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Examining the Problem-Posing Skills of Prospective Classroom Teachers

Year 2024, Volume: 11 Issue: 5, 1 - 23, 12.09.2024
https://doi.org/10.17275/per.24.61.11.5

Abstract

The study investigates the integration of problem-posing techniques within mathematics pedagogy. The aim is to examine the competencies in posing problems by prospective fourth-grade classroom teachers during lesson preparation and figure out what changes need to be made. We designed this research as a quasi-experimental design involving 50 teacher candidates enrolled at a public university during the academic year of 2021-2022 in Turkey. We delved into the effects of problem-posing instruction by giving it to 25 prospective teachers who volunteered to be in the experimental group. We used the Problem-Posing Test as the data collection tool. The Problem-Posing Test consists of 12 distinct scenarios for posing problems, ranging from highly structured to semi-structures, and extending to open-ended problem posing situations. We collected the quantitative data using a rubric developed to evaluate the Problem Posing-Test. We employed the T-test and the Mann-Whitney U test for the analysis of quantitative data. Based on the pre-test results of problem posing, the prospective teachers’ problem-posing skills in the measurement and learning areas were insufficient. However, both groups were able to use the daily life contexts to address the problems they posed. The experimental group demonstrated a notable advantage in problem-posing skills on the post-test administered after receiving problem-posing instruction. We also concluded that problem-posing instruction positively affected the problems posed by prospective classroom teachers in the measurement and learning area. In this regard, offering an elective course on problem posing for the classroom teacher training program in education faculties would be beneficial.

References

  • Abu-Elwan, R., 2002. Effectiveness of problem posing strategies on prospective mathematics teachers problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.
  • Bayazi̇t, İ. & Kırnap-Dönmez, S . (2017). Prospective teachers’ proficiencies at problem posing in the context of proportional reasoning. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(1), 130-160.
  • Bonotto, C. & Dal Santo, L. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. In F. M. Singer, N. F. Ellerton, And J. Cai (Eds), Mathematical Problem Posing (s.103-123). Springer.
  • Boyraz, C. (2019). Analysis of prospective teachers middle school mathematics teachers’ problem posing abilities about equations [Master Dissertation]. Erciyes University.
  • Büyüköztürk, Ş. (2018). Sosyal bilimler için veri analizi el kitabı [Data analysis Handbook for social Sciences] (24. Edition). Pegem Academia.
  • Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., Zhang, L., & Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design. International Journal of Educational Research 102(2020) 101404.
  • Cai, J. (2022). What research says about teaching mathematics through problem posing. Éducation et 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. Journal of Mathematical Behavior, 21, 401–421.
  • Christou, C., Pitta-Pantazi, D., & Chimoni, M. (2024). Teachers' mathematical problem posing: The role of processes and complexity levels in posing problems on the fraction part-whole concept. The Journal of Mathematical Behavior, 73, 101134.
  • Çepni, S. (2010). Araştırma ve proje çalışmalarına giriş [Introduction to research and project studies] (5.Edition). Celepler Publications.
  • Crespo, S. & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11, 395-415.
  • Creswell, J. W. (2012). Educational research: planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson.
  • Cohen, J. (1988). Statistical power analysis in the behavioral sciences (2. Edition). Lawrence Erlbaum Associates
  • Çomarlı, S. K. (2018). Examining the free problem posing skills of secondary school mathematics teachers regarding data processing learning field [Master Dissertation] Bartın University.
  • Demirci, Ö. (2018). An Investigation of the development of pre-service mathematics teachers’ problem posing skills in probability [Doctoral Dissertation] Atatürk University.
  • Divrik, R. & Pilten, P. (2021). An Analysis of 4th grade students' errors in the topics of perimeter and area]. Batı Anadolu Journal of Educational Sciences, 12(1), 333-356.
  • Doğan Coşkun, S. (2017). Investigation of primary school teachers' mathematical knowledge in teaching for length measurement and perimeter topics with the knowledge quartet model [Doctoral Dissertation] Gazi University.
  • Drake, M. (2013). How heavy is my rock? An exploration of students’ understanding of the measurement of weight. In V.Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australia pp. 250-257). Melbourne: MERGA.
  • Durmaz, B. (2019). Erken çocuklukta matematik eğitimi. [Mathematics education in early childhood] Pegem Akademi.
  • Ellerton, N. F. (2013). Engaging prospective middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87-101.
  • Ellerton, N. F., Singer, F. M. & Cai, J. (2015). Problem posing in mathematics: Reflecting on the past, energizing the present, and foreshadowing the future. Mathematical problem posing (s. 547-556) in. Springer.
  • Field, A. (2009). Discovering statistics using SPSS. Sage Publications.
  • Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2013). Multivariate Data Analysis. Pearson Education Limited.
  • Hošpesová, A. & Tichá, M. (2015). Problem posing in primary school teacher training. In F. M. Singer, N. Ellerton, J. Cai (Eds.), Mathematical problem posing: From research to effective practice (s. 433–447) Springer.
  • Işık, C. & Kar, T. (2012). Pre-Service Elementary Teachers’ Problem Posing Skills. Mehmet Akif Ersoy University Faculty of Education Journal, 23, 190-214.
  • Işık, C., Kar, T., İpek, A. S. & Işık, A. (2012). Difficulties encountered by prospective classroom teachers in constructing stories about line graphs. International Online Journal of Educational Sciences, 4(3).
  • Kamii, C. & Russell, K. A. (2012). Elapsed time: Why is it so difficult to teach? Journal for Research in Mathematics Education, 43(3), 296-315.
  • Kanbur, B. (2017). Problem-posing situations and opinions of prospective elementary mathematics teachers' in dynamic geometry environment [Master Dissertation] Gazi University.
  • Kar, T. (2014). Investigating middle school mathematics teachers' mathematical knowledge for teaching in the context of problem posing: the example of addition operation with fractions. [Doctoral Dissertation] Atatürk University.
  • Karasar, N. (2018). Bilimsel araştırma yöntemi [Scientific research method] (33. Edition). Nobel Publications.
  • Karaaslan, G. K. (2018). Investigation of students' algebra learning and problem posing skills in a mathematics classroom supported by problem posing approach [Doctoral Dissertation] Hacettepe University.
  • Kilmen, S. (2015). Eğitim araştırmacıları için SPSS uygulamalı istatistik. Edge Akademi.
  • Leavy, A. & Hourigan, M. (2019). Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 1-21.
  • Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3(1), 257- 264.
  • Ministry of National Education [MoNE]. (2018). School mathematics curriculum (Primary and Secondary School Grades 1, 2, 3, 4, 5, 6, 7 and 8). Ministry of National Education.
  • Pallant, J. (2007). SPSS survival manual, a step by step guide to data analysis using spss for windows (3. Edition). McGraw-Hill.
  • Pesen, C. (2019). İlkokullarda matematik öğretimi [Teaching mathematics in primary schools] (7. Edition). Pegem A Academia
  • Rosli, R., Capraro, M. M., Goldsby, D., Elsa, G. G., Capraro, R. M. & Onwuegbuzie, A. J. (2015). Middle-grade prospective teachers’ mathematical problem solving and problem posing. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (s. 333-354) in. Springer.
  • Serin, M. K. (2019). Analysis of the problems posed by prospective primary school teachers in terms of type, cognitive structure and content knowledge. International Journal of Educational Methodology, 5(4), 577-590.
  • Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (s. 518–525) in. Mathematics Education Research Group of Australasia.
  • Şengül, S. & Katranci, Y. (2015). Free problem posing cases of prospective mathematics teachers: Difficulties and solutions. Procedia-Social and Behavioral Sciences, 174, 1983-1990.
  • Şimşek, N. & Boz, N. (2015). Investigating of pedagogical content knowledge of prospective primary teachers’ related to the length measurement in the context students’ understanding. Cumhuriyet International Journal of Education-CIJE, 4(3), 10-30.
  • Örnek, T. (2020). The assessment of problem posing learning model designed for the development of problem posing skill [Doctoral Dissertation] Atatürk University.
  • Örnek, T. & Soylu, Y. (2021). The Assessment of problem posing learning model designed for the development of problem posing skill. Journal of Computer and Educational Research, 9(18), 929-960.
  • Özdemir Yıldız, Ö. (2019). Investigation of problem posing skills of mathematics teacher candidates and the determination of teachers' views on problem posing [Master Dissertation] Gazi University.
  • Özer, T. & İnci̇kabı, L. (2019). Analysis of fractıon questions placed in the primary school mathematics textbooks. Medeniyet Journal of Educational Research, 3(1), 20-37.
  • Özgen, K., Aydın, M., Geçici, M.E. & Bayram, B. (2017). Investigation of problem posing skills of eighth grade students in terms of some variables. Turkish Journal of Computer and Mathematics Education, 8(2), 218-243.
  • Özmen, H. (2019). Experimental research method. H. Özmen and O. Karamustafaoğlu (Ed). Research Methods in Education (s.197-227) in. Pegem Academia.
  • Teki̇n Si̇trava R. & Işık, A. (2018). Investigation of prospective primary school teachers' problem posing skills based on comprehending and selecting problem-posing situations. Journol of Erzincan University Faculty of Education, 20 (3), 767-781.
  • Tichá, M. & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in prospective teacher training. In V. Durand-Guerrier, S. SouryLavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (s. 1941–1950) in. Institut National de Recherche Pédagogique.
  • Usta, A. & İpek, A. S. (2019). Investıgatıon of problems multiplication and division operations with natural numbers for primary school in Turkish mathematics textbooks. National Education Journal, Primary Education, 241-265.
  • 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.
  • Van De Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2012). Elementary and middle school mathematics - Teaching developmentally. (Tranlation Editor: Soner Durmuş). Nobel Akademik Publishing.
  • Yıldız, Z. (2014).The effects of problem posing studies in mathematics to problem posing skills and metacognitive awareness of prospective teachers teachers [Master Dissertation]. Marmara University.
  • Zehir, K. (2013). Investigation of prospective elementary mathematics teachers' problem posing skilss for fraction operations [Doctoral Dissertation]. Atatürk University.
Year 2024, Volume: 11 Issue: 5, 1 - 23, 12.09.2024
https://doi.org/10.17275/per.24.61.11.5

Abstract

References

  • Abu-Elwan, R., 2002. Effectiveness of problem posing strategies on prospective mathematics teachers problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.
  • Bayazi̇t, İ. & Kırnap-Dönmez, S . (2017). Prospective teachers’ proficiencies at problem posing in the context of proportional reasoning. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(1), 130-160.
  • Bonotto, C. & Dal Santo, L. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. In F. M. Singer, N. F. Ellerton, And J. Cai (Eds), Mathematical Problem Posing (s.103-123). Springer.
  • Boyraz, C. (2019). Analysis of prospective teachers middle school mathematics teachers’ problem posing abilities about equations [Master Dissertation]. Erciyes University.
  • Büyüköztürk, Ş. (2018). Sosyal bilimler için veri analizi el kitabı [Data analysis Handbook for social Sciences] (24. Edition). Pegem Academia.
  • Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., Zhang, L., & Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design. International Journal of Educational Research 102(2020) 101404.
  • Cai, J. (2022). What research says about teaching mathematics through problem posing. Éducation et 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. Journal of Mathematical Behavior, 21, 401–421.
  • Christou, C., Pitta-Pantazi, D., & Chimoni, M. (2024). Teachers' mathematical problem posing: The role of processes and complexity levels in posing problems on the fraction part-whole concept. The Journal of Mathematical Behavior, 73, 101134.
  • Çepni, S. (2010). Araştırma ve proje çalışmalarına giriş [Introduction to research and project studies] (5.Edition). Celepler Publications.
  • Crespo, S. & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11, 395-415.
  • Creswell, J. W. (2012). Educational research: planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson.
  • Cohen, J. (1988). Statistical power analysis in the behavioral sciences (2. Edition). Lawrence Erlbaum Associates
  • Çomarlı, S. K. (2018). Examining the free problem posing skills of secondary school mathematics teachers regarding data processing learning field [Master Dissertation] Bartın University.
  • Demirci, Ö. (2018). An Investigation of the development of pre-service mathematics teachers’ problem posing skills in probability [Doctoral Dissertation] Atatürk University.
  • Divrik, R. & Pilten, P. (2021). An Analysis of 4th grade students' errors in the topics of perimeter and area]. Batı Anadolu Journal of Educational Sciences, 12(1), 333-356.
  • Doğan Coşkun, S. (2017). Investigation of primary school teachers' mathematical knowledge in teaching for length measurement and perimeter topics with the knowledge quartet model [Doctoral Dissertation] Gazi University.
  • Drake, M. (2013). How heavy is my rock? An exploration of students’ understanding of the measurement of weight. In V.Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australia pp. 250-257). Melbourne: MERGA.
  • Durmaz, B. (2019). Erken çocuklukta matematik eğitimi. [Mathematics education in early childhood] Pegem Akademi.
  • Ellerton, N. F. (2013). Engaging prospective middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87-101.
  • Ellerton, N. F., Singer, F. M. & Cai, J. (2015). Problem posing in mathematics: Reflecting on the past, energizing the present, and foreshadowing the future. Mathematical problem posing (s. 547-556) in. Springer.
  • Field, A. (2009). Discovering statistics using SPSS. Sage Publications.
  • Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2013). Multivariate Data Analysis. Pearson Education Limited.
  • Hošpesová, A. & Tichá, M. (2015). Problem posing in primary school teacher training. In F. M. Singer, N. Ellerton, J. Cai (Eds.), Mathematical problem posing: From research to effective practice (s. 433–447) Springer.
  • Işık, C. & Kar, T. (2012). Pre-Service Elementary Teachers’ Problem Posing Skills. Mehmet Akif Ersoy University Faculty of Education Journal, 23, 190-214.
  • Işık, C., Kar, T., İpek, A. S. & Işık, A. (2012). Difficulties encountered by prospective classroom teachers in constructing stories about line graphs. International Online Journal of Educational Sciences, 4(3).
  • Kamii, C. & Russell, K. A. (2012). Elapsed time: Why is it so difficult to teach? Journal for Research in Mathematics Education, 43(3), 296-315.
  • Kanbur, B. (2017). Problem-posing situations and opinions of prospective elementary mathematics teachers' in dynamic geometry environment [Master Dissertation] Gazi University.
  • Kar, T. (2014). Investigating middle school mathematics teachers' mathematical knowledge for teaching in the context of problem posing: the example of addition operation with fractions. [Doctoral Dissertation] Atatürk University.
  • Karasar, N. (2018). Bilimsel araştırma yöntemi [Scientific research method] (33. Edition). Nobel Publications.
  • Karaaslan, G. K. (2018). Investigation of students' algebra learning and problem posing skills in a mathematics classroom supported by problem posing approach [Doctoral Dissertation] Hacettepe University.
  • Kilmen, S. (2015). Eğitim araştırmacıları için SPSS uygulamalı istatistik. Edge Akademi.
  • Leavy, A. & Hourigan, M. (2019). Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 1-21.
  • Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 3(1), 257- 264.
  • Ministry of National Education [MoNE]. (2018). School mathematics curriculum (Primary and Secondary School Grades 1, 2, 3, 4, 5, 6, 7 and 8). Ministry of National Education.
  • Pallant, J. (2007). SPSS survival manual, a step by step guide to data analysis using spss for windows (3. Edition). McGraw-Hill.
  • Pesen, C. (2019). İlkokullarda matematik öğretimi [Teaching mathematics in primary schools] (7. Edition). Pegem A Academia
  • Rosli, R., Capraro, M. M., Goldsby, D., Elsa, G. G., Capraro, R. M. & Onwuegbuzie, A. J. (2015). Middle-grade prospective teachers’ mathematical problem solving and problem posing. In F. M. Singer, N. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (s. 333-354) in. Springer.
  • Serin, M. K. (2019). Analysis of the problems posed by prospective primary school teachers in terms of type, cognitive structure and content knowledge. International Journal of Educational Methodology, 5(4), 577-590.
  • Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (s. 518–525) in. Mathematics Education Research Group of Australasia.
  • Şengül, S. & Katranci, Y. (2015). Free problem posing cases of prospective mathematics teachers: Difficulties and solutions. Procedia-Social and Behavioral Sciences, 174, 1983-1990.
  • Şimşek, N. & Boz, N. (2015). Investigating of pedagogical content knowledge of prospective primary teachers’ related to the length measurement in the context students’ understanding. Cumhuriyet International Journal of Education-CIJE, 4(3), 10-30.
  • Örnek, T. (2020). The assessment of problem posing learning model designed for the development of problem posing skill [Doctoral Dissertation] Atatürk University.
  • Örnek, T. & Soylu, Y. (2021). The Assessment of problem posing learning model designed for the development of problem posing skill. Journal of Computer and Educational Research, 9(18), 929-960.
  • Özdemir Yıldız, Ö. (2019). Investigation of problem posing skills of mathematics teacher candidates and the determination of teachers' views on problem posing [Master Dissertation] Gazi University.
  • Özer, T. & İnci̇kabı, L. (2019). Analysis of fractıon questions placed in the primary school mathematics textbooks. Medeniyet Journal of Educational Research, 3(1), 20-37.
  • Özgen, K., Aydın, M., Geçici, M.E. & Bayram, B. (2017). Investigation of problem posing skills of eighth grade students in terms of some variables. Turkish Journal of Computer and Mathematics Education, 8(2), 218-243.
  • Özmen, H. (2019). Experimental research method. H. Özmen and O. Karamustafaoğlu (Ed). Research Methods in Education (s.197-227) in. Pegem Academia.
  • Teki̇n Si̇trava R. & Işık, A. (2018). Investigation of prospective primary school teachers' problem posing skills based on comprehending and selecting problem-posing situations. Journol of Erzincan University Faculty of Education, 20 (3), 767-781.
  • Tichá, M. & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in prospective teacher training. In V. Durand-Guerrier, S. SouryLavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (s. 1941–1950) in. Institut National de Recherche Pédagogique.
  • Usta, A. & İpek, A. S. (2019). Investıgatıon of problems multiplication and division operations with natural numbers for primary school in Turkish mathematics textbooks. National Education Journal, Primary Education, 241-265.
  • 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.
  • Van De Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2012). Elementary and middle school mathematics - Teaching developmentally. (Tranlation Editor: Soner Durmuş). Nobel Akademik Publishing.
  • Yıldız, Z. (2014).The effects of problem posing studies in mathematics to problem posing skills and metacognitive awareness of prospective teachers teachers [Master Dissertation]. Marmara University.
  • Zehir, K. (2013). Investigation of prospective elementary mathematics teachers' problem posing skilss for fraction operations [Doctoral Dissertation]. Atatürk University.
There are 55 citations in total.

Details

Primary Language English
Subjects Applied and Developmental Psychology (Other)
Journal Section Research Articles
Authors

Volkan Sayın 0000-0002-7365-0050

Keziban Orbay 0000-0002-7642-4139

Early Pub Date September 11, 2024
Publication Date September 12, 2024
Submission Date November 22, 2023
Acceptance Date August 13, 2024
Published in Issue Year 2024 Volume: 11 Issue: 5

Cite

APA Sayın, V., & Orbay, K. (2024). Examining the Problem-Posing Skills of Prospective Classroom Teachers. Participatory Educational Research, 11(5), 1-23. https://doi.org/10.17275/per.24.61.11.5