Araştırma Makalesi

Yıl 2021,
Cilt: 8 Sayı: 1, 1 - 15, 08.03.2021
### Öz

### Anahtar Kelimeler

### Kaynakça

Nonverbal proofs are diagrams or illustrations that will help us see what a mathematical expression means, why it is true, and how it is proved. The aim of this study is to examine the effects of nonverbal proof-based education on preservice mathematics teachers. The study was conducted using case study research methods, one of the qualitative research designs. The participants of the study consisted of 31 preservice mathematics teachers. The data were collected in writing at the beginning and end of the process with questions directed to preservice teachers. These questions in the data collection tool were used to compare the responses of the preservice teachers who had an experience with nonverbal proof in the pre and post assesment and compare the changes. In the analysis of the data, descriptive analysis, which is a qualitative data analysis, was used. Firstly, each preservice teacher’s responses in the post assesment are classified according to their similarities and differences and then are categorized. Then, the answers in the pre assesment were examined and the responses were compared whether there was a change or not. The findings of the study showed that the preservice mathematics teachers’ experience of nonverbal proof effect on the recognition of the given image and establishing a relationship with different mathematics subjects.

proof nonverbal proof nonverbal proof visual proof visualization preservice mathematics teachers

- Almeida, D. (1996). Variation in proof standarts: Implication for mathematics education. International Journal of Mathematical Education in Science and Technology, 27, 659–665. DOI:10.1080/0020739960270504.
- Almeida, D. (2001). Pupils’ proof potential. International Journal of Mathematical Education in Science and Technology, 32(1), 53-60. DOI:10.1080/00207390150207059.
- Alsina, C. & Nelsen R. (2010). An invitation to proofs without words. European Journal of Pure and Applied Mathematics, 3(1), 118-127.
- Bell, C. (2011). Proofs without words: A visual application of reasoning and proof. Mathematics Teacher, 104(1), 690-695.
- Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), Proceedings of the International Congress of Mathematicians, 3, 907–920. Beijing: Higher Education.
- Bardelle, C. (2009). Visual proofs: an experiment. In V. Durand-Guerrier et al (Eds), Paper presented at the annual meeting of CERME6, Lyon, France. INRP, 251-260.
- Casselman, B. (2000). Pictures and proofs. Notices of the American Mathematical Monthly, 47(10), 1257-1266.
- Davis, P.J. (1993). Visual theorems. Educational Studies in Mathematics, 24(4), 333–344. doi:10.1007/BF01273369.
- Demircioğlu, H., & Polat, K. (2015) Ortaöğretim Matematik Öğretmeni Adaylarının “Sözsüz İspatlar” Yöntemine Yönelik Görüşleri. The Journal of Academic Social Science Studies, 41, Winter II, 233-254, Doi number:http://dx.doi.org/10.9761/JASSS3171.
- Doruk, M. & Güler, G. (2014). İlköğretim Matematik Öğretmeni Adaylarının Matematiksel İspata Yönelik Görüşleri. Uluslararası Türk Eğitim Bilimleri Dergisi, 71-93.
- Flores, A. (1992). A geometrical approach no mathematical induction: Proofs that explain. PRIMUS, Vol. II (4), 393-400.
- Flores, A. (2000). Geometric representations in the transition from arithmetic to algebra. In F. Hitt (Ed.), North American Chapter of the International Group for the Psychology of Mathematics Education. Reprensentation and Mathematics Visualization (pp. 9-29).
- Foo, N., Pagnucco, M. & Nayak, A.(1999) .Diagrammatic Proofs, Proceedings of the 16th International Joint Conference on Artificial Intelligence, (IJCAI- 99), Morgan Kaufman pp. 378 – 383.
- Gierdien, F. (2007). From “Proofs without words” to “Proofs that explain” in secondary mathematics. Pythagoras, 65, 53 – 62.
- Hammack, R. H., & Lyons, D. W. (2006). Alternating series convergence: a visual proof. Teaching Mathematics and its Applications, 25(2), 58.
- Hanna, G. (2000). Proof, Explanation and Exploration: An Overview. Educational Studies in Mathematics, 44, 5-23. DOI:10.1023/A:1012737223465.
- Harel, G. & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof [DX Reader version]. Retrieved from http://www.math.ucsd.edu/~harel/ publications/ Downloadable/ TowardComprehensivePerspective.pdf.
- Harel, G., & Sowder, L. (1998). Students’proof schemes: results from exploratory studies. CBMS Issues in Mathematics Education, 7, 234-282. DOI:10.1090/cbmath/007/07.
- Heinze, A., & Reiss, K. (2004). The teaching ofproof at lower secondary level – a video study. ZDM Mathematics Education, 36(3), 98–104.
- 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.
- Knuth, E. J. (2002a). Secondary school mathematics teachers‘ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379–405.
- Knuth, E. J. (2002b). Teachers‘ conceptions of proof in the context of secondary school mathematics. Journal for Mathematics Teacher Education, 5, 61–88.
- Kulpa, Z. (2009). Main problems of diagrammatic reasoning. Part I: The generalization problem, Foundations of Science 14: 75–96.
- Lockhart, P. (2009). A Mathematician’s lament. Retrieved from https://www.maa.org/external_archive/ devlin/LockhartsLament.pdf
- Maanen, J. V. (2006). Diagrams and mathematical reasoning: Some points, lines and figures. Journal of British Society for the History of Mathematics, 21(2), 97-101.
- Miller R. L. (2012). On proofs without words, Retrieved from: http://www.whitman.edu/mathematics/ SeniorProjectArchive/2012/Miller.pdf
- Miyazaki M. (2000) Levels of proof in lower secondary school mathematics. Educational Studies in Mathematics, 41(1), 47-68.
- Morash, R. P. (1987). Bridge to abstract mathematics: Mathematical proof and structures, New York: Random House.
- Nelsen. R. (1993). Proofs without words: exercises in visual thinking. Washington: Mathematical Association of America.
- Nelsen. R (2000). Proofs without words ıı: more exercises in visual thinking. Washington: Mathematical Association of America.
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards For School Mathematics. Reston VA: NCTM.
- Norman, J.(2003). Visual reasoning in Euclid’s geometry, University College London: PhD Dissertation.
- Rodd, M. M. (2000). On mathematical warrants: Proof does not always warrant, and a warrant may be other than a proof. Mathematical Thinking and Learning, 2(3), 221–244. DOI:10.1207/S15327833MTL0203_4
- Rösken, B. & Rolka, K. (2006). A picture is worth a 1000 words- the role of visualization in mathematics learning. In J. Novotná, H. Moraová, M. Krátká & N.Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 441-448). Prague, Czech Republic: PME.
- Sekiguchi, Y. (2002). Mathematical proof, argumentation, and classroom communication：From a cultural perspective. Tsukuba Journal of Educational Study in Mathematics．21，11-20
- Štrausová, I., & Hašek, R. (2013) Dynamic visual proofs using DGS. The Electronic Journal of Mathematics and Technology, zv. 7, 1. vyd.2, pp. 130-142
- Stucky,B.(2015). Another Visual Proof of Nicomachus' Theorem. http://bstucky.com/bstucky_files/nico.pdf
- Thornton, S. (2001). A picture is worth a thousand words. New ideas in mathematics education: Proceedings of the International Conference of the Mathematics Education into the 21st Century Project
- Uğurel, I., Moralı, H. S. & Karahan, Ö. (2011). Matematikte Yetenekli Olan Ortaöğretim Öğrencilerin Sözsüz İspat Oluşturma Yaklaşımları, I. Uluslararası Eğitim Programları ve Öğretimi Kongresi, 5-8 Ekim, Eskişehir.
- Wallace, E. C. & West S. F. (2004). Roads to geometry (3. Ed). New Jersey : Pearson Education.
- Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. DOI:10.1023/A:1015535614355

Yıl 2021,
Cilt: 8 Sayı: 1, 1 - 15, 08.03.2021
### Öz

### Anahtar Kelimeler

### Kaynakça

Nonverbal proofs are diagrams or illustrations that will help us see what a mathematical expression means, why it is true, and how it is proved. The aim of this study is to examine the effects of nonverbal proof-based education on preservice mathematics teachers. The study was conducted using case study research methods, one of the qualitative research designs. The participants of the study consisted of 31 preservice mathematics teachers. The data were collected in writing at the beginning and end of the process with questions directed to preservice teachers. These questions in the data collection tool were used to compare the responses of the preservice teachers who had an experience with nonverbal proof in the pre and post assesment and compare the changes. In the analysis of the data, descriptive analysis, which is a qualitative data analysis, was used. Firstly, each preservice teacher’s responses in the post assesment are classified according to their similarities and differences and then are categorized. Then, the answers in the pre assesment were examined and the responses were compared whether there was a change or not. The findings of the study showed that the preservice mathematics teachers’ experience of nonverbal proof effect on the recognition of the given image and establishing a relationship with different mathematics subjects.

proof nonverbal proof visual proof visualization preservice mathematics teachers

- Almeida, D. (1996). Variation in proof standarts: Implication for mathematics education. International Journal of Mathematical Education in Science and Technology, 27, 659–665. DOI:10.1080/0020739960270504.
- Almeida, D. (2001). Pupils’ proof potential. International Journal of Mathematical Education in Science and Technology, 32(1), 53-60. DOI:10.1080/00207390150207059.
- Alsina, C. & Nelsen R. (2010). An invitation to proofs without words. European Journal of Pure and Applied Mathematics, 3(1), 118-127.
- Bell, C. (2011). Proofs without words: A visual application of reasoning and proof. Mathematics Teacher, 104(1), 690-695.
- Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), Proceedings of the International Congress of Mathematicians, 3, 907–920. Beijing: Higher Education.
- Bardelle, C. (2009). Visual proofs: an experiment. In V. Durand-Guerrier et al (Eds), Paper presented at the annual meeting of CERME6, Lyon, France. INRP, 251-260.
- Casselman, B. (2000). Pictures and proofs. Notices of the American Mathematical Monthly, 47(10), 1257-1266.
- Davis, P.J. (1993). Visual theorems. Educational Studies in Mathematics, 24(4), 333–344. doi:10.1007/BF01273369.
- Demircioğlu, H., & Polat, K. (2015) Ortaöğretim Matematik Öğretmeni Adaylarının “Sözsüz İspatlar” Yöntemine Yönelik Görüşleri. The Journal of Academic Social Science Studies, 41, Winter II, 233-254, Doi number:http://dx.doi.org/10.9761/JASSS3171.
- Doruk, M. & Güler, G. (2014). İlköğretim Matematik Öğretmeni Adaylarının Matematiksel İspata Yönelik Görüşleri. Uluslararası Türk Eğitim Bilimleri Dergisi, 71-93.
- Flores, A. (1992). A geometrical approach no mathematical induction: Proofs that explain. PRIMUS, Vol. II (4), 393-400.
- Flores, A. (2000). Geometric representations in the transition from arithmetic to algebra. In F. Hitt (Ed.), North American Chapter of the International Group for the Psychology of Mathematics Education. Reprensentation and Mathematics Visualization (pp. 9-29).
- Foo, N., Pagnucco, M. & Nayak, A.(1999) .Diagrammatic Proofs, Proceedings of the 16th International Joint Conference on Artificial Intelligence, (IJCAI- 99), Morgan Kaufman pp. 378 – 383.
- Gierdien, F. (2007). From “Proofs without words” to “Proofs that explain” in secondary mathematics. Pythagoras, 65, 53 – 62.
- Hammack, R. H., & Lyons, D. W. (2006). Alternating series convergence: a visual proof. Teaching Mathematics and its Applications, 25(2), 58.
- Hanna, G. (2000). Proof, Explanation and Exploration: An Overview. Educational Studies in Mathematics, 44, 5-23. DOI:10.1023/A:1012737223465.
- Harel, G. & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof [DX Reader version]. Retrieved from http://www.math.ucsd.edu/~harel/ publications/ Downloadable/ TowardComprehensivePerspective.pdf.
- Harel, G., & Sowder, L. (1998). Students’proof schemes: results from exploratory studies. CBMS Issues in Mathematics Education, 7, 234-282. DOI:10.1090/cbmath/007/07.
- Heinze, A., & Reiss, K. (2004). The teaching ofproof at lower secondary level – a video study. ZDM Mathematics Education, 36(3), 98–104.
- 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.
- Knuth, E. J. (2002a). Secondary school mathematics teachers‘ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379–405.
- Knuth, E. J. (2002b). Teachers‘ conceptions of proof in the context of secondary school mathematics. Journal for Mathematics Teacher Education, 5, 61–88.
- Kulpa, Z. (2009). Main problems of diagrammatic reasoning. Part I: The generalization problem, Foundations of Science 14: 75–96.
- Lockhart, P. (2009). A Mathematician’s lament. Retrieved from https://www.maa.org/external_archive/ devlin/LockhartsLament.pdf
- Maanen, J. V. (2006). Diagrams and mathematical reasoning: Some points, lines and figures. Journal of British Society for the History of Mathematics, 21(2), 97-101.
- Miller R. L. (2012). On proofs without words, Retrieved from: http://www.whitman.edu/mathematics/ SeniorProjectArchive/2012/Miller.pdf
- Miyazaki M. (2000) Levels of proof in lower secondary school mathematics. Educational Studies in Mathematics, 41(1), 47-68.
- Morash, R. P. (1987). Bridge to abstract mathematics: Mathematical proof and structures, New York: Random House.
- Nelsen. R. (1993). Proofs without words: exercises in visual thinking. Washington: Mathematical Association of America.
- Nelsen. R (2000). Proofs without words ıı: more exercises in visual thinking. Washington: Mathematical Association of America.
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards For School Mathematics. Reston VA: NCTM.
- Norman, J.(2003). Visual reasoning in Euclid’s geometry, University College London: PhD Dissertation.
- Rodd, M. M. (2000). On mathematical warrants: Proof does not always warrant, and a warrant may be other than a proof. Mathematical Thinking and Learning, 2(3), 221–244. DOI:10.1207/S15327833MTL0203_4
- Rösken, B. & Rolka, K. (2006). A picture is worth a 1000 words- the role of visualization in mathematics learning. In J. Novotná, H. Moraová, M. Krátká & N.Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 441-448). Prague, Czech Republic: PME.
- Sekiguchi, Y. (2002). Mathematical proof, argumentation, and classroom communication：From a cultural perspective. Tsukuba Journal of Educational Study in Mathematics．21，11-20
- Štrausová, I., & Hašek, R. (2013) Dynamic visual proofs using DGS. The Electronic Journal of Mathematics and Technology, zv. 7, 1. vyd.2, pp. 130-142
- Stucky,B.(2015). Another Visual Proof of Nicomachus' Theorem. http://bstucky.com/bstucky_files/nico.pdf
- Thornton, S. (2001). A picture is worth a thousand words. New ideas in mathematics education: Proceedings of the International Conference of the Mathematics Education into the 21st Century Project
- Uğurel, I., Moralı, H. S. & Karahan, Ö. (2011). Matematikte Yetenekli Olan Ortaöğretim Öğrencilerin Sözsüz İspat Oluşturma Yaklaşımları, I. Uluslararası Eğitim Programları ve Öğretimi Kongresi, 5-8 Ekim, Eskişehir.
- Wallace, E. C. & West S. F. (2004). Roads to geometry (3. Ed). New Jersey : Pearson Education.
- Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. DOI:10.1023/A:1015535614355

Toplam 41 adet kaynakça vardır.

Birincil Dil | İngilizce |
---|---|

Konular | Alan Eğitimleri |

Bölüm | Araştırma Makalesi |

Yazarlar | |

Yayımlanma Tarihi | 8 Mart 2021 |

Yayımlandığı Sayı | Yıl 2021 Cilt: 8 Sayı: 1 |