Research Article
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Year 2021, Volume 8, Issue 1, 54 - 71, 31.03.2021
https://doi.org/10.33200/ijcer.820714

Abstract

References

  • Bernardo, A. B. I. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19(2), 149-163.
  • Bonotto, C., & Santo, L. D. (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 to effective practice (pp. 103-123). New York: Springer.
  • Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.
  • Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., … 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, 1-12. DOI: https://doi.org/10.1016/j.ijer.2019.02.004
  • Cai, J., & Ding, M. (2017). On mathematical understanding: Perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education, 20(1), 5-29.
  • 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 to effective practice (pp. 3-34). New York: Springer.
  • Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics. 105, 287-301. doi:10.1007/s10649-020-10008-x
  • 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.
  • Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA: Revista de Investigación en Didáctica de la Matemática, 6(4), 135–146.
  • Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2007). The relationship between posing and solving arithmetic word problems among Chinese elementary school children. Research in Mathematics Education, 11(1), 1-31.
  • Chen, L. C., 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. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. From research to effective practice (pp. 309-329). New York: Springer.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt Für Didaktik Der Mathematik- International Journal on Mathematics Education, 37(3), 149–158.
  • Cohen, J. (1988). Statistical power analysis for the behavioral science. Hillsdale, NJ: Erlbaum.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.
  • Çetinkaya, A., & Soybaş, D. (2018). An investigation of problem posing skills of elementary school 8th grade students. Journal of Theoretical Educational Science, 11(1), 169-200.
  • Downton, A., & Sullivan, P. (2017). Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections. Educational Studies in Mathematics, 95(3), 303-328.
  • Ellerton, N. F. (1986). Children’s made-up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271.
  • Geçici, M. E., & Aydın, M. (2020). Determining the geometry problem posing performances of eighth grade students in different problem posing situations. International Journal of Contemporary Educational Research, 7(1), 1-17. DOI: https://doi.org/10.33200/ijcer.575063
  • Kar, T., Özdemir, E., Öçal, M. F., Güler, G., ve İpek, A. S. (2019). Indicators of prospective mathematics teachers’ success in problem solving: the case of creativity in problem posing. M. Graven, H. Venkat, A. Essien, ve P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, s. 456-463). Pretoria, South Africa: PU.
  • Kar, T. (2015). Analysis of problems posed by sixth-grade middle school students for the addition of fractions in terms of semantic structures. International Journal of Mathematical Education in Science and Technology, 46(6), 879-894.
  • Kılıç, Ç. (2013). Determining performance of elementary students related to problem posing activities requiring four arithmetical operations with natural numbers. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 20, 256-274.
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
  • Kopparla, M., Biçer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., … Capraro, R. M. (2019). The Effects of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 1–18.
  • Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. From research to effective practice (pp. 273-292). New York: Springer.
  • Lee, S. Y. (2020). Research Status of mathematical problem posing in mathematics education journals. International Journal of Science and Mathematics Education. 1-17. https://doi.org/10.1007/s10763-020-10128-z
  • Lee, F. L., & Heyworth, R. (2000). Problem complexity: A measure of problem difficulty in algebra by using computer. Education Journal, 28(1), 85–107.
  • Leung, S. S., & 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.
  • Lowrie, T. (1999). Free problem posing: Year 3/4 students constructing problems for friends to solve. In J. Truran & K. Truran (Eds.), Making a Difference: Proceedings of the 22nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 328–335). Sydney: MERGA.
  • Lowrie, T. (2002). Designing a framework for problem posing: Young children generating open-ended tasks. Contemporary Issues in Early Childhood, 3(3), 354-364.
  • Lowrie, T., & Whitland, J. (2000). Problem posing as a tool for learning, planning and assessment in the primary school. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the Psychology of Mathematics Education (pp. 247-254). Japan: Hiroshima.
  • Luo, F. (2009). Evaluating the effectiveness and insights of preservice elementary teachers’ abilities to construct word problems for fraction multiplication. Journal of Mathematics Education, 2(1), 83–98.
  • Marshall, S. P. (1995). Schemas in problem solving. New York, NY: Cambridge University Press.
  • Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children's ıntuitive models of multiplication and division. Journal for Research in Mathematics Education, 28(3), 309-330.
  • National Council of Teachers of Mathematics (2000). Principles and standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2019). Investigation of eighth grade students’ skills in problem-posing. International Journal for Mathematics Teaching and Learning, 20(1), 106-130.
  • Papadopoulos, I., & Patsiala, N. (2019). Capturing problem posing landscape in a grade-4 classroom: A pilot study. Paper presented at the Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht, Netherlands.
  • Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton, N.J.: Princeton University Press.
  • Rosli, R., Capraro, M. M., Goldsby, D., Gonzalez, E. G., Onwuegbuzie, A. J., & Capraro, R. M. (2015). Middle grade preservice teachers’ mathematical problem solving and problem posing. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 333-354). New York: Springer.
  • Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing. International Journal of Mathematical Education in Science and Technology, 48(2), 163-184.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics. 14(1), 19–28.
  • Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt für Didaktik der Mathematik, 29(3), 75–80.
  • Silver, E. A. (2009). Cross-national comparisons of mathematics curriculum materials: what might we learn? Zentralblatt Für Didaktik Der Mathematik- International Journal on Mathematics Education, 41(6), 827–832.
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Re¬search in Mathematics Education, 27(5), 521-539.
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
  • Singer, F. M., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9–26.
  • 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., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in mathematics education. Melbourne, Australia: Mathematics Education Research Group of Australasia
  • Winograd, K. (1997). Ways of sharing student-authored story problems. Teaching Children Mathematics, 4(1), 40-47.
  • 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.
  • Yeap, B. H., & Kaur, B. (2000). Exploring the relationship between mathematical problem posing and problem solving, type of task and grade level. In J. Ee, B. Kaur, N. H. Lee, & B. H. Yeap (Eds.), New ‘Literacies’: Educational response to a knowledge-based society: Proceedings of the ERA-AME-AMIC Joint Conference (pp. 605-611). Singapore: Educational Research Association.
  • Yeap, B. H., & Kaur, B. (2001). Semantic characteristics that make arithmetic word problems difficult. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and Beyond: Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (pp. 555-562). Sydney: MERGA.

Problem Posing with Third-grade Children: Examining the Complexity of Problems

Year 2021, Volume 8, Issue 1, 54 - 71, 31.03.2021
https://doi.org/10.33200/ijcer.820714

Abstract

The purpose of this study was to investigate what factors third-grade students took into consideration when posing problems for their peers and how these factors affected the mathematical complexities of the problems. Free and semi-structured problem-posing tasks were given to 27 third-grade students, and the problems they created for their peers were analyzed in terms of their semantic structure and arithmetic complexity. According to the findings of the study, there was a statistically significant difference between the semantic structures of the problems in both tasks created for the more mathematically proficient student, but there was no difference between their arithmetic complexities. In addition, according to the qualitative findings of the study, the magnitude of the numbers, the operation types, the number of operations used, and the interests of the students were taken into consideration in posing problems for students with low and high levels of mathematical ability.

References

  • Bernardo, A. B. I. (1999). Overcoming obstacles to understanding and solving word problems in mathematics. Educational Psychology, 19(2), 149-163.
  • Bonotto, C., & Santo, L. D. (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 to effective practice (pp. 103-123). New York: Springer.
  • Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719-737.
  • Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., … 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, 1-12. DOI: https://doi.org/10.1016/j.ijer.2019.02.004
  • Cai, J., & Ding, M. (2017). On mathematical understanding: Perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education, 20(1), 5-29.
  • 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 to effective practice (pp. 3-34). New York: Springer.
  • Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics. 105, 287-301. doi:10.1007/s10649-020-10008-x
  • 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.
  • Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA: Revista de Investigación en Didáctica de la Matemática, 6(4), 135–146.
  • Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2007). The relationship between posing and solving arithmetic word problems among Chinese elementary school children. Research in Mathematics Education, 11(1), 1-31.
  • Chen, L. C., 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. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. From research to effective practice (pp. 309-329). New York: Springer.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt Für Didaktik Der Mathematik- International Journal on Mathematics Education, 37(3), 149–158.
  • Cohen, J. (1988). Statistical power analysis for the behavioral science. Hillsdale, NJ: Erlbaum.
  • Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.
  • Çetinkaya, A., & Soybaş, D. (2018). An investigation of problem posing skills of elementary school 8th grade students. Journal of Theoretical Educational Science, 11(1), 169-200.
  • Downton, A., & Sullivan, P. (2017). Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections. Educational Studies in Mathematics, 95(3), 303-328.
  • Ellerton, N. F. (1986). Children’s made-up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271.
  • Geçici, M. E., & Aydın, M. (2020). Determining the geometry problem posing performances of eighth grade students in different problem posing situations. International Journal of Contemporary Educational Research, 7(1), 1-17. DOI: https://doi.org/10.33200/ijcer.575063
  • Kar, T., Özdemir, E., Öçal, M. F., Güler, G., ve İpek, A. S. (2019). Indicators of prospective mathematics teachers’ success in problem solving: the case of creativity in problem posing. M. Graven, H. Venkat, A. Essien, ve P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, s. 456-463). Pretoria, South Africa: PU.
  • Kar, T. (2015). Analysis of problems posed by sixth-grade middle school students for the addition of fractions in terms of semantic structures. International Journal of Mathematical Education in Science and Technology, 46(6), 879-894.
  • Kılıç, Ç. (2013). Determining performance of elementary students related to problem posing activities requiring four arithmetical operations with natural numbers. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 20, 256-274.
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
  • Kopparla, M., Biçer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., … Capraro, R. M. (2019). The Effects of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 1–18.
  • Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. From research to effective practice (pp. 273-292). New York: Springer.
  • Lee, S. Y. (2020). Research Status of mathematical problem posing in mathematics education journals. International Journal of Science and Mathematics Education. 1-17. https://doi.org/10.1007/s10763-020-10128-z
  • Lee, F. L., & Heyworth, R. (2000). Problem complexity: A measure of problem difficulty in algebra by using computer. Education Journal, 28(1), 85–107.
  • Leung, S. S., & 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.
  • Lowrie, T. (1999). Free problem posing: Year 3/4 students constructing problems for friends to solve. In J. Truran & K. Truran (Eds.), Making a Difference: Proceedings of the 22nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 328–335). Sydney: MERGA.
  • Lowrie, T. (2002). Designing a framework for problem posing: Young children generating open-ended tasks. Contemporary Issues in Early Childhood, 3(3), 354-364.
  • Lowrie, T., & Whitland, J. (2000). Problem posing as a tool for learning, planning and assessment in the primary school. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the Psychology of Mathematics Education (pp. 247-254). Japan: Hiroshima.
  • Luo, F. (2009). Evaluating the effectiveness and insights of preservice elementary teachers’ abilities to construct word problems for fraction multiplication. Journal of Mathematics Education, 2(1), 83–98.
  • Marshall, S. P. (1995). Schemas in problem solving. New York, NY: Cambridge University Press.
  • Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children's ıntuitive models of multiplication and division. Journal for Research in Mathematics Education, 28(3), 309-330.
  • National Council of Teachers of Mathematics (2000). Principles and standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2019). Investigation of eighth grade students’ skills in problem-posing. International Journal for Mathematics Teaching and Learning, 20(1), 106-130.
  • Papadopoulos, I., & Patsiala, N. (2019). Capturing problem posing landscape in a grade-4 classroom: A pilot study. Paper presented at the Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht, Netherlands.
  • Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton, N.J.: Princeton University Press.
  • Rosli, R., Capraro, M. M., Goldsby, D., Gonzalez, E. G., Onwuegbuzie, A. J., & Capraro, R. M. (2015). Middle grade preservice teachers’ mathematical problem solving and problem posing. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 333-354). New York: Springer.
  • Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing. International Journal of Mathematical Education in Science and Technology, 48(2), 163-184.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics. 14(1), 19–28.
  • Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt für Didaktik der Mathematik, 29(3), 75–80.
  • Silver, E. A. (2009). Cross-national comparisons of mathematics curriculum materials: what might we learn? Zentralblatt Für Didaktik Der Mathematik- International Journal on Mathematics Education, 41(6), 827–832.
  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Re¬search in Mathematics Education, 27(5), 521-539.
  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
  • Singer, F. M., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9–26.
  • 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., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in mathematics education. Melbourne, Australia: Mathematics Education Research Group of Australasia
  • Winograd, K. (1997). Ways of sharing student-authored story problems. Teaching Children Mathematics, 4(1), 40-47.
  • 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.
  • Yeap, B. H., & Kaur, B. (2000). Exploring the relationship between mathematical problem posing and problem solving, type of task and grade level. In J. Ee, B. Kaur, N. H. Lee, & B. H. Yeap (Eds.), New ‘Literacies’: Educational response to a knowledge-based society: Proceedings of the ERA-AME-AMIC Joint Conference (pp. 605-611). Singapore: Educational Research Association.
  • Yeap, B. H., & Kaur, B. (2001). Semantic characteristics that make arithmetic word problems difficult. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and Beyond: Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (pp. 555-562). Sydney: MERGA.

Details

Primary Language English
Subjects Social
Journal Section Articles
Authors

Tuğrul KAR (Primary Author)
Recep Tayyip Erdoğan Üniversitesi
0000-0001-8336-1327
Türkiye


Tuğba ÖÇAL
AGRI IBRAHIM CECEN UNIVERSITY
0000-0003-1628-3546
Türkiye


Mehmet Fatih ÖÇAL
AGRI IBRAHIM CECEN UNIVERSITY
0000-0003-0428-6176
Türkiye


Ömer DEMİRCİ
EĞİTİM FAKÜLTESİ
0000-0002-7806-9767
Türkiye

Publication Date March 31, 2021
Published in Issue Year 2021, Volume 8, Issue 1

Cite

APA Kar, T. , Öçal, T. , Öçal, M. F. & Demirci, Ö. (2021). Problem Posing with Third-grade Children: Examining the Complexity of Problems . International Journal of Contemporary Educational Research , 8 (1) , 54-71 . DOI: 10.33200/ijcer.820714

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