Research Article
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Year 2023, Volume: 11 Issue: 4 - December 2023, 541 - 556, 30.12.2023
https://doi.org/10.17478/jegys.1365213

Abstract

References

  • 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
  • Angelides, M. C., & Agius, H. V. (2002). An interactive multimedia learning environment for VLSI built with Cosmos. Computers & Education, 39, 145-160. https://doi.org/10.1016/S0360-1315(02)00028-3
  • Arsac, G. (2007). Origin of mathematical proof: History and epistemology. In P. Boero (Ed.), Theorems in schools: From history, epistemology and cognition to classroom practice (pp. 27-42). Sense Publishing.
  • Arslan, Ç. (2007). İlköğretim öğrencilerinde muhakeme etme ve ispatlama düşüncesinin gelişimi [The development of elementary school students on their reasoning and proof ideas] (Unpublished doctoral dissertation). Uludağ University, Türkiye.
  • Balacheff, N. (1998). Aspects of proof in pupils' practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216-235). Hodder and Stoughton Publishing.
  • Bell, A. (1976). A study of pupils’ proof-explanations in mathematical situations. Education Studies in Mathematics 7(1-2), 23-40. https://www.jstor.org/stable/3481809
  • Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80. https://doi.org/10.1016/j.ijer.2013.06.005
  • Botana, F., & Valcarce, J. L. (2002). A dynamic-symbolic interface for geometric theorem discovery. Computers & Education, 38, 21-35. https://doi.org/10.1016/S0360-1315(01)00089-6
  • Cai, J., & Howson, G. (2012). Toward an international mathematics curriculum. In: Clements, M., Bishop, A., Keitel, C., Kilpatrick, J., Leung, F. (Eds.) Third international handbook of mathematics education. Springer international handbooks of education. Springer. https://doi.org/10.1007/978-1-4614-4684-2_29
  • Çalışkan, Ç. (2012). 8. sınıf öğrencilerinin matematik başarılarıyla ispat yapabilme seviyelerinin ilişkilendirilmesi [The interrelations between 8th grade class students' mathematics success and proving levels] (Unpublished master's thesis). Uludağ University, Türkiye.
  • de Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras 24, 17-24.
  • Demircioğlu, H. (2023). Preservice mathematics teachers’ proving skills in an incorrect statement: Sums of triangular numbers. Pegem Journal of Education and Instruction, 13(1), 326-333. https://doi.org/10.47750/pegegog.13.01.36
  • Doruk, M., & Kaplan, A. (2017). İlköğretim matematik öğretmeni adaylarının analiz alanında yaptıkları ispatların özellikleri [The characteristics of proofs produced by preservice primary mathematics teachers in calculus]. Mehmet Akif Ersoy University Journal of Education Faculty, 44, 467-498. https://doi.org/10.21764/maeuefd.305605
  • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13. https://doi.org/10.1007/BF01809605
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1-2), 5-23. https://doi.org/10.1023/A:1012737223465
  • Hanna, G., & Barbeau, E. (2002). What is a proof. History of Modern Science and Mathematics, 1, 36-48.
  • Harel, G., & Sowder, L. (1998). Types of students justifications. The Mathematics Teacher, 91(8), 670-675. https://doi.org/10.5951/MT.91.8.0670
  • Hartter, B. J. (1995). Concept image and concept definition for the topic of the derivative (Unpublished doctoral dissertation). Illinois State University, USA.
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428. https://doi.org/10.2307/749651
  • Jones, K. (1997). Student teachers’ conceptions of mathematical proof. Mathematics Education Review, 9, 21-32.
  • 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
  • Knuth, E. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5, 61-88. https://doi.org/10.1023/A:1013838713648
  • Knuth, E. J., Choppin, J. M., & Bieda, K. N. (2009). Proof: Examples and beyond. Mathematics Teaching in the Middle School, 15(4), 206-211. https://doi.org/10.5951/MTMS.15.4.0206
  • Kotelawala, U. M. (2007). Exploring teachers’ attitudes and beliefs about proving in the mathematics classroom (Unpublished doctoral dissertation). Columbia University, USA.
  • Lesseig, K. (2016). Investigating mathematical knowledge for teaching proof in Professional development. International Journal of Research in Education and Science, 2(2), 253-270.
  • Martin, G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20, 41-51. https://doi.org/10.5951/jresematheduc.20.1.0041
  • Miyazaki, M. (2000). Levels of proof in lover secondary school mathematics. Educational Studies in Mathematics, 41, 47-68. https://doi.org/10.1023/A:1003956532587
  • Moralı, S., Uğurel, İ., Türnüklü, E., & Yeşildere, S. (2006). Matematik öğretmen adaylarının ispat yapmaya yönelik görüşleri [The views of the mathematics teachers on proving]. Kastamonu Education Journal, 14(1), 147-160.
  • Morris, A. K. (2002). Mathematical reasoning: Adults' ability to make the inductive-deductive distinction. Cognition and Instruction, 20(1), 79-118. https://doi.org/10.1207/S1532690XCI2001_4
  • Polat, K., & Akgün, L. (2023). High school students’ and their teacher’s experiences with visual proofs. Erzincan University Journal of Education Faculty, 25(1), 126-136. https://doi.org/10.17556/erziefd.1092716
  • Quinn, A. L. (2009). Count on number theory to inspire proof. Mathematics Teacher, 103(4), 298-304. https://doi.org/10.5951/MT.103.4.0298
  • Raman, M. (2003). Key ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics, 52(3), 319-325. https://doi.org/10.1023/A:1024360204239
  • Saeed, R., M. (1996). An exploratory study of college student’s understanding of mathematical proof and the relationship of this understanding to their attitude toward mathematics (Unpublished doctoral dissertation). Ohio University, USA.
  • 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.
  • Schabel, C. (2005). An instructional model for teaching proof writing in the number theory classroom. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 15(1), 45-59. https://doi.org/10.1080/10511970508984105
  • Schoenfeld, A. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55-80. https://doi.org/10.1016/0732-3123(94)90035-3
  • Strijbos, J. W., Martens, R. L., & Jochems, W. M. G. (2003). Designing for interaction: Six steps to designing computer-supported group-based learning. Computers & Education, 42, 403-424. https://doi.org/10.1016/j.compedu.2003.10.004
  • Stylianides, G. J., & Stylianides, A. J. (2023). Preservice teachers' ways of addressing challenges when teaching reasoning-and-proving in their mentor teachers' mathematics classrooms. In practical theorising in teacher education (pp. 97-112). Routledge Publishing.
  • Stylianides, G. J., Stylianides, A. J., & Philippou. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, 145-166. https://doi.org/10.1007/s10857-007-9034-z
  • Tavşancıl, E., & Aslan, A. E. (2001). Content analysis and application examples for verbal, written and other materials. Epsilon Publishing.
  • Urhan, S., & Bülbül, A. (2016). The relationship is between argumentation and mathematical proof processes. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 10(1), 351-373. https://doi.org/10.17522/nefefmed.00387
  • Weber, K (2006). Investigating and teaching the processes used to construct proofs. Research in Collegiate Mathematics Education, 6, 197-232.
  • Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-119. https://doi.org/10.1023/A:1015535614355
  • Weber, K., Maher, C., Powell, A. & Lee, H. S. (2008). Learning opportunities from group discussions: warrants become the objects of debate. Educational Studies in Mathematics, 68, 247-261. https://doi.org/10.1007/s10649-008-9114-8
  • Wheeler, D. (1990). Aspects of mathematical proof. Interchange, 21(1), 1-5. https://doi.org/10.1007/BF01809604
  • Yıldırım, A., & Şimşek, H. (2008). Qualitative research methods in social sciences. Seçkin Publishing,
  • Yin, R. K. (2003). Case study research: Design and methods. Sage Publishing.

Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers

Year 2023, Volume: 11 Issue: 4 - December 2023, 541 - 556, 30.12.2023
https://doi.org/10.17478/jegys.1365213

Abstract

This study examined the subject(s) that elementary mathematics teacher candidates find most suitable for proving in analysis courses, the functional structure of proof they remember most, the level of proof, and the reasons for preferring this proof. For this reason, this research aims to reveal the pre-service teachers' preferences for proof in analysis courses, the proof they keep in mind the most and its functional structure, their level of proof, and their views on proof relationally and holistically. In this study, which was conducted with a qualitative research approach, a form consisting of open-ended questions was applied to teacher candidates. In this form, teacher candidates were asked various questions about the mathematical proofs they made. With descriptive analysis, the answers of the pre-service teachers who participated in the research were systematically defined, and data were tried to be defined through content analysis. Accordingly, while the subject that the pre-service teachers found the most appropriate application of the proof approach to be the subject of trigonometry, it was determined that the proof that remained in their minds the most was also related to the subject of trigonometry. By examining the functional structure of these proofs written by pre-service teachers, it has been seen that they have the function of explanation and systematization. In addition, the reasons for preferring the proof they made were asked of the pre-service teachers, and the answers were gathered on the fact that proof provides the most permanence and causal learning. It was emphasized that theorems that require formula memorization generally become more understandable with the proof method. According to the results of the research, it is stated that the common opinion of the prospective teachers is that teaching how to obtain the proof method of formulas in trigonometry, instead of memorizing them, is beneficial in ensuring both meaningful and permanent learning. In light of the findings of these studies, more sensible suggestions can be made to improve pre-service teachers' knowledge systems and classroom teaching on proof. By determining which topics and theorems students have difficulty in proving in addition to trigonometry, additional learning on these subjects can be recommended.

References

  • 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
  • Angelides, M. C., & Agius, H. V. (2002). An interactive multimedia learning environment for VLSI built with Cosmos. Computers & Education, 39, 145-160. https://doi.org/10.1016/S0360-1315(02)00028-3
  • Arsac, G. (2007). Origin of mathematical proof: History and epistemology. In P. Boero (Ed.), Theorems in schools: From history, epistemology and cognition to classroom practice (pp. 27-42). Sense Publishing.
  • Arslan, Ç. (2007). İlköğretim öğrencilerinde muhakeme etme ve ispatlama düşüncesinin gelişimi [The development of elementary school students on their reasoning and proof ideas] (Unpublished doctoral dissertation). Uludağ University, Türkiye.
  • Balacheff, N. (1998). Aspects of proof in pupils' practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers and children (pp. 216-235). Hodder and Stoughton Publishing.
  • Bell, A. (1976). A study of pupils’ proof-explanations in mathematical situations. Education Studies in Mathematics 7(1-2), 23-40. https://www.jstor.org/stable/3481809
  • Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80. https://doi.org/10.1016/j.ijer.2013.06.005
  • Botana, F., & Valcarce, J. L. (2002). A dynamic-symbolic interface for geometric theorem discovery. Computers & Education, 38, 21-35. https://doi.org/10.1016/S0360-1315(01)00089-6
  • Cai, J., & Howson, G. (2012). Toward an international mathematics curriculum. In: Clements, M., Bishop, A., Keitel, C., Kilpatrick, J., Leung, F. (Eds.) Third international handbook of mathematics education. Springer international handbooks of education. Springer. https://doi.org/10.1007/978-1-4614-4684-2_29
  • Çalışkan, Ç. (2012). 8. sınıf öğrencilerinin matematik başarılarıyla ispat yapabilme seviyelerinin ilişkilendirilmesi [The interrelations between 8th grade class students' mathematics success and proving levels] (Unpublished master's thesis). Uludağ University, Türkiye.
  • de Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras 24, 17-24.
  • Demircioğlu, H. (2023). Preservice mathematics teachers’ proving skills in an incorrect statement: Sums of triangular numbers. Pegem Journal of Education and Instruction, 13(1), 326-333. https://doi.org/10.47750/pegegog.13.01.36
  • Doruk, M., & Kaplan, A. (2017). İlköğretim matematik öğretmeni adaylarının analiz alanında yaptıkları ispatların özellikleri [The characteristics of proofs produced by preservice primary mathematics teachers in calculus]. Mehmet Akif Ersoy University Journal of Education Faculty, 44, 467-498. https://doi.org/10.21764/maeuefd.305605
  • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13. https://doi.org/10.1007/BF01809605
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1-2), 5-23. https://doi.org/10.1023/A:1012737223465
  • Hanna, G., & Barbeau, E. (2002). What is a proof. History of Modern Science and Mathematics, 1, 36-48.
  • Harel, G., & Sowder, L. (1998). Types of students justifications. The Mathematics Teacher, 91(8), 670-675. https://doi.org/10.5951/MT.91.8.0670
  • Hartter, B. J. (1995). Concept image and concept definition for the topic of the derivative (Unpublished doctoral dissertation). Illinois State University, USA.
  • Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428. https://doi.org/10.2307/749651
  • Jones, K. (1997). Student teachers’ conceptions of mathematical proof. Mathematics Education Review, 9, 21-32.
  • 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
  • Knuth, E. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5, 61-88. https://doi.org/10.1023/A:1013838713648
  • Knuth, E. J., Choppin, J. M., & Bieda, K. N. (2009). Proof: Examples and beyond. Mathematics Teaching in the Middle School, 15(4), 206-211. https://doi.org/10.5951/MTMS.15.4.0206
  • Kotelawala, U. M. (2007). Exploring teachers’ attitudes and beliefs about proving in the mathematics classroom (Unpublished doctoral dissertation). Columbia University, USA.
  • Lesseig, K. (2016). Investigating mathematical knowledge for teaching proof in Professional development. International Journal of Research in Education and Science, 2(2), 253-270.
  • Martin, G., & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20, 41-51. https://doi.org/10.5951/jresematheduc.20.1.0041
  • Miyazaki, M. (2000). Levels of proof in lover secondary school mathematics. Educational Studies in Mathematics, 41, 47-68. https://doi.org/10.1023/A:1003956532587
  • Moralı, S., Uğurel, İ., Türnüklü, E., & Yeşildere, S. (2006). Matematik öğretmen adaylarının ispat yapmaya yönelik görüşleri [The views of the mathematics teachers on proving]. Kastamonu Education Journal, 14(1), 147-160.
  • Morris, A. K. (2002). Mathematical reasoning: Adults' ability to make the inductive-deductive distinction. Cognition and Instruction, 20(1), 79-118. https://doi.org/10.1207/S1532690XCI2001_4
  • Polat, K., & Akgün, L. (2023). High school students’ and their teacher’s experiences with visual proofs. Erzincan University Journal of Education Faculty, 25(1), 126-136. https://doi.org/10.17556/erziefd.1092716
  • Quinn, A. L. (2009). Count on number theory to inspire proof. Mathematics Teacher, 103(4), 298-304. https://doi.org/10.5951/MT.103.4.0298
  • Raman, M. (2003). Key ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics, 52(3), 319-325. https://doi.org/10.1023/A:1024360204239
  • Saeed, R., M. (1996). An exploratory study of college student’s understanding of mathematical proof and the relationship of this understanding to their attitude toward mathematics (Unpublished doctoral dissertation). Ohio University, USA.
  • 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.
  • Schabel, C. (2005). An instructional model for teaching proof writing in the number theory classroom. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 15(1), 45-59. https://doi.org/10.1080/10511970508984105
  • Schoenfeld, A. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55-80. https://doi.org/10.1016/0732-3123(94)90035-3
  • Strijbos, J. W., Martens, R. L., & Jochems, W. M. G. (2003). Designing for interaction: Six steps to designing computer-supported group-based learning. Computers & Education, 42, 403-424. https://doi.org/10.1016/j.compedu.2003.10.004
  • Stylianides, G. J., & Stylianides, A. J. (2023). Preservice teachers' ways of addressing challenges when teaching reasoning-and-proving in their mentor teachers' mathematics classrooms. In practical theorising in teacher education (pp. 97-112). Routledge Publishing.
  • Stylianides, G. J., Stylianides, A. J., & Philippou. (2007). Preservice teachers’ knowledge of proof by mathematical induction. Journal of Mathematics Teacher Education, 10, 145-166. https://doi.org/10.1007/s10857-007-9034-z
  • Tavşancıl, E., & Aslan, A. E. (2001). Content analysis and application examples for verbal, written and other materials. Epsilon Publishing.
  • Urhan, S., & Bülbül, A. (2016). The relationship is between argumentation and mathematical proof processes. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 10(1), 351-373. https://doi.org/10.17522/nefefmed.00387
  • Weber, K (2006). Investigating and teaching the processes used to construct proofs. Research in Collegiate Mathematics Education, 6, 197-232.
  • Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-119. https://doi.org/10.1023/A:1015535614355
  • Weber, K., Maher, C., Powell, A. & Lee, H. S. (2008). Learning opportunities from group discussions: warrants become the objects of debate. Educational Studies in Mathematics, 68, 247-261. https://doi.org/10.1007/s10649-008-9114-8
  • Wheeler, D. (1990). Aspects of mathematical proof. Interchange, 21(1), 1-5. https://doi.org/10.1007/BF01809604
  • Yıldırım, A., & Şimşek, H. (2008). Qualitative research methods in social sciences. Seçkin Publishing,
  • Yin, R. K. (2003). Case study research: Design and methods. Sage Publishing.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Teacher Education
Authors

Bahar DİNÇER 0000-0003-4767-7791

Deniz KAYA 0000-0002-7804-1772

Early Pub Date December 15, 2023
Publication Date December 30, 2023
Published in Issue Year 2023 Volume: 11 Issue: 4 - December 2023

Cite

APA DİNÇER, B., & KAYA, D. (2023). Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers. Journal for the Education of Gifted Young Scientists, 11(4), 541-556. https://doi.org/10.17478/jegys.1365213
AMA DİNÇER B, KAYA D. Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers. JEGYS. December 2023;11(4):541-556. doi:10.17478/jegys.1365213
Chicago DİNÇER, Bahar, and Deniz KAYA. “Subject, Functionality and Level of Proofs Preferred by Pre-Service Elementary Mathematics Teachers”. Journal for the Education of Gifted Young Scientists 11, no. 4 (December 2023): 541-56. https://doi.org/10.17478/jegys.1365213.
EndNote DİNÇER B, KAYA D (December 1, 2023) Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers. Journal for the Education of Gifted Young Scientists 11 4 541–556.
IEEE B. DİNÇER and D. KAYA, “Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers”, JEGYS, vol. 11, no. 4, pp. 541–556, 2023, doi: 10.17478/jegys.1365213.
ISNAD DİNÇER, Bahar - KAYA, Deniz. “Subject, Functionality and Level of Proofs Preferred by Pre-Service Elementary Mathematics Teachers”. Journal for the Education of Gifted Young Scientists 11/4 (December 2023), 541-556. https://doi.org/10.17478/jegys.1365213.
JAMA DİNÇER B, KAYA D. Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers. JEGYS. 2023;11:541–556.
MLA DİNÇER, Bahar and Deniz KAYA. “Subject, Functionality and Level of Proofs Preferred by Pre-Service Elementary Mathematics Teachers”. Journal for the Education of Gifted Young Scientists, vol. 11, no. 4, 2023, pp. 541-56, doi:10.17478/jegys.1365213.
Vancouver DİNÇER B, KAYA D. Subject, functionality and level of proofs preferred by pre-service elementary mathematics teachers. JEGYS. 2023;11(4):541-56.