015) explains that when students face problems at a certain level of understanding, they will return to the inner level of understanding, but the understanding does not become thicker. This condition is known as pseudo folding back. This study aims to describe students' pseudo folding back when solving Real Analysis problems.

Article Details

How to Cite
Edi Purwanto, & Solehudin, M. (2021). Pseudo Folding Back When Students Solve Real Analysis Problems. Nusantara Journal of Social Sciences and Humanities, 1(1), 80-90. Retrieved from https://www.lekantara.com/journal/index.php/njsh/article/view/10
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References

1. Bartle, Robert G. & Sherbert, Donald R. (2011) Introduction to real analysis. Urbana: John Wiley & Sons, Inc.
2. Ciltas, A. & Tatar, E. (2011) diagnosing learning difficulties related to the equation and inequality that contain terms with absolute value. International Online Journal of Educational Sciences, Volume 3, Nomor 2: 461-473.
3. Cottrill, J., Dubinsky, Ed, & Nichols, D. (1996) Understanding the limit concept: beginning with a coordinated process schema. Journal of Mathematical Behavior. Vol.15: 167-192. http://dx.doi.org/10.1016/S0732-3123(96)90015-2
4. Droujkova A. M., Berenson B. S., Slaten, K., & Tombes S. (2005) A conceptual framework for studying teacher preparation: The pirie-kieren model, collective understanding, and metaphor. Proceedings of the 29th conference of the international group for the psychology of mathematics education, Vol. 2, pp. 289-296.
5. Duru, A. (2011) Pre-Service teachers’ perception about the concept of limit. Kuram ve Uygulamada Eğitim Bilimleri Educational Sciences: Theory and Practice. Vol.11, Numbers 3: 1710-1715.
6. Hiebert, J. (1986) Conceptual and prosedural knowledge: The case of mathematics. London: Lawrence Erlbaum Associates.
7. Juter, K. (2007) Students’ conceptions of limits: High achievers versus low achievers. The Montana Mathematics Enthusiast, ISSN 1551-3440, Vol. 4, no.1, pp. 53-65.
8. Kilpatrick, J., Swafford, J., dan Findell, B. (2001) Ading It Up Helping Children Learn Mathematics. Washington DC. National Research Council.
9. Lithner, Johan. (2012) Learning mathematics by creative or imitative reasoning. International Congress on Mathematical Education.
10. Martin, C., LaCroix, L. & Fownes, L. (2005) Folding back and the growth of mathematical understanding in workplace training. Adults Learning Mathematics An International Journal.Vol.1, Nomor 1.
11. Meel, E. (2003) Model and theories of mathematical understanding: Comparing pirie- kieren’s model of the growth of mathematical understanding and APOS theory. CBMS Issues in Mathematics Education.Vol. 12.
12. Muzangwa, J. dan Chifamba, P. (2012) Analysis of errors and misconceptions in the learning of calculus by undergraduate students. Acta didactica napocensia. Volume 5 Nomer 2.Parameswaran, R. (2010). Expert mathematicians’ approach to understanding definitions. The mathematics educator. Volume 20, Nomor 1: 43-51.
13. Pirie, S. & Kieren, T. (1994) Growth in mathematical understanding: How we can characterize it and how we can represent it. Educational studies in mathematics, Vol. 9: 160–190. http://dx.doi.org/10.1007/978-94-017-2057-1_3.
14. Sidebotham, Thomas H. (2003) The a to z of mathematics: a basic guide, Hlm. 181, ISBN 9780471461630
15. Skemp, R. (1987) Psychology of learning mathematics. Lawrence erlbaum associates. New Jersey. Hillsdale.
16. Susiswo (2015) Students’ form folding back in solving limit problems. Disertasi doktor pascasarjana. universitas negeri malang, pendidikan matematika.
17. Swinyard, C. & Larsen, S. (2012) Coming to understand the formal definition of limit: insights gained from engaging students in reinvention. Journal for Research in Mathematics Education. Vol. 43, No. 4, 465-493.
18. Tall, D. (2002) Advanced mathematical thinking. New York : Kluwer Academic Publisher.
19. Tall, D.& Vinner, S. (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity. educational studies in mathematics. Vol.12: 151–169. http://dx.doi.org/10.1007/BF00305619.
20. Vinner, S. (1997) The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning. Educational studies in mathematics. Volume 34: 97-129. 69–302. https://doi.org/10.1628/001522112x653840