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Matematik Öğretmeni Adaylarının Geometrik İspatlarda İspat Yazma Becerilerinin İncelenmesi: Van Hiele Modeli

Yıl 2022, Cilt: 23 Sayı: Özel Sayı, 128 - 176, 26.03.2022

Öz

Bu çalışmanın amacı, van Hiele modeline dayalı öğretim etkinliklerinde matematik öğretmeni adaylarının ispat yazma becerilerindeki gelişimlerinin incelenmesidir. Çalışma, ilköğretim matematik öğretmenliği programı birinci sınıfında öğrenim görmekte olan on öğretmen adayıyla gerçekleştirilmiştir. Çalışmada, van Hiele modelinin öğretmen adaylarının ispat yazma becerilerindeki etkiliğinin ortaya konulması amaçlandığından nitel araştırma yöntemlerinden öğretim deneyi deseni benimsenmiştir. Bu amaçla nitel veri toplama araçları (bireysel görüşmeler, öğretmen adaylarının çalışma kağıtları ve araştırmacı alan notları) veri toplanması için kullanılmıştır. Öğretmen adaylarının ispat yazma becerilerinin gelişimleri van Hiele modelinde yer alan öğretim aşamaları ve düzeyleri kapsamında ele alınmıştır. Çalışma sonucunda, VH modelinde öğretmen adaylarının ispat yazma becerilerinin gelişimsel bir süreç ile desteklendiği ve ispat yazmada van Hiele-4 düzeyine erişebildikleri görülmüştür. Matematik öğretmen adaylarının gelişimsel olarak desteklenmesinde ise van Hiele modelinde yer alan bilgi ve sorgulama, rehberlik etme/destekleyici yönlendirme, açıklama/yorumlama, serbest yönlendirme ve entegrasyon öğretim ortamı unsurları etkili olduğu sonucuna ulaşılmıştır. Bu sonuçlar doğrultusunda matematik öğretmen adaylarının geometri öğrenimlerinde van Hiele geometrik düşünme gelişimlerini destekleyici önerilerde bulunulmuştur.

Kaynakça

  • Almeida, D. (2000). A survey of mathematics undergraduates’ interaction with proof: some implications form mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6), 869-890. https://doi.org/10.1080/00207390050203360
  • Armah, R. B., Cofie, P. O., & Okpoti, C. A. (2018). Investigating the effect of van Hiele Phase-based instruction on pre-service teachers’ geometric thinking. International Journal of Research in Education and Science, 4(1), 314-330. https://doi.org/10.21890/ijres.383201
  • Aslan-Tutak, F., & Adams, T. L. (2015). A study of geometry content knowledge of elementary preservice teachers. International Electronic Journal of Elementary Education, 7(3), 301-318.
  • Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216-230). Hodder & Stoughton.
  • Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 27–44). National Council of Teachers of Mathematics.
  • Battista, M. T. & Clements, D. H. (1995). Geometry and Proof. Mathematics Teacher, 88(1), 48-54. https://doi.org/10.5951/MT.88.1.0048
  • Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1/2), 23-40. https://doi.org/10.1007/BF00144356
  • Burger, W. & Shaughnessy, J.M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31-48. https://doi.org/10.2307/749317
  • Clements, D. H. (2003). Teaching and learning geometry. A research companion to principls and standards for school mathematics. National Council of Teachers of Mathematics.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). Macmillan.
  • Clements, D. H., Battista, M. T., Sarama, J., & Swaminathan, S. (1997). Development of students' spatial thinking in a unit on geometric motions and area. The Elementary School Journal, 98(2), 171-186. https://doi.org/10.1086/461890
  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307-333). Lawrence Erlbaum Associates.
  • Daguplo, M. (2014). How well do you write proof? Characterizing students proof-writing skill vis-à-vis van Hiele’s model in geometrical proving. Journal of Educational and Human Resource Development, 2, 104-114.
  • De Villiers, D. M. (1987). Research evidence of hierarchical thinking, teaching strategies, and the van hiele theory: some critical comments. Paper presented at Learning an Teaching Geometry: Issues for Research and Practice Working Conference. Syracuse University.
  • Dickerson, D. S. (2008). High school mathematics teachers’ understandings of the purposes of mathematical proof. (Doctoral dissertation), Syracuse University.
  • Diezmann, C., Watters, J., & English, L. (2002). Teacher behaviours that influence young children's reasoning. In Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 289-296). University ot East Anglia.
  • Dimakos, G., Nikoloudakis, E., Ferentinos, S., & Choustoulakis, E. (2007). Developing a proof-writing tool for novice lyceum geometry students. The Teaching of Mathematics, X(2), 87-106.
  • Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38, 85-109. https://doi.org/10.1023/A:1003660018579
  • Fraenkel, J. R., & Wallen, N. E. (2009). How to design and evaluate research in education (7th ed.). McGraw Hill Higher Education.
  • Freedman, H. (1983). A way of teaching abstract algebra. The American Mathematical Monthly, 90 (9), 641-644.
  • Fuys, D. (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447-462.
  • Fuys, D., Geddes, D., & Tischer, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph, 3, 1-196.
  • Goetting, M. (1995). The college students’ understanding of mathematical proof. (Doctoral dissertation), University of Maryland.
  • Güler, G., Özdemir, E., & Dikici, R. (2012). Öğretmen adaylarının matematiksel tümevarım yoluyla ispat becerileri ve matematiksel ispat hakkındaki görüşleri. Kastamonu Eğitim Dergisi, 20(1), 219-236.
  • Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(1/2), 127-150. https://doi.org/10.1023/A:1012781005718
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational studies in mathematics, 44, 5-23. https://doi.org/10.1023/A:1012737223465
  • Hershkowitz, R., Bruckheimer, M., & Vinner, S. (1987). Activities with teachers based on cognitive research. In M.Linquist & A. Schulte (Eds.) Learning and teaching geometry, K-12 1987 Yearbook (pp. 222–235). The National Council of Teachers of Mathematics.
  • Howse, T. D., & Howse, M. E. (2014). Linking the van Hiele theory to instruction. Teaching Children Mathematics, 21(5), 304-313. https://doi.org/10.5951/teacchilmath.21.5.0304
  • Jones, K. (2000). The student experience of mathematical proof at university level. International Journal of Mathematical Education in Science and Technology, 31(1), 53-60. https://doi.org/10.1080/002073900287381
  • Jupri, A. (2018). Using the van Hiele theory to analyze primary school teachers' written work on geometrical proof problems. 4th International Seminar of Mathematics, Science and Computer Science Education IOP Conf. Series, 1013(012117). https://doi.org/10.1088/1742-6596/1013/1/012117
  • Knight, K. C. (2006). An investigation into the change in the van Hiele levels of understanding geometry of preservice elementary and secondary mathematics teachers. (Master thesis). University of Maine.
  • Knuth, E. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959
  • Knuth, E., Choppin, J., Slaughter, M. & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students’ competencies in justifying and proving. In D. Mewborn, P. Sztajn, D. White, H. Wiegel, R. Bryant & K. Noony (Eds.), Proceedings of the Twenty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1693-1670), University of Georgia.
  • Kotzé, G. (2007). Investigating shape and space in mathematics: a case study. South African Journal of Education, 27(1), 19-35.
  • Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children's reasoning about space and geometry: In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Lawrence Erlbaum Associates Publishers.
  • Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, 87-125. https://doi.org/10.1023/A:1012785106627
  • Marriotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44, 25-43. https://doi.org/10.1023/A:1012733122556
  • Martin, T., & McCrone, S. (2009). Formal proof in high school geometry: Students perceptions of structure, validity, and purpose. In Stylianou, D. A., Blanton, M. L. & Knuth, E. J. (Eds.), Teaching and learning proof across the grades: A K-l6 perspective (pp. 204-221). Routledge.
  • McCrone, S. M. S., & Martin, T. S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Science, Mathematics and Technology Education, 4(2), 223-242. https://doi.org/ 10.1080/14926150409556607
  • Ministry of National Education. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum: Elementary andmiddle schools 3, 4, 5, 6, 7 and 8th grades)]. Talim Terbiye Kurul Başkanlığı.
  • Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in mathematics, 27, 249-266. https://doi.org/10.1007/BF01273731
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
  • Raman, M., & Weber, K. (2006). Key ideas and insights in the context of three high school geometry proofs. Mathematics Teacher, 99(9), 644-649. https://doi.org/10.5951/MT.99.9.0644
  • Reisel, R. B. (1982). How to construct and analyze proofs-a seminar course. The American Mathematical Monthly, 89(7), 490-492. https://doi.org/10.1080/00029890.1982.11995483
  • Senk, S. L. (1985). How well do students write geometry proofs? Mathematics Teacher, 78(6), 448-456.
  • Senk, S. L. (1989). Van Hiele levels and achievement in writing proofs. Journal for Research in Mathematics Education, 20(3), 309-321. https://doi.org/10.2307/749519
  • Sevgi, S., & Orman, F. (2020). Eighth grade students’ views about giving proof and their proof abilities in the geometry and measurement. International Journal of Mathematical Education in Science and Technology, 1-24. https://doi.org/10.1080/0020739X.2020.1782493
  • Shanghai Education Committee. (2004). Shanghai Primary and Secondary School Curriculum Standard. Shanghai: Shanghai Education Press.
  • Sowder, L., & Harel, G. (1998). Types of students' justifications. Mathematics Teacher, 91(8), 670-675. https://doi.org/10.5951/MT.91.8.0670
  • Sowder, L., & Harel, G. (2003). Case studies of mathematics majors proof understanding, production, and appreciation. Canadian Journal of Science, Mathematics, and Technology Education 3(2), 251-267. https://doi.org/10.1080/14926150309556563
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289-321. https://doi.org/10.2307/30034869
  • Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2004). Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55(1), 133-162. https://doi.org/10.1023/B:EDUC.0000017671.47700.0b
  • Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10(3), 145-166. https://doi.org/10.1007/s10857-007-9034-z
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. University of Chicago.
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Examining Proof Writing Skills of Pre-Service Mathematics Teachers' in Geometric Proofs: Van Hiele Model

Yıl 2022, Cilt: 23 Sayı: Özel Sayı, 128 - 176, 26.03.2022

Öz

The aim of this study is to examine the development of pre-service mathematics teachers' proof-writing skills in teaching activities based on the van Hiele model. The study was carried out with 10 pre-service mathematics teachers studying in the first year of the primary school mathematics teaching programme. In the study, teaching experiment design, one of the qualitative research methods, was adopted since it was aimed to reveal the effectiveness of the van Hiele model on pre-service mathematics teachers' proof-writing skills. For this purpose, qualitative data collection tools (personal interviews, pre-service teachers' worksheets, and researcher field notes) were used to collect data. The development of pre-service mathematics teachers' proof-writing skills was discussed within the scope of teaching stages and levels in the van Hiele model. As a result of the study, it was seen that the pre-service mathematics teachers' proof-writing skills were supported by a developmental process in the van Hiele model, and they were able to reach the van Hiele-4 level in proof-writing. It was concluded that knowledge and inquiry, guidance/directed orientation, explicitation/interpretation, free guidance and integration, which are the components of the teaching environment in the van Hiele model, are effective in supporting the pre-service mathematics teachers developmentally. In line with these results, suggestions were made to support the development of van Hiele geometric thinking in geometry learning of pre-service mathematics teachers.

Kaynakça

  • Almeida, D. (2000). A survey of mathematics undergraduates’ interaction with proof: some implications form mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6), 869-890. https://doi.org/10.1080/00207390050203360
  • Armah, R. B., Cofie, P. O., & Okpoti, C. A. (2018). Investigating the effect of van Hiele Phase-based instruction on pre-service teachers’ geometric thinking. International Journal of Research in Education and Science, 4(1), 314-330. https://doi.org/10.21890/ijres.383201
  • Aslan-Tutak, F., & Adams, T. L. (2015). A study of geometry content knowledge of elementary preservice teachers. International Electronic Journal of Elementary Education, 7(3), 301-318.
  • Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216-230). Hodder & Stoughton.
  • Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 27–44). National Council of Teachers of Mathematics.
  • Battista, M. T. & Clements, D. H. (1995). Geometry and Proof. Mathematics Teacher, 88(1), 48-54. https://doi.org/10.5951/MT.88.1.0048
  • Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1/2), 23-40. https://doi.org/10.1007/BF00144356
  • Burger, W. & Shaughnessy, J.M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17(1), 31-48. https://doi.org/10.2307/749317
  • Clements, D. H. (2003). Teaching and learning geometry. A research companion to principls and standards for school mathematics. National Council of Teachers of Mathematics.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). Macmillan.
  • Clements, D. H., Battista, M. T., Sarama, J., & Swaminathan, S. (1997). Development of students' spatial thinking in a unit on geometric motions and area. The Elementary School Journal, 98(2), 171-186. https://doi.org/10.1086/461890
  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307-333). Lawrence Erlbaum Associates.
  • Daguplo, M. (2014). How well do you write proof? Characterizing students proof-writing skill vis-à-vis van Hiele’s model in geometrical proving. Journal of Educational and Human Resource Development, 2, 104-114.
  • De Villiers, D. M. (1987). Research evidence of hierarchical thinking, teaching strategies, and the van hiele theory: some critical comments. Paper presented at Learning an Teaching Geometry: Issues for Research and Practice Working Conference. Syracuse University.
  • Dickerson, D. S. (2008). High school mathematics teachers’ understandings of the purposes of mathematical proof. (Doctoral dissertation), Syracuse University.
  • Diezmann, C., Watters, J., & English, L. (2002). Teacher behaviours that influence young children's reasoning. In Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 289-296). University ot East Anglia.
  • Dimakos, G., Nikoloudakis, E., Ferentinos, S., & Choustoulakis, E. (2007). Developing a proof-writing tool for novice lyceum geometry students. The Teaching of Mathematics, X(2), 87-106.
  • Dreyfus, T. (1999). Why Johnny can’t prove. Educational Studies in Mathematics, 38, 85-109. https://doi.org/10.1023/A:1003660018579
  • Fraenkel, J. R., & Wallen, N. E. (2009). How to design and evaluate research in education (7th ed.). McGraw Hill Higher Education.
  • Freedman, H. (1983). A way of teaching abstract algebra. The American Mathematical Monthly, 90 (9), 641-644.
  • Fuys, D. (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447-462.
  • Fuys, D., Geddes, D., & Tischer, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph, 3, 1-196.
  • Goetting, M. (1995). The college students’ understanding of mathematical proof. (Doctoral dissertation), University of Maryland.
  • Güler, G., Özdemir, E., & Dikici, R. (2012). Öğretmen adaylarının matematiksel tümevarım yoluyla ispat becerileri ve matematiksel ispat hakkındaki görüşleri. Kastamonu Eğitim Dergisi, 20(1), 219-236.
  • Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(1/2), 127-150. https://doi.org/10.1023/A:1012781005718
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational studies in mathematics, 44, 5-23. https://doi.org/10.1023/A:1012737223465
  • Hershkowitz, R., Bruckheimer, M., & Vinner, S. (1987). Activities with teachers based on cognitive research. In M.Linquist & A. Schulte (Eds.) Learning and teaching geometry, K-12 1987 Yearbook (pp. 222–235). The National Council of Teachers of Mathematics.
  • Howse, T. D., & Howse, M. E. (2014). Linking the van Hiele theory to instruction. Teaching Children Mathematics, 21(5), 304-313. https://doi.org/10.5951/teacchilmath.21.5.0304
  • Jones, K. (2000). The student experience of mathematical proof at university level. International Journal of Mathematical Education in Science and Technology, 31(1), 53-60. https://doi.org/10.1080/002073900287381
  • Jupri, A. (2018). Using the van Hiele theory to analyze primary school teachers' written work on geometrical proof problems. 4th International Seminar of Mathematics, Science and Computer Science Education IOP Conf. Series, 1013(012117). https://doi.org/10.1088/1742-6596/1013/1/012117
  • Knight, K. C. (2006). An investigation into the change in the van Hiele levels of understanding geometry of preservice elementary and secondary mathematics teachers. (Master thesis). University of Maine.
  • Knuth, E. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959
  • Knuth, E., Choppin, J., Slaughter, M. & Sutherland, J. (2002). Mapping the conceptual terrain of middle school students’ competencies in justifying and proving. In D. Mewborn, P. Sztajn, D. White, H. Wiegel, R. Bryant & K. Noony (Eds.), Proceedings of the Twenty-fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1693-1670), University of Georgia.
  • Kotzé, G. (2007). Investigating shape and space in mathematics: a case study. South African Journal of Education, 27(1), 19-35.
  • Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children's reasoning about space and geometry: In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Lawrence Erlbaum Associates Publishers.
  • Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, 87-125. https://doi.org/10.1023/A:1012785106627
  • Marriotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44, 25-43. https://doi.org/10.1023/A:1012733122556
  • Martin, T., & McCrone, S. (2009). Formal proof in high school geometry: Students perceptions of structure, validity, and purpose. In Stylianou, D. A., Blanton, M. L. & Knuth, E. J. (Eds.), Teaching and learning proof across the grades: A K-l6 perspective (pp. 204-221). Routledge.
  • McCrone, S. M. S., & Martin, T. S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Science, Mathematics and Technology Education, 4(2), 223-242. https://doi.org/ 10.1080/14926150409556607
  • Ministry of National Education. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics curriculum: Elementary andmiddle schools 3, 4, 5, 6, 7 and 8th grades)]. Talim Terbiye Kurul Başkanlığı.
  • Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in mathematics, 27, 249-266. https://doi.org/10.1007/BF01273731
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
  • Raman, M., & Weber, K. (2006). Key ideas and insights in the context of three high school geometry proofs. Mathematics Teacher, 99(9), 644-649. https://doi.org/10.5951/MT.99.9.0644
  • Reisel, R. B. (1982). How to construct and analyze proofs-a seminar course. The American Mathematical Monthly, 89(7), 490-492. https://doi.org/10.1080/00029890.1982.11995483
  • Senk, S. L. (1985). How well do students write geometry proofs? Mathematics Teacher, 78(6), 448-456.
  • Senk, S. L. (1989). Van Hiele levels and achievement in writing proofs. Journal for Research in Mathematics Education, 20(3), 309-321. https://doi.org/10.2307/749519
  • Sevgi, S., & Orman, F. (2020). Eighth grade students’ views about giving proof and their proof abilities in the geometry and measurement. International Journal of Mathematical Education in Science and Technology, 1-24. https://doi.org/10.1080/0020739X.2020.1782493
  • Shanghai Education Committee. (2004). Shanghai Primary and Secondary School Curriculum Standard. Shanghai: Shanghai Education Press.
  • Sowder, L., & Harel, G. (1998). Types of students' justifications. Mathematics Teacher, 91(8), 670-675. https://doi.org/10.5951/MT.91.8.0670
  • Sowder, L., & Harel, G. (2003). Case studies of mathematics majors proof understanding, production, and appreciation. Canadian Journal of Science, Mathematics, and Technology Education 3(2), 251-267. https://doi.org/10.1080/14926150309556563
  • Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38, 289-321. https://doi.org/10.2307/30034869
  • Stylianides, A. J., Stylianides, G. J., & Philippou, G. N. (2004). Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55(1), 133-162. https://doi.org/10.1023/B:EDUC.0000017671.47700.0b
  • Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10(3), 145-166. https://doi.org/10.1007/s10857-007-9034-z
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. University of Chicago.
  • Sarı Uzun, M., & Bülbül, A. (2013). A teaching experiment on development of pre-service mathematics teachers’ proving skills. Education and Science, 38(169), 372-390.
  • van Dormolen, J. (1977). Learning to understand what giving a proof really means. Educational Studies in Mathematics, 8(1), 27-34.
  • van Hiele, P. M. (1984). The child’s through and geometry. In D. Fuys, D. Geddes, & R. Tischler (Eds.), English translation of selected writings of Dina van Hiele-Geldof & Pierre M. van Hiele (pp. 243-252). Brooklyn. Varghese, T. (2008). Student teachers’ conceptions of mathematical proof. (Master thesis), University of Alberta.
  • Wahlberg, M. (1997). Lecturing at the “Bored”. The American Mathematical Monthly, 104(6), 551-556. https://doi.org/10.1080/00029890.1997.11990677
  • Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-119. https://doi.org/10.1023/A:1015535614355
  • Wu, D. B. (1994). A study of the use of the van Hiele model in the teaching of non-Euclidean geometry to prospective elementary school teachers in Taiwan, the Republic of China. (Doctoral dissertation), University of Northern Colorado.
  • Wu, H. H. (1996). The role of Euclidean geometry in high school. Journal of Mathematical Behavior, 15(3), 221-237. https://doi.org/10.1016/S0732-3123(96)90002-4
  • Yackel, E., Gravemeijer, K. & Sfard, A. (Eds.) (2011). A journey in mathematics education research. Springer Science.
  • Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri (9. baskı). Seçkin Yayınevi.
  • Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038
  • Yılmaz, G. K., & Koparan, T. (2016). The effect of designed geometry teaching lesson to the candidate teachers’ van Hiele geometric thinking level. Journal of Education and Training Studies, 4(1), 129-141. https://doi.org/10.11114/jets.v4i1.1067
  • Zaslavsky, O. (2005). Seizing opportunity to create uncertainty in learning mathematics. Educational Studies in Mathematics, 60, 297-321. https://doi.org/10.1007/s10649-005-0606-5
Toplam 66 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Alan Eğitimleri
Bölüm Araştırma Makaleleri
Yazarlar

Ceylan Şen 0000-0002-6384-7941

Gürsel Güler 0000-0003-1429-1585

Yayımlanma Tarihi 26 Mart 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 23 Sayı: Özel Sayı

Kaynak Göster

APA Şen, C., & Güler, G. (2022). Matematik Öğretmeni Adaylarının Geometrik İspatlarda İspat Yazma Becerilerinin İncelenmesi: Van Hiele Modeli. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 23(Özel Sayı), 128-176. https://doi.org/10.29299/kefad.997311

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