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problem posing problem types content knowledge cognitive structure pre service primary school teachers

Analysis of the Problems Posed by Pre-Service Primary School Teachers in Terms of Type, Cognitive Structure and Content Knowledge

Mehmet Koray Serin

In the current study, the problems posed by pre-service primary school teachers within the context of semi-structured problem formation were analyzed .

I

In the current study, the problems posed by pre-service primary school teachers within the context of semi-structured problem formation were analyzed according to their type, cognitive structure, and content knowledge. A total of 134 pre-service primary school teachers attending a state university in Turkey participated in the current study designed in line with the case study design. The pre-service teachers were presented with a table and they were asked to establish a problem suitable for the elementary level using the data given in the table. The data were collected through the established problem statements and written explanations of the participants. The collected data were analyzed by using both content and descriptive analyses. The findings have revealed that the pre-service teachers less preferred real-life problems than routine type of problems and the problems at the level of reasoning than the problems at the levels of knowing and applying. Moreover, nearly half of the pre-service teachers erroneously expressed the grade level for which they established their problem. The results have shown that the pre-service teachers do not adequately use real-life problems and problems at the level of reasoning and that there are deficiencies in their mathematical content knowledge depending on their knowledge of the curriculum.

Keywords: Problem-posing, problem types, content knowledge, cognitive structure, pre-service primary school teachers.

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References

Abu-Elwan, R. (1999, November). The development of mathematical problem posing skills for prospective middle school teachers. In F. Mina & A. Rogerson (Eds.), Paper presented at the proceedings of the International Conference on Mathematical Education into the 21st Century: Societal Challenges, Issues and Approaches (pp. 1–8). Cairo, Egypt: Triforum.

Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education, 25(1), 56-69.

Akay, H., Soybas, D., & Argun, Z. (2006). Problem posing experiences and using open-ended questions in mathematics teaching. Kastamonu Education Journal, 14(1), 129-146.

Anderson, J.  (2009, October).  Mathematics curriculum development and the role of problem solving.  In K. School (Ed), Proceedings of  the 2009 ACSA National Biennial Conference Curriculum: a national conversation (pp. 1-8). Canberra, Australia: ACT.

Artut, P., & Tarim, K. (2016). Ilkokul matematik dersi programlarinin problem cozme acisindan incelenmesi [Examination of elementary school mathematics curriculum in terms of problem solving]. In M. F. Ozmantar, A. Ozturk & E. Bay (Eds.), Reform ve degisim baglaminda ilkokul matematik ogretim programlari [Primary school mathematics curricula in the context of reform and change] (pp. 293-316). Ankara, Turkey: Pegem Academy Publishing.

Baki, A. (2018). Matematigi ogretme bilgisi [Knowledge of teaching mathematics]. Ankara, Turkey: Pegem Academy Publishing.

Bal, A. P. (2015). Examination of the mathematical problem-solving beliefs and success levels of primary school teacher candidates through the variables of mathematical success and gender. Educational Sciences: Theory and Practice15(5), 1373-1390.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education59(5), 389-407.

Bayazit, I., & Kirnap-Donmez, S. M. (2017). Prospective teachers’ proficiencies at problem posing in the context of proportional reasoning. Turkish Journal of Computer and Mathematics Education, 8(1), 130-160.

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research on Mathematics Education, 29(1). 41-62.

Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for Psychology of Mathematics Education (Vol. 2, pp. 773–782). Toronto, Canada: PMENA.

Bonotto, C. (2001). How to connect school mathematics with students' out-of-school knowledge. ZDM33(3), 75-84.

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 & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 103-123). New York, NY: Springer.

Bragg, L., & Nicol, C. (2008). Designing open-ended problems to challenge preservice teachers’ views on mathematics and pedagogy. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education and 20th Conference of the North-American Chapter (Vol. 2, pp. 256–270). Morelia, Mexico: PME.

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. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 141-174). New York, NY: Springer.

Cakmak, Z., Konyalioglu, A. C., & Isik, A. (2014). The investigation of pre-service elementary mathematics teachers’ content knowledge on three dimensional objects. Middle Eastern and African Journal of Educational Research8, 28-44.

Cankoy, O., & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe University Journal of Education, 38, 11-24.

Charles, R., & Lester, F. (1982). Teaching problem solving: What, why and how. Palo Alto, CA: Dale Seymour Pub.

Christensen, L., Johnson, R., & Turner, L. (2013). Research methods, design, and analysis (12nd ed.). Upper Saddle River, NJ: Pearson Education.

Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM Mathematics Education, 37(3), 149-158.

Cifarelli, V. V., & Cai, J. (2005). The evolution of mathematical explorations in open-ended problem- solving situations. The Journal of Mathematical Behavior, 24(3), 302–324.

Cifarelli, V. V., & Sevim, V. (2015). Problem posing as reformulation and sense-making within problem solving. In F. M. Singer, N. F. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 177-194). New York, NY: Springer.

Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243-270.

Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education41(5), 605-618.

English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.

English, L. D. (2003). Engaging students in problem posing in an inquiry-oriented mathematics classroom. In F. K. Lester & R. I. Charles (Eds.), Teaching mathematics through problem solving, Prekindergarten-Grade 6 (pp. 187-196). Reston, VA: National Council of Teachers of Mathematics.

English, L. D., & Watson, J. M. (2015). Statistical literacy in the elementary school: Opportunities for problem posing. In F. M. Singer, N. F. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 241-256). New York, NY: Springer.

Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116.

Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380–392.

Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics94(2), 78-85.

Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College Press.

Grundmeier, T. A. (2015). Developing the problem-posing abilities of prospective elementary and middle school teachers. In F. M. Singer, N. F. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 411-431). New York, NY: Springer.

Hospesova, A., & Ticha, M. (2015). Problem posing in primary school teacher training. In F. M. Singer, N. F. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 433-447). New York, NY: Springer.

Isik, A., Isik, C., & Kar, T. (2011). Analysis of the problems related to verbal and visual representations posed by pre-service mathematics teachers. Pamukkale University Journal of Education, 30(1), 40-49.

Isik, C., & Kar, T. (2012). Analyzing problems posed by 7th grade students for addition operation with fractions. Elementary Education Online11(4), 1021-1035.

Kar, T. (2016). Prospective middle school mathematics teachers' knowledge of linear graphs in context of problem-posing. International Electronic Journal of Elementary Education, 8(4), 643–657.

Kilic, C. (2013). Determining the performances of pre-service primary school teachers in problem posing situations. Educational Sciences: Theory & Practice, 13(2), 1195–1211.

Kilic, C. (2017). A new problem-posing approach based on problem-solving strategy: Analyzing pre-service primary school teachers' performance. Educational Sciences: Theory and Practice17(3), 771-789.

Lavy, I. (2015). Problem-posing activities in a dynamic geometry environment: When and how. In F. M. Singer, N. F. Ellerton & J. Cai (Eds.), Mathematical problem posing: From research into effective practice (pp. 393-410). New York, NY: Springer.

Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In W. Jeong-Ho, P. Kyo-Sik, L. Hee-Chan & S. Dong-Yeop (Eds.), Proceedings of the 31st International Conference on the Psychology of Mathematics Education (Vol. 3, pp. 129–136). Seoul, South Korea: PME.

Leung, S. S. (1996). Problem posing as assessment: Reflections and re-constructions. The Mathematics Educators, 1(2), 159–171.

Leung, S. K., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5-24.

Lindquist, M., Philpot, R., Mullis, I. V. S., & Cotter, K. E. (2019). TIMSS 2019 mathematics framework. In I. V. S. Mullis & M. O. Martin (Eds.), TIMSS 2019 assessment frameworks (pp. 11–25). Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Lowrie, T.  (2002).  Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87-98.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.

Mamona-Downs, J. (1993). On analyzing problem posing. In I. Hirabayashi, N. Nohda, K. Shigematsu & F. L. Lin (Eds.), Proceedings of the 17th International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 41–47). Tsukuba, Japan: International Group for the Psychology in Mathematics Education.

McLeod, D. B. (1994). Research on affect in mathematics learning in the JRME: 1970 to the present. Journal for Research in Mathematics Education, 25(6),637-647.

Mestre, P. J. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Applied Developmental Psychology, 23, 9–50.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA, US: Sage Publications, Inc.

Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record108(6), 1017-1054.

Ministry of National Education (MoNE). (2009). Ilkogretim matematik dersi 1-5. siniflar ogretim programi [Elementary mathematics lesson 1-5. grades curriculum]. Retrieved from http://talimterbiye.mebnet.net/Ogretim%20Programlari/ilkokul/2013-2014/Matematik1-5.pdf

Ministry of National Education (MoNE). (2015). Matematik dersi ogretim programi ve kilavuzu (1.2.3.4. Siniflar) [Mathematics curriculum and guide (1.2.3.4. Grades)]. Retrieved from http://matematikogretimi.weebly.com/uploads/2/6/5/4/26548246/matematik1-4_prg.pdf

Ministry of National Education (MoNE). (2018). Matematik dersi ogretim programi (Ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. siniflar) [Mathematics curriculum (1st, 2nd, 3rd, 4th, 5th, 6th, 7th and 8th grades)]. Retrieved from http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329

National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

Peace, H., Quebec Fuentes, S., & Bloom, M. (2018). Preservice teachers’ transforming perceptions of science and mathematics teacher knowledge. International Journal of Educational Methodology, 4(4), 227-241. https://doi.org/10.12973/ijem.4.4.227

Perrin, J. R. (2007). Problem posing at all levels in the calculus classroom. School Science and Mathematics107(5), 182-192.

Pirie, S. (2002). Problem posing: What can it tell us about students’ mathematical understanding? In D. Mewborn, P. Sztajn, E. White, H. Wiegel, R. Bryant & K. Nooney (Eds.), Psychology of Mathematics Education North America (PME-NA), Athens, GA (vol. 11, pp. 927–958). Columbus, OH: Eric Clearinghouse for Science, Mathematics, and Environmental Education.

Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense – making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan.

Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 53-70). Hillsdale, NJ: Erlbaum.

Shulman, L.S. (1986). Those who understand; knowledge growth in teaching. Educational Researcher, 15(2), 4-31.

Silver, E. A. (1993). On mathematical problem posing. In R. Hirabayasshi, N. Nohda, K. Shigematsu & F. L. Lin (Eds.), Proceedings of the 17th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 66-85). Tsukuba, Japan: PME.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.

Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching children mathematics, 12(3), 129-135.

Singer, F. M., Ellerton, N. F., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. New York, NY: Springer.

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press.

Stickles, P. R. (2011). An analysis of secondary and middle school teachers’ mathematical problem posing. Investigations in Mathematics Learning, 3(2), 1–34.

Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh, & N.  Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp.164 185). Perth, Australia: MASTEC Publication.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Melbourne, Australia: Mathematics Education Research Group of Australasia.

Tekin Sitrava, R., & Isik, A. (2018). An investigation into prospective primary school teachers’ free problem posing skills. Gazi University Journal of Gazi Education Faculty, 38(3), 919-947. 

Ticha, M., & Hospesova, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, F. Arzarello, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 1941–1950). Lyon, France: Institute National de Recherche Pedagogique.

Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25.

Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175.

Ulusoy, F., & Kepceoglu, I. (2018). The contextual and cognitive structure of prospective middle school mathematics teachers' problems in semi-structured problem-posing context, Journal of Kirsehir Education Faculty, 19(3), 1937-1963.

Unlu, M., & Sarpkaya-Aktas, G. (2017). Examination of pre-service elementary mathematics teachers’ problems posed about algebraic expressions and equations. Turkish Journal of Computer and Mathematics Education, 8(1), 161-187.

Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics83(1), 117-132.

Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction4(4), 273-294.

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