Examining Mathematical Proof and Problem-Solving Processes of Mathematics Teacher Candidates by Think-Aloud Method
Abstract
This research was carried out in order to reveal how the mental processes of pre-service mathematics teachers are while making mathematical proofs and solving problems, and what their views are about the thinking aloud method. Within the scope of this research based on the case study design, 4 pre-service teachers were asked to express their thoughts aloud, to solve 2 problems, and to do 2 algebraic proofs. Teacher candidates' thinking-aloud processes were video-recorded. The data obtained by transcribing the videos were analyzed and interpreted with the descriptive analysis method. As a result of the research, it was seen that although the pre-service teachers had a general understanding of how to prove the theorem and problem-solving, they did not know how to advance the process of proving and problem-solving and how to use the knowledge they had before in a way suitable for their purpose. In addition, according to the pre-service teachers who participated in the application, the thinking aloud method is a method that develops higher-order thinking and allows the individual to understand what he or she is really thinking.
Keywords
Problem solving mathematical proof algebraic proof pre-service mathematics teacher think aloud
References
- Agustyaningrum, N., Husna, A., Hanggara, Y., Abadi, A. M., & Mahmudi, A. (2020). Analysis of mathematical proof ability in abstract algebra course. Universal Journal of Educational Research, 8(3), 823-834.
- Boero, P. (1999). Argumentation and mathematical proof: a complex, productive, unavoidable relationship in mathematics and mathematics education. International Newsletter on The Teaching and Learning of Mathematical Proof, 7(8). Retrieved from http://www.lettredelapreuve.org/OldPreuve/Newsletter/990708Theme/990708ThemeUK.html
- Bostic, J. D. (2021). Think alouds: Informing scholarship and broadening partnerships through assessment. Applied Measurement in Education, 34(1), 1-9. doi: 10.1080/08957347.2020.1835914
- Cellucci, C. (2017). Is mathematics problem solving or theorem proving?. Foundations of Science, 22(1), 183-199.
- Deshpande, D. S., Riccomini, P. J., Hughes, E. M., & Raulston, T. J. (2021). Problem solving with the pythagorean theorem: A think aloud analysis of secondary students with learning disabilities. Learning Disabilities: A Contemporary Journal, 19(1), 23-47.
- Güneş, F. (2012). Eğitimde sesli düşünme. Akademik Araştırmalar Dergisi, 55, 83-104.
- Krulik, S., & Rudnick, J. A. (1989). Problem solving: A handbook for senior high school teachers. Allyn and Bacon.
- Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. Journal of Mathematical Behavior, 24, 385–401.
- Mamona-Downs, J., & Downs, M. (2013). Problem solving and its elements in forming proof, The Mathematics Enthusiast, 10(1), 136-162.
- Montague, M., & Applegate, B. (2000). Middle school students' perceptions, persistence, and performance in mathematical problem solving. Learning Disability Quarterly, 23(3), 215-227.
- Moralı, S., Uğurel, I., Türnüklü, E., & Yeşildere S. (2006). Matematik öğretmen adaylarının ispat yapmaya yönelik görüşleri, Kastamonu Eğitim Dergisi, 14(1), 147–160.
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standarts for school mathematics, https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/ adresinden 01.01.2021 tarihinde edinilmiştir.
- Öçal, M. F., & Güler, G. (2010). Pre-service mathematics teachers’ views about proof by using concept maps. Procedia-Social and Behavioral Sciences, 9, 318-323.
- Özkubat, U., & Özmen, E. R. (2018). Öğrenme güçlüğü olan öğrencilerin matematik problemi çözme süreçlerinin incelenmesi: sesli düşünme protokolü uygulaması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 19(1), 155-180. doi: 10.21565/ozelegitimdergisi.299494
- Öztürk, M. (2021). Cognitive and metacognitive skills performed by math teachers in the proving process of number theory. Athens Journal of Education, 8(1), 53-71.
- Öztürk, M., & Kaplan, A. (2022). Ortaöğretim matematik öğretmeni adaylarının geometrik ispat yapma süreci: bir durum çalışması. Eurasian Journal of Teacher Education, 3(1), 39-54.
- Polya, G. (1945). How to Solve it. Princeton, NJ: Princeton University Press.
- Rosenzweig, C., Krawec, J., & Montague, M. (2011). Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: a think-aloud analysis. Journal of Learning Disabilities, 44(6), 508–520. https://doi.org/10.1177/0022219410378445
- Van Someren, M. W., Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method: a practical approach to modelling cognitive processes. (Knowledge-based systems). London: Academic Press.
- Yeşilyurt-Çetin, A. (2017). Matematik öğretmeni adaylarının matematiksel ispatta önceden belirlenen anahtar fikirleri yazabilme süreçleri. (Yayımlanmış doktora tezi). Ulusal Tez Merkezi Veri Tabanından Erişildi. ( UMİ No: 480352)
- Yeşilyurt-Çetin, A., & Dikici, R. (2020). Examination of pre-service mathematics teachers’ ability to make algebraic proof. Online Journal of Mathematics, Science and Technology Education, 1(1), 75-85.
- Yeşilyurt-Çetin, A., & Dikici, R. (2021). Organizing the mathematical proof process with the help of basic components in teaching proof: Abstract algebra example. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 235–255. https://doi.org/10.31129/LUMAT.9.1.1497
- Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Publishing.
- Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Thousand Oaks, CA: Sage.
Matematik Öğretmeni Adaylarının Matematiksel İspat Yapma ve Problem Çözme Süreçlerinin Sesli Düşünme Yöntemi ile İncelenmesi
Abstract
Bu araştırma matematik öğretmeni adaylarının matematiksel ispat yaparken ve problem çözerken zihinsel süreçlerinin nasıl ilerlediğini ve sesli düşünme yöntemine ilişkin görüşlerinin neler olduğunu ortaya çıkarabilmek amacıyla yapılmıştır. Durum çalışması deseninin esas alındığı bu araştırma kapsamında 4 öğretmen adayından düşüncelerini sesli olarak ifade ederek 2 problemi çözmeleri ve 2 cebirsel ispatı yapmaları istenmiştir. Öğretmen adaylarının sesli düşünme süreçleri video ile kayıt altına alınmıştır. Videolar transkript edilerek elde edilen veriler, betimsel analiz yöntemi ile analiz edilerek yorumlanmıştır. Araştırma sonucunda öğretmen adaylarının teorem ispatının ve problem çözümünün nasıl olacağına yönelik genel bir anlayışa sahip olmalarına rağmen, ispat yapma ve problem çözme sürecini nasıl ilerleteceklerini ve önceden sahip oldukları bilgileri amacına uygun bir biçimde nasıl kullanacaklarını bilemedikleri görülmüştür. Ayrıca uygulamaya katılan öğretmen adaylarına göre sesli düşünme yöntemi üst düzey düşünmeyi geliştiren ve bireyin gerçekte ne düşündüğünü anlamasına imkân tanıyan bir yöntemdir.
Keywords
Problem çözme matematiksel ispat yapma cebirsel ispat matematik öğretmeni adayları sesli düşünme
References
- Agustyaningrum, N., Husna, A., Hanggara, Y., Abadi, A. M., & Mahmudi, A. (2020). Analysis of mathematical proof ability in abstract algebra course. Universal Journal of Educational Research, 8(3), 823-834.
- Boero, P. (1999). Argumentation and mathematical proof: a complex, productive, unavoidable relationship in mathematics and mathematics education. International Newsletter on The Teaching and Learning of Mathematical Proof, 7(8). Retrieved from http://www.lettredelapreuve.org/OldPreuve/Newsletter/990708Theme/990708ThemeUK.html
- Bostic, J. D. (2021). Think alouds: Informing scholarship and broadening partnerships through assessment. Applied Measurement in Education, 34(1), 1-9. doi: 10.1080/08957347.2020.1835914
- Cellucci, C. (2017). Is mathematics problem solving or theorem proving?. Foundations of Science, 22(1), 183-199.
- Deshpande, D. S., Riccomini, P. J., Hughes, E. M., & Raulston, T. J. (2021). Problem solving with the pythagorean theorem: A think aloud analysis of secondary students with learning disabilities. Learning Disabilities: A Contemporary Journal, 19(1), 23-47.
- Güneş, F. (2012). Eğitimde sesli düşünme. Akademik Araştırmalar Dergisi, 55, 83-104.
- Krulik, S., & Rudnick, J. A. (1989). Problem solving: A handbook for senior high school teachers. Allyn and Bacon.
- Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. Journal of Mathematical Behavior, 24, 385–401.
- Mamona-Downs, J., & Downs, M. (2013). Problem solving and its elements in forming proof, The Mathematics Enthusiast, 10(1), 136-162.
- Montague, M., & Applegate, B. (2000). Middle school students' perceptions, persistence, and performance in mathematical problem solving. Learning Disability Quarterly, 23(3), 215-227.
- Moralı, S., Uğurel, I., Türnüklü, E., & Yeşildere S. (2006). Matematik öğretmen adaylarının ispat yapmaya yönelik görüşleri, Kastamonu Eğitim Dergisi, 14(1), 147–160.
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standarts for school mathematics, https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/ adresinden 01.01.2021 tarihinde edinilmiştir.
- Öçal, M. F., & Güler, G. (2010). Pre-service mathematics teachers’ views about proof by using concept maps. Procedia-Social and Behavioral Sciences, 9, 318-323.
- Özkubat, U., & Özmen, E. R. (2018). Öğrenme güçlüğü olan öğrencilerin matematik problemi çözme süreçlerinin incelenmesi: sesli düşünme protokolü uygulaması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 19(1), 155-180. doi: 10.21565/ozelegitimdergisi.299494
- Öztürk, M. (2021). Cognitive and metacognitive skills performed by math teachers in the proving process of number theory. Athens Journal of Education, 8(1), 53-71.
- Öztürk, M., & Kaplan, A. (2022). Ortaöğretim matematik öğretmeni adaylarının geometrik ispat yapma süreci: bir durum çalışması. Eurasian Journal of Teacher Education, 3(1), 39-54.
- Polya, G. (1945). How to Solve it. Princeton, NJ: Princeton University Press.
- Rosenzweig, C., Krawec, J., & Montague, M. (2011). Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: a think-aloud analysis. Journal of Learning Disabilities, 44(6), 508–520. https://doi.org/10.1177/0022219410378445
- Van Someren, M. W., Barnard, Y. F., & Sandberg, J. A. C. (1994). The think aloud method: a practical approach to modelling cognitive processes. (Knowledge-based systems). London: Academic Press.
- Yeşilyurt-Çetin, A. (2017). Matematik öğretmeni adaylarının matematiksel ispatta önceden belirlenen anahtar fikirleri yazabilme süreçleri. (Yayımlanmış doktora tezi). Ulusal Tez Merkezi Veri Tabanından Erişildi. ( UMİ No: 480352)
- Yeşilyurt-Çetin, A., & Dikici, R. (2020). Examination of pre-service mathematics teachers’ ability to make algebraic proof. Online Journal of Mathematics, Science and Technology Education, 1(1), 75-85.
- Yeşilyurt-Çetin, A., & Dikici, R. (2021). Organizing the mathematical proof process with the help of basic components in teaching proof: Abstract algebra example. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 235–255. https://doi.org/10.31129/LUMAT.9.1.1497
- Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Publishing.
- Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Thousand Oaks, CA: Sage.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematics Education |
| Journal Section | Research Article |
| Authors | |
| Publication Date | December 26, 2023 |
| Published in Issue | Year 2023Volume: 12 Issue: 4 |
