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Pre-Service Middle School Mathematics Teachers’ Ways of Thinking, Ways of Understanding and Pedagogical Approaches in Problem-Solving Process

Year 2017, Volume: 25 Issue: 2, 849 - 868, 15.03.2017

Abstract

The aim of this study is to investigate pre-service middle school mathematics teachers’ways of thinking (WoT), ways of understanding (WoU) and pedagogical approaches as well as


the relationships among them in the context of problem-solving within the DNR framework. In


this qualitatively designed study, the data was collected through clinical interviews with four


pre-service middle school mathematics teachers and analyzed through open and axial coding


approach. The results of the analysis indicated that pre-service mathematics teachers’ WoTs in


the context of problem-solving were fell into two categories. This study also revealed that WoTs


and particularly proof schemes in the context of problem-solving might play effective role in


pre-service middle school mathematics teachers’ pedagogical approaches.

References

  • Cuoco, A., Goldenberg, E. P. and Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402.
  • English, L. D., Lesh, R. and Fennewald, T. (2008). Future directions and perspectives for problem-solving research and curriculum development. In M. Santillan (Ed.), Proceedings of the 11th ICME (pp. 6-13), Monterrey, Mexico.
  • Fraenkel, J. R. and Wallen, N. E. (1996). How to design and evaluate research in education (3th Edition). New York: McGraw-Hill.
  • Harel, G. (2008). DNR perspective on mathematics curriculum and instruction, Part I: focus on proving. ZDM, 40(3), 487-500.
  • Harel, G. and Lim, K. H. (2004). Mathematics teachers’ knowledge base: Preliminary results. In M.J. Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th Conference of the ICME (Vol. 3(3), pp. 25 - 32). Bergen, Norway.
  • Harel, G. and Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283). Province, RI: American Mathematical Society.
  • Koichu, B. and Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65, 349-365.
  • Lesh, R. and Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2-3), 157-189.
  • Lim, K. H. (2006). Students’ mental acts of anticipating in solving problems involving alge-braic inequalities and equations. Unpublished dissertation, San Diego State University.
  • Lim, K. H., Morera, O. and Tchoshanov, M. (2009). Assessing problem-solving dispositions: Likelihood-to-act survey. In S. L. Swars, D. W. Stinson and S. Lemons-Smith (Eds.), Pro-ceedings of the 31th of the PME-NA (pp. 700-708). Atlanta: Georgia State University.
  • Lim, K. H. and Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stin-son and S. Lemons-Smith (Eds.), Proceedings of the 31th of the PME-NA (pp. 1576-1583). Atlanta: Georgia State University.
  • Pólya, G. (1945). How to solve it. Princeton. New Jersey: Princeton University.
  • Ramnarain, U. (2014). Empowering educationally disadvantaged mathematics students through a strategies-based problem solving approach. The Australian Educational Research-er, 41(1), 43-57.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem-solving, metacognition and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathemat-ics teaching and learning: A Project of the NCTM (pp. 334–370). New York: Macmillan.
  • Strauss, A. L. and Corbin, J. M. (1998). Basics of qualitative research: Techniques and pro-cedures for developing grounded theory (2nd ed.). Thousand Oaks: Sage Publications.
  • Viholainen, A. (2011). Critical features of formal and informal reasoning in the case of the concept of derivative. In B. Ubuz (Ed.), Proceedings of 35th PME (pp. 305-312). Ankara, Turkey.
  • Watson, A., and Harel, G. (2013). The role of teachers’ knowledge of functions in their teach-ing: A conceptual approach with illustrations from two cases. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 154-168.

Ortaokul Matematik Öğretmeni Adaylarının Problem Çözme Sürecindeki Düşünme Yolları, Anlama Yolları ve Pedagojik Yaklaşımları

Year 2017, Volume: 25 Issue: 2, 849 - 868, 15.03.2017

Abstract

Bu çalışmada ortaokul matematik öğretmeni adaylarının problem çözme bağlamındaki

düşünme yolları, anlama yolları ve pedagojik açıklamaları ile bunlar arasındaki ilişkilerin

DNR çerçevesi kapsamında araştırılması amaçlanmaktadır. Dört ortaokul matematik

öğretmeni adayından nitel araştırma yöntemlerinden klinik görüşme yoluyla toplanan veriler

açık ve eksensel kodlama yaklaşımı ile analiz edilmiştir. Analiz sonuçları matematik öğretmeni

adaylarının problem çözme bağlamındaki düşünme yollarının iki kategoriye ayrıldığını

göstermiştir. Ayrıca bu çalışma problem çözme bağlamındaki düşünme yollarının ve özellikle

kanıt şemalarının ilköğretim matematik öğretmen adaylarının pedagojik açıklamalarında etkili

bir rol oynadığını açığa çıkarmıştır.


References

  • Cuoco, A., Goldenberg, E. P. and Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior, 15(4), 375-402.
  • English, L. D., Lesh, R. and Fennewald, T. (2008). Future directions and perspectives for problem-solving research and curriculum development. In M. Santillan (Ed.), Proceedings of the 11th ICME (pp. 6-13), Monterrey, Mexico.
  • Fraenkel, J. R. and Wallen, N. E. (1996). How to design and evaluate research in education (3th Edition). New York: McGraw-Hill.
  • Harel, G. (2008). DNR perspective on mathematics curriculum and instruction, Part I: focus on proving. ZDM, 40(3), 487-500.
  • Harel, G. and Lim, K. H. (2004). Mathematics teachers’ knowledge base: Preliminary results. In M.J. Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th Conference of the ICME (Vol. 3(3), pp. 25 - 32). Bergen, Norway.
  • Harel, G. and Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283). Province, RI: American Mathematical Society.
  • Koichu, B. and Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65, 349-365.
  • Lesh, R. and Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2-3), 157-189.
  • Lim, K. H. (2006). Students’ mental acts of anticipating in solving problems involving alge-braic inequalities and equations. Unpublished dissertation, San Diego State University.
  • Lim, K. H., Morera, O. and Tchoshanov, M. (2009). Assessing problem-solving dispositions: Likelihood-to-act survey. In S. L. Swars, D. W. Stinson and S. Lemons-Smith (Eds.), Pro-ceedings of the 31th of the PME-NA (pp. 700-708). Atlanta: Georgia State University.
  • Lim, K. H. and Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stin-son and S. Lemons-Smith (Eds.), Proceedings of the 31th of the PME-NA (pp. 1576-1583). Atlanta: Georgia State University.
  • Pólya, G. (1945). How to solve it. Princeton. New Jersey: Princeton University.
  • Ramnarain, U. (2014). Empowering educationally disadvantaged mathematics students through a strategies-based problem solving approach. The Australian Educational Research-er, 41(1), 43-57.
  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem-solving, metacognition and sense making in mathematics. In D. Grouws (Ed.), Handbook of research on mathemat-ics teaching and learning: A Project of the NCTM (pp. 334–370). New York: Macmillan.
  • Strauss, A. L. and Corbin, J. M. (1998). Basics of qualitative research: Techniques and pro-cedures for developing grounded theory (2nd ed.). Thousand Oaks: Sage Publications.
  • Viholainen, A. (2011). Critical features of formal and informal reasoning in the case of the concept of derivative. In B. Ubuz (Ed.), Proceedings of 35th PME (pp. 305-312). Ankara, Turkey.
  • Watson, A., and Harel, G. (2013). The role of teachers’ knowledge of functions in their teach-ing: A conceptual approach with illustrations from two cases. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 154-168.
There are 17 citations in total.

Details

Subjects Studies on Education
Journal Section Review Article
Authors

Tangül Kabael This is me

Ayça Akın

Fatma Kızıltoprak This is me

Onur Toprak This is me

Publication Date March 15, 2017
Acceptance Date January 9, 2016
Published in Issue Year 2017 Volume: 25 Issue: 2

Cite

APA Kabael, T., Akın, A., Kızıltoprak, F., Toprak, O. (2017). Pre-Service Middle School Mathematics Teachers’ Ways of Thinking, Ways of Understanding and Pedagogical Approaches in Problem-Solving Process. Kastamonu Eğitim Dergisi, 25(2), 849-868.

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