Research Article
The Influence of Mistake-Handling Activities on Mathematics Education: An Example of Definitions

Solmaz Damla Gedik Altun , Alper Cihan Konyalioglu


APA 6th edition
Altun, S.D.G., & Konyalioglu, A.C. (2019). The Influence of Mistake-Handling Activities on Mathematics Education: An Example of Definitions. European Journal of Educational Research, 8(2), 467-476. doi:10.12973/eu-jer.8.2.467

Harvard
Altun S.D.G., and Konyalioglu A.C. 2019 'The Influence of Mistake-Handling Activities on Mathematics Education: An Example of Definitions', European Journal of Educational Research , vol. 8, no. 2, pp. 467-476. Available from: https://dx.doi.org/10.12973/eu-jer.8.2.467

Chicago 16th edition
Altun, Solmaz Damla Gedik and Konyalioglu, Alper Cihan . "The Influence of Mistake-Handling Activities on Mathematics Education: An Example of Definitions". (2019)European Journal of Educational Research 8, no. 2(2019): 467-476. doi:10.12973/eu-jer.8.2.467

Abstract

The study aims to find out the influence of Mistake-Handling Activities to determine mathematical definitions knowledge, which can be regarded as a component of mathematics content knowledge, of teachers on the development of teachers in providing mathematical definitions. Within this framework, Mistake-Handling Activities were carried out with five volunteer mathematics teachers. Written opinions and semi-structured face-to-face interviews were used as data collection tools. During the application, focus group interviews were carried out, and the application was enhanced with discussions. The data were analyzed using the document review method, and codes, categories, and themes were also determined. The results revealed that Mistake-Handling Activities yielded certain emotional advantages such as increasing teachers’ interest and curiosity, critical thinking, self-confidence, awareness, and offering different viewpoints as well as yielding cognitive advantages such as recognizing their shortcomings, acknowledging the importance of knowing the definition of a concept, and using the definition.

Keywords: Mistake-handling activities, definition, mathematics content knowledge, mathematics teacher


References

Akpinar, B., & Akdogan, S. (2010). Negatif bilgi kavrami: hata ve basarisizliklardan ogrenme [Negative knowledge concept: Learning from mistakes and failures]. The Western Anatolia Journal of Educational Sciences, 1(1), 14-22.

Borasi, R. (1986). On the educational roles of mathematical errors: Beyond diagnosis and remediation (Unpublished doctoral dissertation). State University of New York, Bufalo, NY, USA.

Borasi, R. (1989, March). Students’ constructive uses of mathematical errors: A taxonomy. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA, USA.

Borasi R. (1994). Capitalizing on errors as "springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25(2), 166-208. doi: 10.2307/749507

Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Norwood, NJ: Ablex.

Brown, P. A. (2008). A Review of the literature on case study research. Canadian Journal for New Scholars in Education, 1(1), 1-13.

Cakiroglu, E. (2013). Matematiksel kavramlarin tanimlanmasi [Defining mathematical concepts]. In I. O. Zembat,  M. F. Ozmantar, E. Bingolbali, H. Sandir, & A. Delice (Eds.), Tanimlari ve tarihsel gelisimleriyle matematiksel kavramlar [Definitions and historical development of mathematical concepts] (pp.2-14). Ankara, Turkey: Pegem Akademi.

Dalehefte, I. M., Seidel, T., & Prenzel, M. (2012). Reflecting on learning from errors in school instruction: Findings and suggestions from a Swiss-German video study. In J. Bauer, & C. Harteis (Eds.), Human fallibility: The ambiguity of errors for work and learning (pp. 197–213). Dordrecht, The Netherlands: Springer.

De Villiers, M. (1998). To teach definitions in geometry or to teach to define? In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education: Vol. 2 (pp. 248-255). Stellenbosch, South Africa: University of Stellenbosch.

Fang, Z. (1996). A review of research on teacher beliefs and practices. Educational Research, 38(1), 47- 65.

Fosnot, C. T. (1989). Enquiring teachers, enquiring learners: a constructivist approach for teaching. New York, NY: Teachers College Press.

Fujita, T., & Jones, K. (2007). Learners' understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.

Furinghetti, F., & Paola, D. (2002). Defining within a dynamic geometry environment: Notesfrom the classroom. In A. D. Cockbum & E. Nardi (Eds.), Proceedings of the 26th annual conference of the international group for the Psychology of Mathematics education (Vol.2, pp. 392-399). Norwich, UK: School of Education and Professional Development, University of East Anglia.

Gagatsis, A., & Kyriakides, L. (2000). Teachers’ attitudes towards their pupils’ mathematical errors. Educational Research and Evaluation, 6(1), 24–58. doi: 10.1076/1380-3611(200003)6:1;1-I;FT024

Gedik, S. D., & Konyalioglu, A. C. (2016). The effect of mistake-handling activities in mathematics education: Example of Proof. In O. Titrek, I. Mikelsone, L. Pavitola & G. Sezen-Gultekin (Eds.),  ICLEL 2016 Conference Proceedings Book (pp.993-898). Sakarya, Turkey: Sakarya University Faculty of Education.

Ginat, D. (2003). The greedy trap and learning from mistakes. In S. Grissom, D. Knox, D. T. Joyce, & W. Dann (Eds.), Proceedings of the 34th SIGCSE Technical Symposium on Computer Science Education (pp. 11-15). Newyork, NY: ACM Publications.

Govender, R., & De Villiers, M. (2002). Constructive evaluation of definitions in a Sketchpad context. In Proceedings of the AMESA 2002 (pp. 1-18). Durban, South Africa: University of Natal.

Harteis, C., Bauer, J., & Gruber, H. (2008). The culture of learning from mistakes: How employees handle mistakes in everyday work. International Journal of Educational Research, 47(4), 223-231.

Heinze, A. (2005). Mistake-handling activities in German Mathematics classroom. 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. 105-112). Melbourne, Australia: PME.

Kagan, D. M. (1992). Implication of research on teacher belief. Educational Psychologist, 27(1), 65-90.

Konyalioglu, A. C., Aksu, Z., Senel, E. O., & Tortumlu, N. (2010, May). Matematik ogretmen adaylarinin matematik soru cozumlerinde yapilan hatalarin nedenlerini sorgulama becerilerinin incelenmesi [The investigation of mathematics teachers cadidates’ skills of interrogating the reasons of errors in the process of solving mathematics questions]. In Uluslararasi Ogretmen Yetistirme Politikalari ve Sorunlari Sempozyumu II Bildiriler Kitabı [Proceedings of the International Teacher Training Policies and Problems Symposium II] (pp. 951-960). Ankara, Turkey: Hacettepe University.

Luo, Z. (2004). Introduction to how to solve mathematical problem (In Chinese). Xi’an, China: Shangxi Normal University Press.

Movshovitz-Hadar, N., & Hadass R. (1990). Perspective education of math teachers using paradoxes. Educational Studies in Mathematics, 21(3), 265-287.

Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332. doi: 10.3102/00346543062003307

Radatz, H. (1979). Error analysis in mathematics education. Journal of Research in Mathematics Education, 10(3), 163-172. doi: 10.2307/748804

Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21(5), 491–508.

Shir, K., & Zaslavsky, O. (2001). What constitutes a (good) definition? The case of square. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 161-168). Utrecht, Netherlands: Utrecht University.

Swan, M. (1983). Teaching decimal place value: A comparative study of conflict and positive only approaches. Nottingham, UK: Shell Centre for Mathematical Education, Nottingham University.

Skott, J. (2001). The emerging practices of novice teachers: The roles of his school mathematics images. Journal of Mathematics Teacher Education, 4(1), 3-28.

Yildirim, S., & Simsek, H. (2011). Sosyal bilimlerde nitel arastirma yontemleri [Qualitative research methods in the social sciences]. Ankara, Turkey: Seckin.