Pre-service Mathematics Teachers’ Views regarding the Role of Examining Students’ Work in Understanding Students’ Ways of Thinking

Year 2015, Volume: 6 Issue: 2, 139 - 162, 08.09.2015

Makbule Didiş Ayhan Erbaş Bülent Çetinkaya Erdinç Çakıroğlu Cengiz Alacacı

https://doi.org/10.16949/turcomat.50978

Abstract

Awareness for and knowledge of students’ ways of thinking is an important component of teachers’ competence that should be gained before starting their career. The purpose of this study was to investigate pre-service secondary mathematics teachers’ views regarding the role of examining students’ work in understanding students’ ways of thinking within the context of an undergraduate mathematical modeling course for pre-service mathematics teachers. The participants were twenty-five pre-service mathematics teachers enrolled in the course. Lasting eight weeks the data were collected through the pre-service teachers’ reflection papers, individual interviews, and a self-evaluation questionnaire. The analyses of data revealed that the pre-service mathematics teachers thought that examining students’ solution papers and video episodes helped them to be aware of, predict, understand, and interpret students’ ways of thinking. The findings of the study suggested that mathematics teacher educators might consider using students’ work from real classroom settings in order to both develop and support the development of pre-service mathematics teachers’ pedagogical content knowledge.

Keywords: Pedagogical content knowledge, students’ ways of thinking, teacher education, student work

Keywords

Pedagogical content knowledge, students’ ways of thinking, teacher education, student work

Öğrenci Çalışmalarını İncelemenin Öğrenci Düşünme Şekillerini Anlamadaki Rolü ile İlgili Matematik Öğretmen Adaylarının Düşünceleri

Abstract

Öğretmenin sahip olması beklenen önemli yeterliliklerden birisi öğrenci düşünme şekilleri bilgisidir. Pedagojik alan bilgisinin bir alt boyutu olan bu bilginin öğretmenlere mesleğe başlamadan önce kazandırılması önemlidir. Bu çalışmanın amacı matematiksel modelleme etkinliklerinin sınıf içi uygulamalarından elde edilen öğrenci çözüm kâğıtları ve videoları incelemenin öğrenci düşünme şekillerini anlamaya olan katkısı konusunda matematik öğretmen adaylarının düşüncelerini incelemektir. Çalışmanın katılımcıları öğretmen adaylarına dönük bir matematiksel modelleme dersine kayıtlı yirmi beş matematik öğretmen adayıdır. Sekiz hafta süren çalışmanın verileri bireysel düşünce raporları, birebir görüşmeler ve bir öz-değerlendirme anketi yoluyla toplanmıştır. Verilerin analizleri, öğretmen adaylarının öğrenci çözüm kâğıtları ve video kesitlerini incelemenin öğrencilerin matematiksel düşünme süreçlerinin farkına varma, tahmin edebilme, anlama ve yorumlamalarına yardım ettiğini düşündüklerini ortaya çıkarmıştır. Bu çalışmanın sonuçları öğretmen eğitimcilerine, öğretmen adaylarının pedagojik alan bilgilerinin gelişimine destek sağlaması açısından gerçek sınıf ortamlarından alınmış öğrenci çalışma ürünlerinin kullanılmasını önermektedir.

Anahtar Kelimeler: Pedagojik alan bilgisi, öğrenci düşünme şekilleri, öğretmen eğitimi, öğrenci çalışmaları

Keywords

Pedagojik alan bilgisi, öğrenci düşünme şekilleri, öğretmen eğitimi, öğrenci çalışmaları

References

• Ball, D. L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In B. Biddle, T. Good & I. Goodson (Eds.), International handbook on teachers and teaching (Vol. 2, pp. 679–718). Dordrecht, the Netherlands: Kluwer Press.
• Ball, D., & Cohen, D. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey Bass.
• Bergqvist, T. (2005). How students verify conjectures: Teachers’ expectations. Journal of Mathematics Teacher Education, 8, 171–191.
• Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
• Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3, 155–181.
• Doerr, H. M. (2006). Examining the tasks of teaching when using students’ mathematical thinking. Educational Studies in Mathematics, 62, 3–24.
• Doerr, H. M., & English, L. D. (2004). Learning through interacting with students' ways of thinking. In I. Putt, R. Faragher, & M. McLean (Eds.), Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australia. Mathematics Education for the Third Millenium: Towards 2010 (pp. 215–222). Townsville, Queensland: James Cook University.
• Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 125–140). Mahwah, NJ: Lawrence Erlbaum.
• English, L. (2003). Reconciling theory, research, and practice: A models and modeling perspective. Educational Studies in Mathematics, 54, 225–248.
• Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C. ve Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar Mathematical modeling in mathematics education: Basic concepts and different approaches. Kuram ve Uygulamada Eğitim Bilimleri-Educational Sciences: Theory and Practice, 14(4), 1607–1627.
• Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College Press.
• Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (1993). Using children’s mathematical knowledge in instruction. American Educational Research Journal, 30(3), 555–583.
• Hadjidemetriou, C., & Williams, J. (2002). Teachers' pedagogical content knowledge: Graphs from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for Psychology of Mathematics Education (Vol. 3, pp. 57–64). Norwich, UK.
• Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17–35.
• Lampert, M., & Ball, D. L. (1998). Teaching, multimedia, and mathematics: Investigations of real practice. New York, NY: Teachers College Press.
• Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum.
• Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The handbook of research on mathematics teaching and learning (2nd ed., pp. 763–804). Reston, VA: National Council of Teachers of Mathematics; Charlotte, NC: Information Age Publishing (joint publication).
• Masingila, J. O., & Doerr, H. M. (2002). Understanding pre-service teachers’ emerging practices through their analyses of multimedia case study of practice. Journal of Mathematics Teacher Education, 5, 235–263.
• Nathan, M. J., & Koedinger, K. R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190.
• Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3–32). New York, NY: Springer.
• Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25.
• Santagata, R., & Yeh, C. (2014). Learning to teach mathematics and to analyze teaching effectiveness: Evidence from a video-and practice-based approach. Journal of Mathematics Teacher Education, 17(6), 491–514.
• Schorr, R. Y., & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 159–174). Mahwah, NJ: Lawrence Erlbaum.
• Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20(2), 163–183.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
• Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.
• Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 157–223). Charlotte, NC: Information Age Publishing.
• Şen-Zeytun, A., Çetinkaya, B., & Erbaş, A. K. (2010). Mathematics teachers’ covariational reasoning levels and their predictions about students’ covariational reasoning abilities. Educational Sciences: Theory & Practice, 10(3), 1573–1612.
• Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244–276.
• Wilson, P. H., Lee, H. S., & Hollebrands, K. (2011). Understanding prospective mathematics teachers’ processes for making sense of students’ work with technology. Journal for Research in Mathematics Education, 42(1), 39–64.