Öz
In this study, the factors affecting mathematics teachers’ problem posing processes involving real-life contexts were examined in depth. The study aims to reveal the difficulties teachers face in the problem posing process, the strategies they use, and the cognitive, pedagogical and contextual factors that are effective in this process. Qualitative research method was adopted in the study and semi-structured interviews were conducted with teachers during the data collection process. The data obtained were analyzed and the main factors shaping teachers’ problem posing processes were identified. The findings of the study reveal the effects of teachers’ tendency to associate real-life contexts with course content, their experiences and professional knowledge on the problem posing process. In addition, the role of teachers in guiding and structuring the problem posing process by taking into account the needs of students and guiding students through the outcomes and explanations in the mathematics curriculum also comes to the fore. The obtained results emphasize the importance of professional development programs that include practical trainings, workshops, and interactive learning environments based on experience sharing among teachers in order to improve mathematics teachers’ problem posing skills related to real-life; in this direction, it offers various suggestions for teacher education.
Anahtar Kelimeler
Kaynakça
- Ayaz, M., & Şekerci, H. (2015). The effects of the constructivist learning approach on student achievement: A meta-analysis study. The Turkish Online Journal of Educational Technology, 14(4), 143–156.
- Blum W., & Borromeo Ferri R. (2009) Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.
- Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems? The example “Sugarloaf” and the DISUM project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 222–231). Chichester: Horwood.
- Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, California: Jossey-Bass, a Wiley Brand
- Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. New York: Springer International.
- Büchter, A., & Leuders, T. (2005). Quality development in mathematics education by focussing on the outcome: new answers or new questions?. ZDM, 37(4), 263-266.
- Cai, J. (2022). What research says about teaching mathematics through problem posing. Éducation & didactique, 16(3), 31-50.
- Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421.
- Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16(1), 1–6.
- Charmaz, K. (2014). Constructing grounded theory. London: Sage.
- Creswell, J. W. (2013). Araştırma deseni: Nitel, nicel ve karma yöntem yaklaşımları. (S. B. Demir, Çev. Ed.). Ankara: Eğiten Kitap.
- Çilingir-Altıner, E. (2021). Gerçekçi matematik eğitimi üzerine bir kuramsal çalışma. Eğitim ve Teknoloji, 3(1), 48-73.
- Divrik, R. (2023). Effect of teaching mathematics supported by problem-posing strategies on problem-posing skills. International Journal of Modern Education Studies, 7(2), 371-408.
- English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183-217.
- Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine.
- Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129.
- Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, North Carolina: Information Age.
- Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
- Kvale, S., & Brinkmann, S. (2009). InterViews: Learning the craft of qualitative research interviewing (2nd edition). Los Angeles: Sage.
- Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. New York: Lawrence Erlbaum Associates. Liljedahl, P. (2019). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. California: Corwin. Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. Cham: Springer International. Merriam, S. B. (2015). Nitel araştırma: Desen ve uygulama için bir rehber. (S. Turan, Çev. Ed.) Ankara: Nobel Akademik. Peng, A., Li, M., Lin, L., Cao, L., & Cai, J. (2022). Problem posing and its relationship with teaching experience of elementary school mathematics teachers from ethnic minority area in Southwest China. Eurasia Journal of Mathematics, Science and Technology Education, 18(2), em2076.
- Polya, G. (1966). On teaching problem solving. In The Conference Board of the Mathematical Sciences (Ed.), The role of axiomatics and problem solving in mathematics (pp. 123–129). Boston: Ginn.
- Schoenfeld, A. H. (2013). Encore. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics (pp. 287–301). Rotterdam: Sense.
- Schoenfeld, A. H. (2023). A theory of teaching. In A. K. Praetorius, & C. Y. Charalambous (Eds.), Theorizing teaching (pp. 159–187). Cham: Springer International.
- Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
- Silver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157-162.
- Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7.
- Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18, 123-140.
- Stillman, G. A., Brown, J. P., & Galbraith, P. (2013). Challenges in modelling challenges: Intents and purposes. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 217–227). Dordrecht: Springer.
- Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 237–243). Boston: Springer.
Matematik Öğretmenlerinin Gerçek Yaşam Bağlamları İçeren Problemleri Kurma Süreçlerine Etki Eden Faktörler
Öz
Bu araştırmada, matematik öğretmenlerinin gerçek yaşam bağlamlarını içeren problemleri kurma süreçlerini etkileyen faktörler derinlemesine incelenmiştir. Araştırma, öğretmenlerin problem kurma sürecinde karşılaştıkları zorlukları, kullandıkları stratejileri ve bu süreçte etkili olan bilişsel, pedagojik ve bağlamsal unsurları ortaya koymayı amaçlamaktadır. Çalışmada nitel araştırma yöntemi benimsenmiş olup, veri toplama sürecinde öğretmenlerle yarı yapılandırılmış görüşmeler yapılmıştır. Elde edilen veriler analiz edilmiş ve öğretmenlerin problem kurma süreçlerini şekillendiren temel faktörler belirlenmiştir. Araştırma bulguları, öğretmenlerin gerçek yaşam bağlamlarını ders içeriğiyle ilişkilendirme eğilimlerinin, sahip oldukları deneyimlerin ve mesleki bilgilerinin problem kurma sürecine olan etkilerini ortaya koymaktadır. Ayrıca öğretmenlerin öğrencilerin ihtiyaçlarını göz önünde bulundurma durumları ile matematik öğretim programının içerdiği kazanımlar ve açıklamalar yoluyla öğrencilere rehberlik ederek problem kurma sürecini yönlendirme ve yapılandırma konusundaki rolü de ön plana çıkmaktadır. Elde edilen sonuçlar, matematik öğretmenlerinin gerçek yaşamla ilişkili problem kurma becerilerini geliştirmek amacıyla, uygulamaya dönük eğitimler, atölye çalışmaları ve öğretmenler arasında deneyim paylaşımına dayalı etkileşimli öğrenme ortamlarını içeren mesleki gelişim programlarının önemini vurgulamakta; bu doğrultuda öğretmen eğitimine yönelik çeşitli öneriler sunmaktadır.
Anahtar Kelimeler
Kaynakça
- Ayaz, M., & Şekerci, H. (2015). The effects of the constructivist learning approach on student achievement: A meta-analysis study. The Turkish Online Journal of Educational Technology, 14(4), 143–156.
- Blum W., & Borromeo Ferri R. (2009) Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.
- Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems? The example “Sugarloaf” and the DISUM project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 222–231). Chichester: Horwood.
- Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, California: Jossey-Bass, a Wiley Brand
- Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. New York: Springer International.
- Büchter, A., & Leuders, T. (2005). Quality development in mathematics education by focussing on the outcome: new answers or new questions?. ZDM, 37(4), 263-266.
- Cai, J. (2022). What research says about teaching mathematics through problem posing. Éducation & didactique, 16(3), 31-50.
- Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421.
- Chapman, O. (2013). Mathematical-task knowledge for teaching. Journal of Mathematics Teacher Education, 16(1), 1–6.
- Charmaz, K. (2014). Constructing grounded theory. London: Sage.
- Creswell, J. W. (2013). Araştırma deseni: Nitel, nicel ve karma yöntem yaklaşımları. (S. B. Demir, Çev. Ed.). Ankara: Eğiten Kitap.
- Çilingir-Altıner, E. (2021). Gerçekçi matematik eğitimi üzerine bir kuramsal çalışma. Eğitim ve Teknoloji, 3(1), 48-73.
- Divrik, R. (2023). Effect of teaching mathematics supported by problem-posing strategies on problem-posing skills. International Journal of Modern Education Studies, 7(2), 371-408.
- English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183-217.
- Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine.
- Gravemeijer, K., & Doorman, M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129.
- Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, North Carolina: Information Age.
- Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
- Kvale, S., & Brinkmann, S. (2009). InterViews: Learning the craft of qualitative research interviewing (2nd edition). Los Angeles: Sage.
- Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. New York: Lawrence Erlbaum Associates. Liljedahl, P. (2019). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. California: Corwin. Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. Cham: Springer International. Merriam, S. B. (2015). Nitel araştırma: Desen ve uygulama için bir rehber. (S. Turan, Çev. Ed.) Ankara: Nobel Akademik. Peng, A., Li, M., Lin, L., Cao, L., & Cai, J. (2022). Problem posing and its relationship with teaching experience of elementary school mathematics teachers from ethnic minority area in Southwest China. Eurasia Journal of Mathematics, Science and Technology Education, 18(2), em2076.
- Polya, G. (1966). On teaching problem solving. In The Conference Board of the Mathematical Sciences (Ed.), The role of axiomatics and problem solving in mathematics (pp. 123–129). Boston: Ginn.
- Schoenfeld, A. H. (2013). Encore. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics (pp. 287–301). Rotterdam: Sense.
- Schoenfeld, A. H. (2023). A theory of teaching. In A. K. Praetorius, & C. Y. Charalambous (Eds.), Theorizing teaching (pp. 159–187). Cham: Springer International.
- Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
- Silver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157-162.
- Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7.
- Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18, 123-140.
- Stillman, G. A., Brown, J. P., & Galbraith, P. (2013). Challenges in modelling challenges: Intents and purposes. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 217–227). Dordrecht: Springer.
- Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 237–243). Boston: Springer.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Alan Eğitimleri (Diğer) |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2025 |
| Gönderilme Tarihi | 2 Mayıs 2025 |
| Kabul Tarihi | 17 Haziran 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 12 Sayı: 1 |
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