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Öğretim Elemanlarının Matematiksel İspatın Önemine Yönelik Görüşlerinin İncelenmesi

Yıl 2019, Sayı: 47, 134 - 156, 09.07.2019

Öz

Bu çalışmanın amacı öğretim elemanlarının ispatın
önemine yönelik görüşlerini incelemektir. Bir eğitim fakültesinde ispat temelli
matematik dersleri veren 7 öğretim elemanını ile mülakat yapılmıştır. İspatın
önemine yönelik görüşlerin analizi sonucunda 25 kategori  oluşmuş ve bu kategoriler 5 tema altında
toplanmıştır. İlk mülakatın analizi ile oluşturulan sıralama anketi ile öğretim
elemanlarının bu temaları kendilerine göre önem sırasına göre sıralamaları
istenmiştir. Sonuç olarak, öğretim elemanlarının ispatları önemli bulmasında en
etkili gerekçenin, ispatın öğrencilerin düşünme becerilerine katkı yaptığını
düşünmeleri olduğu söylenebilir. Bu temayı sırasıyla, “teoremin/konunun
öğrenilmesine katkı”, “matematiğin tanıtılmasına katkı”, “duyuşsal özelliklere
katkı” ve son olarak “uygulamaya katkı” temaları takip etmektedir. İspatın önemine
yönelik oluşan kategoriler çoğunlukla literatürdeki görüşlere paralellik
göstermekle birlikte  ispatın öğrenciye
güven vermesi ve heyecan duymaya sebep olması gibi farklı görüşlerin de ortaya
çıktığı görülmüştür. 

Kaynakça

  • Alcock, L., & Inglis, M. (2008). Doctoral students’ use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69(2), 111-129.
  • Almeida, D. (2000). A Survey of Mathematics Undergraduates’ Interaction With Proof:Some Implications for Mathematics Education. Int. J. Math. Educ. Sci. Technol. 31(6), pp. 896-890.
  • Bell, A. W. (1976). A study of pupils' proof-explanations in mathematical situations. Educational studies in mathematics, 7(1-2), 23-40.
  • Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351-382.
  • Bills, E. & Tall, D. (1998). Operable definitions in advanced mathematics: The case of least upper bound. In A. Olivier and K. Newstead (Eds.), Proceedings of the 22nd Conference for the International Group for the Psychology of Mathematics Education, 2, 104-111.
  • Blanton, M. L., & Stylianou, D. A. (2003). The nature of scaffolding in undergraduate students' transition to mathematical proof. In N. A. Pateman, B. J. Dougherty & J. T. Zilliox (Eds.), Proceedings of the 27th conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th annual conference of PME-NA, Vol. 2 (pp. 113-120). Honolulu, HI: University of Hawai'i.
  • Bleiler, S. K., Thompson, D. R., & Krajčevski, M. (2014). Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17(2), 105-127.
  • Cilli-Turner, E. (2017). Impacts of inquiry pedagogy on undergraduate students conceptions of the function of proof. The Journal of Mathematical Behavior, 48, 14-21.
  • Coe, R., & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20(1), 41-53.
  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research, 3e. London: Sage.
  • De Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.
  • De Villiers, M. (1999). The role and function of proof with Sketchpad. Rethinking proof with Sketchpad, 3-10.
  • Demiray, E., & Bostan, M. I. (2017). An investigation of pre-service middle school mathematics teachers’ ability to conduct valid proofs, methods used, and reasons for invalid arguments. International Journal of Science and Mathematics Education, 15(1), 109-130.
  • Dimmel, J. K., & Herbst, P. G. (2018). What Details Do Teachers Expect From Student Proofs? A Study of Proof Checking in Geometry. Journal for Research in Mathematics Education, 49(3), 261-291.
  • Fukawa-Connelly, T. P. (2012). A case study of one instructor’s lecture-based teaching of proof in abstract algebra: making sense of her pedagogical moves. Educational Studies in Mathematics, 81(3), 325-345.
  • Fukawa-Connelly, T. (2014). Using Toulmin analysis to analyse an instructor's proof presentation in abstract algebra. International Journal of Mathematical Education in Science and Technology, 45(1), 75-88.
  • Glaser, B. & Strauss, A.L. (1967) Discovery of grounded theory: Strategies for qualitative research, Chicago: Aidine.
  • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13.
  • Hanna, G. (1995). Challenges to the importance of proof. For the Learning of mathematics, 15(3), 42-49.
  • Hanna, G., (2000). Proof, Explanation and Exploration: An Overview, Educational Studies in Mathematics. 44, 5–23.
  • Hanna, G., & Barbeau, E. (2010). Proofs as bearers of mathematical knowledge. In Explanation and proof in mathematics (pp. 85-100). Springer, Boston, MA.
  • Hanna, G., & Jahnke, H. N. (1996). Proof and proving. In International handbook of mathematics education (pp. 877-908). Springer, Dordrecht.
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning, 2, 805-842.
  • Hemmi, K. (2010). Three styles characterising mathematicians' pedagogical perspectives on proof. Educational Studies in Mathematics, 271-291.
  • Herbst, P. G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3), 283-312.
  • Herbst, P., & Brach, C. (2006). Proving and doing proofs in high school geometry classes: What is it that is going on for students?. Cognition and Instruction, 24(1), 73-122.
  • Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389-399.
  • Knuth, E. J. (2002). Secondary school mathematics teachers' conceptions of proof. Journal for research in mathematics education, 379-405.
  • Ko, Y. Y. (2010). Mathematics teachers’ conceptions of proof: Implications for educational research. International Journal of Science and Mathematics Education, 8(6), 1109-1129.
  • Ko, Y. Y., & Knuth, E. J. (2013). Validating proofs and counterexamples across content domains: Practices of importance for mathematics majors. The Journal of Mathematical Behavior, 32(1), 20-35.
  • Lai, Y., & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. Educational Studies in Mathematics, 85(1), 93-108.
  • Levenson, E. (2013). Exploring one student’s explanations at different ages: the case of Sharon. Educational Studies in Mathematics, 83(2), 181-203.
  • Lew, K., Fukawa-Connelly, T. P., Mejia-Ramos, J. P., & Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the mathematics professor is trying to convey. Journal for Research in Mathematics Education, 47(2), 162-198.
  • Lynch, A. G., & Lockwood, E. (2017). A comparison between mathematicians’ and students’ use of examples for conjecturing and proving. The Journal of Mathematical Behavior. Erişim adresi: https://doi.org/10.1016/j.jmathb.2017.07.004
  • Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for research in mathematics education, 41-51.
  • McCrory, R., & Stylianides, A. J. (2014). Reasoning-and-proving in mathematics textbooks for prospective elementary teachers. International Journal of Educational Research, 64, 119-131.
  • Miller, D., Infante, N., & Weber, K. (2018). How mathematicians assign points to student proofs. The Journal of Mathematical Behavior, 49, 24-34.
  • Mills, M. (2014). A framework for example usage in proof presentations. The Journal of Mathematical Behavior, 33, 106-118.
  • Nardi, E., & Knuth, E. (2017). Changing classroom culture, curricula, and instruction for proof and proving: How amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions? Educational Studies in Mathematics, 96(2), 267–274.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (Çev. M. Bütün, S. B. Demir). Ankara: Pegem Akademi.
  • Pinto, A., & Karsenty, R. (2017). From course design to presentations of proofs: How mathematics professors attend to student independent proof reading. The Journal of Mathematical Behavior, 49, 129-144.
  • Sears, R., & Chávez, Ó. (2014). Opportunities to engage with proof: the nature of proof tasks in two geometry textbooks and its influence on enacted lessons. ZDM, 46(5), 767-780.
  • Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4–36.
  • Speer, N. M., Smith III, J. P., & Horvath, A. (2010). Collegiate mathematics teaching: An unexamined practice. The Journal of Mathematical Behavior, 29(2), 99-114.
  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American educational research journal, 33(2), 455-488.
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for research in Mathematics Education, 289-321.
  • Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237-253.
  • Stylianides, G. J., Stylianides, A. J., & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463-1490.
  • Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (2009). Teaching and learning proof across the grades: A K-16 perspective. New York: Routledge.
  • Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate students’ understanding of proof: Relationships between proof conceptions, beliefs, and classroom experiences with learning proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91-134.
  • Teppo, A. R. (2015). Grounded theory methods. In Approaches to qualitative research in mathematics education (pp. 3-21). Springer, Dordrecht.
  • Weber, K. (2002). Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique. For the learning of Mathematics, 22(3), 14-17.
  • Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. The Journal of Mathematical Behavior, 23(2), 115-133.
  • Weber, K. (2010). Mathematics’ majors perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12, 306–336.
  • Weber, K. (2012). Mathematicians’ perspectives on their pedagogical practice with respect to proof. Int J Math Educ Sci Technol. 43(4), 463–482.
  • Weinberg, A., Fukawa-Connelly, T., & Wiesner, E. (2015). Characterizing instructor gestures in a lecture in a proof-based mathematics class. Educational Studies in Mathematics, 90(3), 233-258.
  • Yopp, D. A. (2011). How some research mathematicians and statisticians use proof in undergraduate mathematics. Journal of Mathematical Behavior, 115-130.
  • Zaslavsky, O., Nickerson, S. D., Stylianides, A. J., Kidron, I., & Winicki-Landman, G. (2011). The need for proof and proving: Mathematical and pedagogical perspectives. In Proof and proving in mathematics education (pp. 215-229). Springer, Dordrecht.
  • Zazkis, D., Weber, K., & Mejía-Ramos, J. P. (2016). Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context. Educational Studies in Mathematics, 93(2), 155-173.
  • Zhen, B., Weber, K., & Mejia-Ramos, J. P. (2016). Mathematics majors’ perceptions of the admissibility of graphical inferences in proofs. International Journal of Research in Undergraduate Mathematics Education, 2(1), 1-29.
Yıl 2019, Sayı: 47, 134 - 156, 09.07.2019

Öz

Kaynakça

  • Alcock, L., & Inglis, M. (2008). Doctoral students’ use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69(2), 111-129.
  • Almeida, D. (2000). A Survey of Mathematics Undergraduates’ Interaction With Proof:Some Implications for Mathematics Education. Int. J. Math. Educ. Sci. Technol. 31(6), pp. 896-890.
  • Bell, A. W. (1976). A study of pupils' proof-explanations in mathematical situations. Educational studies in mathematics, 7(1-2), 23-40.
  • Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351-382.
  • Bills, E. & Tall, D. (1998). Operable definitions in advanced mathematics: The case of least upper bound. In A. Olivier and K. Newstead (Eds.), Proceedings of the 22nd Conference for the International Group for the Psychology of Mathematics Education, 2, 104-111.
  • Blanton, M. L., & Stylianou, D. A. (2003). The nature of scaffolding in undergraduate students' transition to mathematical proof. In N. A. Pateman, B. J. Dougherty & J. T. Zilliox (Eds.), Proceedings of the 27th conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th annual conference of PME-NA, Vol. 2 (pp. 113-120). Honolulu, HI: University of Hawai'i.
  • Bleiler, S. K., Thompson, D. R., & Krajčevski, M. (2014). Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17(2), 105-127.
  • Cilli-Turner, E. (2017). Impacts of inquiry pedagogy on undergraduate students conceptions of the function of proof. The Journal of Mathematical Behavior, 48, 14-21.
  • Coe, R., & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20(1), 41-53.
  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research, 3e. London: Sage.
  • De Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.
  • De Villiers, M. (1999). The role and function of proof with Sketchpad. Rethinking proof with Sketchpad, 3-10.
  • Demiray, E., & Bostan, M. I. (2017). An investigation of pre-service middle school mathematics teachers’ ability to conduct valid proofs, methods used, and reasons for invalid arguments. International Journal of Science and Mathematics Education, 15(1), 109-130.
  • Dimmel, J. K., & Herbst, P. G. (2018). What Details Do Teachers Expect From Student Proofs? A Study of Proof Checking in Geometry. Journal for Research in Mathematics Education, 49(3), 261-291.
  • Fukawa-Connelly, T. P. (2012). A case study of one instructor’s lecture-based teaching of proof in abstract algebra: making sense of her pedagogical moves. Educational Studies in Mathematics, 81(3), 325-345.
  • Fukawa-Connelly, T. (2014). Using Toulmin analysis to analyse an instructor's proof presentation in abstract algebra. International Journal of Mathematical Education in Science and Technology, 45(1), 75-88.
  • Glaser, B. & Strauss, A.L. (1967) Discovery of grounded theory: Strategies for qualitative research, Chicago: Aidine.
  • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13.
  • Hanna, G. (1995). Challenges to the importance of proof. For the Learning of mathematics, 15(3), 42-49.
  • Hanna, G., (2000). Proof, Explanation and Exploration: An Overview, Educational Studies in Mathematics. 44, 5–23.
  • Hanna, G., & Barbeau, E. (2010). Proofs as bearers of mathematical knowledge. In Explanation and proof in mathematics (pp. 85-100). Springer, Boston, MA.
  • Hanna, G., & Jahnke, H. N. (1996). Proof and proving. In International handbook of mathematics education (pp. 877-908). Springer, Dordrecht.
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning, 2, 805-842.
  • Hemmi, K. (2010). Three styles characterising mathematicians' pedagogical perspectives on proof. Educational Studies in Mathematics, 271-291.
  • Herbst, P. G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(3), 283-312.
  • Herbst, P., & Brach, C. (2006). Proving and doing proofs in high school geometry classes: What is it that is going on for students?. Cognition and Instruction, 24(1), 73-122.
  • Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389-399.
  • Knuth, E. J. (2002). Secondary school mathematics teachers' conceptions of proof. Journal for research in mathematics education, 379-405.
  • Ko, Y. Y. (2010). Mathematics teachers’ conceptions of proof: Implications for educational research. International Journal of Science and Mathematics Education, 8(6), 1109-1129.
  • Ko, Y. Y., & Knuth, E. J. (2013). Validating proofs and counterexamples across content domains: Practices of importance for mathematics majors. The Journal of Mathematical Behavior, 32(1), 20-35.
  • Lai, Y., & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. Educational Studies in Mathematics, 85(1), 93-108.
  • Levenson, E. (2013). Exploring one student’s explanations at different ages: the case of Sharon. Educational Studies in Mathematics, 83(2), 181-203.
  • Lew, K., Fukawa-Connelly, T. P., Mejia-Ramos, J. P., & Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the mathematics professor is trying to convey. Journal for Research in Mathematics Education, 47(2), 162-198.
  • Lynch, A. G., & Lockwood, E. (2017). A comparison between mathematicians’ and students’ use of examples for conjecturing and proving. The Journal of Mathematical Behavior. Erişim adresi: https://doi.org/10.1016/j.jmathb.2017.07.004
  • Martin, W. G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for research in mathematics education, 41-51.
  • McCrory, R., & Stylianides, A. J. (2014). Reasoning-and-proving in mathematics textbooks for prospective elementary teachers. International Journal of Educational Research, 64, 119-131.
  • Miller, D., Infante, N., & Weber, K. (2018). How mathematicians assign points to student proofs. The Journal of Mathematical Behavior, 49, 24-34.
  • Mills, M. (2014). A framework for example usage in proof presentations. The Journal of Mathematical Behavior, 33, 106-118.
  • Nardi, E., & Knuth, E. (2017). Changing classroom culture, curricula, and instruction for proof and proving: How amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions? Educational Studies in Mathematics, 96(2), 267–274.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (Çev. M. Bütün, S. B. Demir). Ankara: Pegem Akademi.
  • Pinto, A., & Karsenty, R. (2017). From course design to presentations of proofs: How mathematics professors attend to student independent proof reading. The Journal of Mathematical Behavior, 49, 129-144.
  • Sears, R., & Chávez, Ó. (2014). Opportunities to engage with proof: the nature of proof tasks in two geometry textbooks and its influence on enacted lessons. ZDM, 46(5), 767-780.
  • Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4–36.
  • Speer, N. M., Smith III, J. P., & Horvath, A. (2010). Collegiate mathematics teaching: An unexamined practice. The Journal of Mathematical Behavior, 29(2), 99-114.
  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American educational research journal, 33(2), 455-488.
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for research in Mathematics Education, 289-321.
  • Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237-253.
  • Stylianides, G. J., Stylianides, A. J., & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463-1490.
  • Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (2009). Teaching and learning proof across the grades: A K-16 perspective. New York: Routledge.
  • Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate students’ understanding of proof: Relationships between proof conceptions, beliefs, and classroom experiences with learning proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91-134.
  • Teppo, A. R. (2015). Grounded theory methods. In Approaches to qualitative research in mathematics education (pp. 3-21). Springer, Dordrecht.
  • Weber, K. (2002). Beyond proving and explaining: Proofs that justify the use of definitions and axiomatic structures and proofs that illustrate technique. For the learning of Mathematics, 22(3), 14-17.
  • Weber, K. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. The Journal of Mathematical Behavior, 23(2), 115-133.
  • Weber, K. (2010). Mathematics’ majors perceptions of conviction, validity, and proof. Mathematical Thinking and Learning, 12, 306–336.
  • Weber, K. (2012). Mathematicians’ perspectives on their pedagogical practice with respect to proof. Int J Math Educ Sci Technol. 43(4), 463–482.
  • Weinberg, A., Fukawa-Connelly, T., & Wiesner, E. (2015). Characterizing instructor gestures in a lecture in a proof-based mathematics class. Educational Studies in Mathematics, 90(3), 233-258.
  • Yopp, D. A. (2011). How some research mathematicians and statisticians use proof in undergraduate mathematics. Journal of Mathematical Behavior, 115-130.
  • Zaslavsky, O., Nickerson, S. D., Stylianides, A. J., Kidron, I., & Winicki-Landman, G. (2011). The need for proof and proving: Mathematical and pedagogical perspectives. In Proof and proving in mathematics education (pp. 215-229). Springer, Dordrecht.
  • Zazkis, D., Weber, K., & Mejía-Ramos, J. P. (2016). Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context. Educational Studies in Mathematics, 93(2), 155-173.
  • Zhen, B., Weber, K., & Mejia-Ramos, J. P. (2016). Mathematics majors’ perceptions of the admissibility of graphical inferences in proofs. International Journal of Research in Undergraduate Mathematics Education, 2(1), 1-29.
Toplam 61 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Esra Aksoy 0000-0001-8829-2383

Serkan Narlı Bu kişi benim

Yayımlanma Tarihi 9 Temmuz 2019
Yayımlandığı Sayı Yıl 2019 Sayı: 47

Kaynak Göster

APA Aksoy, E., & Narlı, S. (2019). Öğretim Elemanlarının Matematiksel İspatın Önemine Yönelik Görüşlerinin İncelenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi(47), 134-156.