Research Article
PDF Zotero Mendeley EndNote BibTex Cite

Developing students' problem posing skills with dynamic geometry software and active learning framework

Year 2022, Volume 11, Issue 2, 93 - 125, 30.04.2022
https://doi.org/10.19128/turje.880173

Abstract

In the present study, the effects of using dynamic geometry software in active learning framework on students’ problem posing skills and their views about problem posing were examined. The participants consisted of 16 eighth-grade students. Data were collected by problem posing tests, open-ended questions, student diaries, and dynamic geometry software supported tasks. The study, designed with the embedded mixed method, lasted 13 weeks. The dependent t-test was used in the analysis of quantitative data, and descriptive analysis was performed in qualitative data. Problem posing skills of students examined according to use of mathematical language, grammar and expression, suitability to acquisitions, quantity and quality of data, solvability, originality, solution of the problem criteria. In the present study, it was determined that the use of dynamic geometry software in active learning framework developed students’ problem posing skills. The problems that students posed in the dynamic geometry software during the implementation process indicated improvement in terms of problem posing skills as the weeks passed. It was found that students had positive views about the problem posing process, while they experienced some difficulties in this process.

References

  • Abramovich, S., & Cho, E. K. (2015). Using digital technology for mathematical problem posing. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp.71-102). Springer. https://doi.org/10.1007/978-1-4614-6258-3_4
  • Abu Elwan, R. (2014). Developing algebraic problem posing skills of prospective teachers using GeoGebra environment. مجلة تربويات الرياضيات [Journal of Mathematics Education], 15(7). 1-15. https://doi.org/10.21608/armin.2014.81882
  • Abu Elwan, R. (1999, November). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Eds.), Proceedings of the International Conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches (Vol. 2, pp. 1-8). Cairo, Egypt.
  • Abu Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69.
  • Afrilianto, M., Sabandar, J., & Wahyudin (2019). Improving students’ mathematical problem posing ability using pace model. In Journal of Physics: Conference Series (Vol. 1315, p. 012007). IOP Publishing. https://doi.org/10.1088/1742-6596/1315/1/012007
  • Beal, C. R., & Cohen, P. R. (2012). Teach ourselves: Technology to support problem posing in the STEM classroom. Creative Education, 3(4), 513-519. https://doi.org/10.4236/ce.2012.34078
  • Bülbül, B. Ö., Güler, M., Gürsoy, K., & Güven, B. (2020). For what purpose do the student teachers use DGS? A qualitative study on the case of continuity. International Online Journal of Education and Teaching (IOJET), 7(3). 785-801. https://iojet.org/index.php/IOJET/article/view/765
  • Cai, J. (1998). An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37-50. https://doi.org/10.1007/BF03217121
  • 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. https://doi.org/10.1016/S0732-3123(02)00142-6
  • Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391. https://doi.org/10.1016/j.ijer.2019.01.001
  • Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3-34). Springer. https://doi.org/10.1007/978-1-4614-6258-3_1
  • Cankoy, O. (2014). Interlocked problem posing and children's problem posing performance in free structured situations. International Journal of Science and Mathematics Education, 12(1), 219-238. https://doi.org/10.1007/s10763-013-9433-9
  • Chen, L., Van Dooren, W., & Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders’ problem-posing and problem-solving abilities, beliefs, and attitudes: A design experiment. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 309-329). Springer. https://doi.org/10.1007/978-1-4614-6258-3_15
  • Chen, T., & Cai, J. (2020). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research, 102, 101420. https://doi.org/10.1016/j.ijer.2019.03.004.
  • Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Mathematics Enthusiast, 2(2), 125-143.
  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155.
  • Creswell, J.W. (2014). Research design: qualitative, quantitative and mixed methods approaches (4th ed.). Sage.
  • Cutugno, P., & Spagnolo, F. (2002). Misconception about triangle in elementary school. Retrieved from http://math.math.unipa.it/~grim/SiCutugnoSpa.PDF
  • Dikovic, L. (2009). Implementing dynamic mathematics resources with GeoGebra at the college level. International Journal of Emerging Technologies in Learning (iJET), 4(3), 51-54. https://doi.org/10.3991/ijet.v4i3.784
  • Ellerton N. F., Singer F. M., & Cai J. (2015). Problem posing in mathematics: reflecting on the past, energizing the present, and foreshadowing the future. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 547-556). Springer. https://doi.org/10.1007/978-1-4614-6258-3_26
  • Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework. Educational Studies in Mathematics, 83(1), 87-101. https://doi.org/10.1007/s10649-012-9449-z
  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183-217. https://doi.org/10.1023/A:1002963618035
  • Field, A. (2009). Discovering statistics using SPSS (3rd ed.). Sage Publications.
  • Hohenwarter, M., & Jones, K. (2007). Ways of linking geometry and algebra: The case of GeoGebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 126-131.
  • Kaya, N. (2018). Ortaokul sekizinci sınıf öğrencilerinin üçgenler konusundaki kavram yanılgılarının incelenmesi [Examination of secondary school 8th grade students’ misconceptions about triangles] (Unpublished master’s thesis). İnönü University.
  • Lavy, I. (2015). Problem-posing activities in a dynamic geometry environment: When and how. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 393-410). Springer. https://doi.org/10.1007/978-1-4614-6258-3_19
  • Lavy, I., & Shriki, A. (2010). Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. The Journal of Mathematical Behavior, 29(1), 11-24. https://doi.org/10.1016/j.jmathb.2009.12.002
  • Leikin, R. (2015). Problem posing for and through investigations in a dynamic geometry environment. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 373-391). Springer. https://doi.org/10.1007/978-1-4614-6258-3_18
  • Lin, K. M., & Leng, L. W. (2008, July). Using problem-posing as an assessment tool. Paper presented at 10th Asia-Pacific Conference on Giftedness, Singapore.
  • 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
  • Miles, M. B., & Huberman, A. M. (1994). An expanded sourcebook: Qualitative data analysis. Sage Publications.
  • Ministry of National Education [MoNE], (2018). Mathematics course (Elementary and Middle School 1, 2, 3, 4, 5, 6, 7 and 8. Grades) curriculum. Ankara.
  • Öçal, M. F., Kar, T., Güler, G., & İpek, A. S. (2020). Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity. REDIMAT – Journal of Research in Mathematics Education, 9(3), 243-272. http://dx.doi.org/10.17583/redimat.2020.3879
  • Örnek, T., & Soylu, Y. (2021). A model design to be used in teaching problem posing to develop problem-posing skills. Thinking Skills and Creativity, 100905. https://doi.org/10.1016/j.tsc.2021.100905
  • Özgen, K., Aparı, B. & Zengin, Y. (2019). Sekizinci sınıf öğrencilerinin problem kurma temelli öğrenme yaklaşımları: GeoGebra destekli aktif öğrenme çerçevesinin uygulanması. [Problem posing based learning approaches of eighth grade students: Implementation of active learning framework supported by GeoGebra]. Turkish Journal of Computer and Mathematics Education, 10(2), 501-538. https://doi.org/10.16949/turkbilmat.471760
  • Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. [Investigation of problem posing skills of eighth grade students in terms of some variables]. Turkish Journal of Computer and Mathematics Education, 8(2), 323-351. https://doi.org/10.16949/turkbilmat.322660
  • Petkova, M. M., & Velikova, E. A. (2015, July). GeoGebra constructions and problems for arbelos and archimedean circles. Paper presented at the GeoGebra Global Gathering, Linz, Austria.
  • Ranasinghe, A. I., & Leisher, D. (2009). The benefit of integrating technology into the classroom. International Mathematical Forum, 4(40), 1955-1961.
  • Shriki, A., & Lavy, I. (2012). Problem posing in a dynamic geometry environment and the development of mathematical insights. The International Journal of Learning, 18(5), 61–70. https://doi.org/10.18848/1447-9494/cgp/v18i05/47613
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.5951/jresematheduc.27.5.0521
  • Siswantoro, M. D., & Siswono, T. Y. E. (2019). Students’ mathematics conceptual understanding in problem posing learning based on GeoGebra application. MATHEdunesa Journal Ilmiah Pendidikan Matematika, 8(2), 338-341. https://doi.org/10.26740/mathedunesa.v8n2.p338-341
  • Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp.164-185). MASTEC Publication.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia.
  • Şengün, K. Ç., & Yılmaz, S. (2021). Ortaokul 8. sınıf öğrencilerinin üçgende açıortay ve kenarortay belirleme durumlarının incelenmesi [Investigation of middle school 8th grade students’ determination of bisector and median in triangle]. International Journal of Active Learning, 6(1), 81-97. https://doi.org/10.48067/ijal.909110
  • Van Harpen, X., & Presmeg, N. (2015). An investigation of high school students’ mathematical problem posing in the United States and China. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 293-308). Springer. https://doi.org/10.1007/978-1-4614-6258-3_14
  • Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101-118. https://doi.org/10.1007/s10649-017-9760-9
  • Xu, B., Cai, J., Liu, Q., & Hwang, S. (2020). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 102, 101427. https://doi.org/10.1016/j.ijer.2019.04.005.
  • Yığ, K. G., & Ay, Z. S. (2021). An analysis of the qualities of the problems posed by the students in a seventh grade mathematics course assisted by the problem posing approach. International Journal of Contemporary Educational Research, 8(2), 13-30. https://doi.org/10.33200/ijcer.795390
  • Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (10th ed.). Seçkin.
  • Zengin, Y. (2018). Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. Educational Studies in Mathematics, 99(3), 311–333. https://doi.org/10.1007/s10649-018-9832-5

Dinamik geometri yazılımı ve aktif öğrenme çerçevesi ile öğrencilerin problem kurma becerilerinin geliştirilmesi

Year 2022, Volume 11, Issue 2, 93 - 125, 30.04.2022
https://doi.org/10.19128/turje.880173

Abstract

Araştırmada, aktif öğrenme çerçevesinde dinamik geometri yazılımı kullanımının öğrencilerin problem kurma becerilerine ve problem kurmaya yönelik görüşlerine etkisi incelenmiştir. Katılımcılar, 16 sekizinci sınıf öğrencisinden oluşmuştur. Veriler problem kurma testi, açık uçlu sorular, öğrenci günlükleri ve dinamik geometri yazılımı destekli etkinlikler ile toplanmıştır. Gömülü karma yöntem ile tasarlanan araştırma 13 hafta sürmüştür. Nicel verilerin analizinde ilişkili örneklemler t-testi, nitel verilerde betimsel analiz yapılmıştır. Öğrencilerin problem kurma becerileri; matematik dilini kullanabilme, dil bilgisi ve anlatım, kazanımlara uygunluk, veri miktarı ve niteliği, çözülebilirlik, özgünlük, problemin çözümü kriterlerine göre incelenmiştir. Araştırmada, aktif öğrenme çerçevesinde dinamik geometri yazılımı kullanımının öğrencilerin problem kurma becerilerini geliştirdiği belirlenmiştir. Öğrencilerin uygulama sürecinde dinamik geometri yazılımında kurdukları problemler ise haftalar ilerledikçe problem kurma becerileri açısından gelişim göstermiştir. Ayrıca öğrencilerin problem kurma sürecine yönelik görüşlerinin olumlu olduğu ancak bu süreçte bazı zorluklar yaşadıkları görülmüştür.

References

  • Abramovich, S., & Cho, E. K. (2015). Using digital technology for mathematical problem posing. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp.71-102). Springer. https://doi.org/10.1007/978-1-4614-6258-3_4
  • Abu Elwan, R. (2014). Developing algebraic problem posing skills of prospective teachers using GeoGebra environment. مجلة تربويات الرياضيات [Journal of Mathematics Education], 15(7). 1-15. https://doi.org/10.21608/armin.2014.81882
  • Abu Elwan, R. (1999, November). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Eds.), Proceedings of the International Conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches (Vol. 2, pp. 1-8). Cairo, Egypt.
  • Abu Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69.
  • Afrilianto, M., Sabandar, J., & Wahyudin (2019). Improving students’ mathematical problem posing ability using pace model. In Journal of Physics: Conference Series (Vol. 1315, p. 012007). IOP Publishing. https://doi.org/10.1088/1742-6596/1315/1/012007
  • Beal, C. R., & Cohen, P. R. (2012). Teach ourselves: Technology to support problem posing in the STEM classroom. Creative Education, 3(4), 513-519. https://doi.org/10.4236/ce.2012.34078
  • Bülbül, B. Ö., Güler, M., Gürsoy, K., & Güven, B. (2020). For what purpose do the student teachers use DGS? A qualitative study on the case of continuity. International Online Journal of Education and Teaching (IOJET), 7(3). 785-801. https://iojet.org/index.php/IOJET/article/view/765
  • Cai, J. (1998). An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37-50. https://doi.org/10.1007/BF03217121
  • 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. https://doi.org/10.1016/S0732-3123(02)00142-6
  • Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391. https://doi.org/10.1016/j.ijer.2019.01.001
  • Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3-34). Springer. https://doi.org/10.1007/978-1-4614-6258-3_1
  • Cankoy, O. (2014). Interlocked problem posing and children's problem posing performance in free structured situations. International Journal of Science and Mathematics Education, 12(1), 219-238. https://doi.org/10.1007/s10763-013-9433-9
  • Chen, L., Van Dooren, W., & Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders’ problem-posing and problem-solving abilities, beliefs, and attitudes: A design experiment. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 309-329). Springer. https://doi.org/10.1007/978-1-4614-6258-3_15
  • Chen, T., & Cai, J. (2020). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research, 102, 101420. https://doi.org/10.1016/j.ijer.2019.03.004.
  • Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Mathematics Enthusiast, 2(2), 125-143.
  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155.
  • Creswell, J.W. (2014). Research design: qualitative, quantitative and mixed methods approaches (4th ed.). Sage.
  • Cutugno, P., & Spagnolo, F. (2002). Misconception about triangle in elementary school. Retrieved from http://math.math.unipa.it/~grim/SiCutugnoSpa.PDF
  • Dikovic, L. (2009). Implementing dynamic mathematics resources with GeoGebra at the college level. International Journal of Emerging Technologies in Learning (iJET), 4(3), 51-54. https://doi.org/10.3991/ijet.v4i3.784
  • Ellerton N. F., Singer F. M., & Cai J. (2015). Problem posing in mathematics: reflecting on the past, energizing the present, and foreshadowing the future. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 547-556). Springer. https://doi.org/10.1007/978-1-4614-6258-3_26
  • Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework. Educational Studies in Mathematics, 83(1), 87-101. https://doi.org/10.1007/s10649-012-9449-z
  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183-217. https://doi.org/10.1023/A:1002963618035
  • Field, A. (2009). Discovering statistics using SPSS (3rd ed.). Sage Publications.
  • Hohenwarter, M., & Jones, K. (2007). Ways of linking geometry and algebra: The case of GeoGebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 126-131.
  • Kaya, N. (2018). Ortaokul sekizinci sınıf öğrencilerinin üçgenler konusundaki kavram yanılgılarının incelenmesi [Examination of secondary school 8th grade students’ misconceptions about triangles] (Unpublished master’s thesis). İnönü University.
  • Lavy, I. (2015). Problem-posing activities in a dynamic geometry environment: When and how. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 393-410). Springer. https://doi.org/10.1007/978-1-4614-6258-3_19
  • Lavy, I., & Shriki, A. (2010). Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. The Journal of Mathematical Behavior, 29(1), 11-24. https://doi.org/10.1016/j.jmathb.2009.12.002
  • Leikin, R. (2015). Problem posing for and through investigations in a dynamic geometry environment. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 373-391). Springer. https://doi.org/10.1007/978-1-4614-6258-3_18
  • Lin, K. M., & Leng, L. W. (2008, July). Using problem-posing as an assessment tool. Paper presented at 10th Asia-Pacific Conference on Giftedness, Singapore.
  • 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
  • Miles, M. B., & Huberman, A. M. (1994). An expanded sourcebook: Qualitative data analysis. Sage Publications.
  • Ministry of National Education [MoNE], (2018). Mathematics course (Elementary and Middle School 1, 2, 3, 4, 5, 6, 7 and 8. Grades) curriculum. Ankara.
  • Öçal, M. F., Kar, T., Güler, G., & İpek, A. S. (2020). Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity. REDIMAT – Journal of Research in Mathematics Education, 9(3), 243-272. http://dx.doi.org/10.17583/redimat.2020.3879
  • Örnek, T., & Soylu, Y. (2021). A model design to be used in teaching problem posing to develop problem-posing skills. Thinking Skills and Creativity, 100905. https://doi.org/10.1016/j.tsc.2021.100905
  • Özgen, K., Aparı, B. & Zengin, Y. (2019). Sekizinci sınıf öğrencilerinin problem kurma temelli öğrenme yaklaşımları: GeoGebra destekli aktif öğrenme çerçevesinin uygulanması. [Problem posing based learning approaches of eighth grade students: Implementation of active learning framework supported by GeoGebra]. Turkish Journal of Computer and Mathematics Education, 10(2), 501-538. https://doi.org/10.16949/turkbilmat.471760
  • Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. [Investigation of problem posing skills of eighth grade students in terms of some variables]. Turkish Journal of Computer and Mathematics Education, 8(2), 323-351. https://doi.org/10.16949/turkbilmat.322660
  • Petkova, M. M., & Velikova, E. A. (2015, July). GeoGebra constructions and problems for arbelos and archimedean circles. Paper presented at the GeoGebra Global Gathering, Linz, Austria.
  • Ranasinghe, A. I., & Leisher, D. (2009). The benefit of integrating technology into the classroom. International Mathematical Forum, 4(40), 1955-1961.
  • Shriki, A., & Lavy, I. (2012). Problem posing in a dynamic geometry environment and the development of mathematical insights. The International Journal of Learning, 18(5), 61–70. https://doi.org/10.18848/1447-9494/cgp/v18i05/47613
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.5951/jresematheduc.27.5.0521
  • Siswantoro, M. D., & Siswono, T. Y. E. (2019). Students’ mathematics conceptual understanding in problem posing learning based on GeoGebra application. MATHEdunesa Journal Ilmiah Pendidikan Matematika, 8(2), 338-341. https://doi.org/10.26740/mathedunesa.v8n2.p338-341
  • Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp.164-185). MASTEC Publication.
  • Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia.
  • Şengün, K. Ç., & Yılmaz, S. (2021). Ortaokul 8. sınıf öğrencilerinin üçgende açıortay ve kenarortay belirleme durumlarının incelenmesi [Investigation of middle school 8th grade students’ determination of bisector and median in triangle]. International Journal of Active Learning, 6(1), 81-97. https://doi.org/10.48067/ijal.909110
  • Van Harpen, X., & Presmeg, N. (2015). An investigation of high school students’ mathematical problem posing in the United States and China. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 293-308). Springer. https://doi.org/10.1007/978-1-4614-6258-3_14
  • Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101-118. https://doi.org/10.1007/s10649-017-9760-9
  • Xu, B., Cai, J., Liu, Q., & Hwang, S. (2020). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 102, 101427. https://doi.org/10.1016/j.ijer.2019.04.005.
  • Yığ, K. G., & Ay, Z. S. (2021). An analysis of the qualities of the problems posed by the students in a seventh grade mathematics course assisted by the problem posing approach. International Journal of Contemporary Educational Research, 8(2), 13-30. https://doi.org/10.33200/ijcer.795390
  • Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences] (10th ed.). Seçkin.
  • Zengin, Y. (2018). Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. Educational Studies in Mathematics, 99(3), 311–333. https://doi.org/10.1007/s10649-018-9832-5

Details

Primary Language English
Subjects Education and Educational Research
Journal Section Research Articles
Authors

Burcu APARI (Primary Author)
T.C. MİLLİ EĞİTİM BAKANLIĞI
0000-0002-5280-0208
Türkiye


Kemal ÖZGEN
DİCLE ÜNİVERSİTESİ
0000-0002-7015-6452
Türkiye


Yılmaz ZENGİN
DİCLE ÜNİVERSİTESİ
0000-0003-1276-457X
Türkiye

Publication Date April 30, 2022
Published in Issue Year 2022, Volume 11, Issue 2

Cite

APA Aparı, B. , Özgen, K. & Zengin, Y. (2022). Developing students' problem posing skills with dynamic geometry software and active learning framework . Turkish Journal of Education , 11 (2) , 93-125 . DOI: 10.19128/turje.880173

Creative Commons License TURJE is licensed to the public under a Creative Commons Attribution 4.0 license.