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Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions

  • Chapter
Mathematical Problem Posing

Part of the book series: Research in Mathematics Education ((RME))

Abstract

This chapter synthesizes the current state of knowledge in problem-posing research and suggests questions and directions for future study. We discuss ten questions representing rich areas for problem-posing research: (a) Why is problem posing important in school mathematics? (b) Are teachers and students capable of posing important mathematical problems? (c) Can students and teachers be effectively trained to pose high-quality problems? (d) What do we know about the cognitive processes of problem posing? (e) How are problem-posing skills related to problem-solving skills? (f) Is it feasible to use problem posing as a measure of creativity and mathematical learning outcomes? (g) How are problem-posing activities included in mathematics curricula? (h) What does a classroom look like when students engage in problem-posing activities? (i) How can technology be used in problem-posing activities? (j) What do we know about the impact of engaging in problem-posing activities on student outcomes?

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References

  • Abramovich, S., & Cho, E. (2006). Technology as a medium for elementary preteachers’ problem-posing experience in mathematics. Journal of Computers in Mathematics and Science Teaching, 25(4), 309–323.

    Google Scholar 

  • Abramovich, S., & Norton, A. (2006). Equations with parameters: A locus approach. Journal of Computers in Mathematics and Science Teaching, 25(1), 5–28.

    Google Scholar 

  • 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.

    Google Scholar 

  • Akay, H., & Boz, N. (2010). The effect of problem posing oriented analyses-II course on the attitudes toward mathematics and mathematics self-efficacy of elementary prospective mathematics teachers. Australian Journal of Teacher Education, 35(1), 6. Retrieved from http://ro.ecu.edu.au/ajte/vol35/iss1/6

  • Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8, 14.

    Google Scholar 

  • Basic Education Curriculum Material Development Center, Chinese Ministry of Education. (2003). National mathematics curriculum standards at the compulsory education level (draft for consultation) [in Chinese]. Beijing, China: Beijing Normal University.

    Google Scholar 

  • Beal, C. R., & Cohen, P. R. (2012). Teach ourselves: Technology to support problem posing in the STEM classroom. Creative Education, 3, 513–519.

    Article  Google Scholar 

  • Boaler, J. (2003). Studying and capturing the complexity of practice—The case of the “dance of agency.” Paper presented at the 27th International Group for the Psychology of Mathematics Education Conference held jointly with the 25th PME-NA Conference, Honolulu, HI.

    Google Scholar 

  • Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83, 37–55.

    Article  Google Scholar 

  • Brousseau, G. (1984). The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics. In H. G. Steiner (Ed.), Theory of mathematics education (pp. 110–119). Occasional paper 54. Bielifeld, Germany: Institut fur Didaktik der Mathematik.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Eds. & Trans.). Dordrecht, The Netherlands: Kluwer Academic.

    Google Scholar 

  • Brown, S. I., & Walter, M. I. (1990). The art of problem posing (2nd ed.). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Brown, S. I., & Walter, M. I. (1993). Problem posing in mathematics education. In S. I. Brown & M. I. Walter (Eds.), Problem posing: Reflections and application (pp. 16–27). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Cai, J. (1998). An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10, 37–50.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Cai, J. (2005). U.S. and Chinese teachers’ knowing, evaluating, and constructing representations in mathematics instruction. Mathematical Thinking and Learning: An International Journal, 7(2), 135–169.

    Article  Google Scholar 

  • Cai, J. (2012). Problem posing as lenses of improving students’ learning in classroom. Newark, DE: University of Delaware.

    Google Scholar 

  • Cai, J., & Brook, M. (2006). New perspectives of looking back in mathematical problem solving. Mathematics Teaching, 196, 42–45.

    Google Scholar 

  • Cai, J., & Cifarelli, V. V. (2005). Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems. Focus on Learning Problems in Mathematics, 27(3), 43–72.

    Google Scholar 

  • Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21, 401–421.

    Article  Google Scholar 

  • Cai, J., & Hwang, S. (2003). A perspective for examining the link between problem posing and problem solving. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA (Vol. 3, pp. 103–110).

    Google Scholar 

  • Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83, 57–69.

    Article  Google Scholar 

  • Cai, J., Jiang, C., Hwang, S., Nie, B., & Hu, D. (in press). Mathematical problem-posing tasks in U.S. and Chinese standards-based textbooks. In P. Felmer, J. Kilpatrick, & E. Pehkonen (Eds.), Problem solving in mathematics education: New advances and perspectives. Springer.

    Google Scholar 

  • Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97, 3–20.

    Article  Google Scholar 

  • Chang, K. E., Wu, L. J., Weng, S. E., & Sung, Y. T. (2012). Embedding game-based problem-solving phase into problem-posing system for mathematics learning. Computers & Education, 58(2), 775–786. doi:10.1016/j.compedu.2011.10.002.

    Article  Google Scholar 

  • Chazan, D. (1990). Students’ microcomputer-aided exploration in geometry. Mathematics Teacher, 83, 628–635.

    Google Scholar 

  • Chinese National Ministry of Education, Office of School Teaching Materials and Institute of Curriculum and Teaching Materials. (1986). A collection of mathematical syllabuses (1949–1985). Beijing, China: Author.

    Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Montana Mathematics Enthusiast, 2, 125–143.

    Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralbatt für Didaktik der Mathematik (ZDM), 37, 149–158.

    Google Scholar 

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

    Article  Google Scholar 

  • Contreras, J. (2007). Unraveling the mystery of the origin of mathematical problems: Using a problem-posing framework with prospective mathematics teachers. The Mathematics Educator, 17(2), 15–23.

    Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Demir, B. B. (2005). The effect of instruction with problem posing on tenth grade students’ probability achievement and attitudes toward probability (Unpublished master’s thesis). Middle East Technical University, Ankara, Turkey.

    Google Scholar 

  • Doyle, W. (1983). Academic work. Review of Educational Research, 53, 159–199.

    Article  Google Scholar 

  • Einstein, A., & Infeld, L. (1938). The evolution of physics. New York, NY: Simon & Schuster.

    Google Scholar 

  • Ellerton, N. F. (1986). Children’s made-up mathematics problems—A new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261–271.

    Article  Google Scholar 

  • 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, 87–101.

    Article  Google Scholar 

  • English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183–217.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403–434.

    Article  Google Scholar 

  • Frensch, P., & Funke, J. (1995). Complex problem solving: The European perspective. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Getzels, J. W. (1979). Problem finding: A theoretical note. Cognitive Science, 3, 167–172.

    Article  Google Scholar 

  • Goldin, G. A., & McClintock, C. E. (Eds.). (1984). Task variables in mathematical problem solving. Philadelphia, PA: Franklin Institute Press.

    Google Scholar 

  • Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers. School Science and Mathematics, 94(2), 78–84.

    Article  Google Scholar 

  • Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics, 98(8), 448–456.

    Article  Google Scholar 

  • Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Hashimoto, Y. (1987). Classroom practice of problem solving in Japanese elementary schools. In J. P. Becker, & T. Miwa (Eds.), Proceedings of the U.S.-Japan Seminar on Mathematical Problem Solving (pp. 94–119). Carbondale, IL: Southern Illinois University.

    Google Scholar 

  • Healy, C. C. (1993). Creating miracles: A story of student discovery. Berkeley, CA: Key Curriculum Press.

    Google Scholar 

  • Herbst, P. G. (2002). Engaging students in proving: A double bind on the teacher. Journal for Research in Mathematics Education, 33, 176–203.

    Article  Google Scholar 

  • Herbst, P., & Chazan, D. (2003). Exploring the practical rationality of mathematics teaching through conversations about videotaped episodes: The case of engaging students in proving. For the Learning of Mathematics, 23(1), 2–14.

    Google Scholar 

  • Isik, C., & Kar, T. (2012). The analysis of the problems the pre-service teachers experience in posing problems about equations. Australian Journal of Teacher Education, 37(9). Retrieved from http://ro.ecu.edu.au/cgi/viewcontent.cgi?article=1568&context=ajte

  • Keil, G. E. (1964/1967). Writing and solving original problems as a means of improving verbal arithmetic problem solving ability (Doctoral dissertation, Indiana University, 1964). Dissertation Abstracts International, 25(12), 7109.

    Google Scholar 

  • Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83, 71–86.

    Article  Google Scholar 

  • Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161. doi:10.1016/j.jmathb.2011.11.002.

    Article  Google Scholar 

  • Kotsopoulos, D., & Cordy, M. (2009). Investigating imagination as a cognitive space for learning mathematics. Educational Studies in Mathematics, 70, 259–274.

    Article  Google Scholar 

  • Lan, Y. F., & Lin, P. C. (2011). Evaluation and improvement of student’s question-posing ability in a web-based learning environment. Australasian Journal of Educational Technology, 27(4), 581–599.

    Google Scholar 

  • Lavy, I., & Bershadsky, I. (2003). Problem posing via “what if not?” strategy in solid geometry—A case study. The Journal of Mathematical Behavior, 22(4), 369–387.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lester, F. K. (1994). Musing about mathematical problem-solving research: 1970–1994. Journal for Research in Mathematics Education, 25(6), 660–675.

    Article  Google Scholar 

  • Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralbatt für Didaktik der Mathematik (ZDM), 29, 81–85.

    Article  Google Scholar 

  • Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics, 83(1), 103–116. doi:10.1007/s10649-012-9436-4.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lu, C., & Wang, B. (2006). Research on mathematics teaching through using mathematical situations and posing problem in high school and primary school [in Chinese]. Guiyang, China: Guizhou People’s Publishing House.

    Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30, 520–540.

    Google Scholar 

  • McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York, NY: Macmillan.

    Google Scholar 

  • McLeod, D., & Adams, V. (Eds.). (1989). Affect and mathematical problem solving: A new perspective. New York, NY: Springer.

    Google Scholar 

  • Ministry of Education of China. (2011). Mathematics curriculum standard of compulsory education (2011 version) [in Chinese]. Beijing, China: Beijing Normal University Press. Retrieved from http://www.moe.gov.cn/publicfiles/business/htmlfiles/moe/moe_711/201201/xxgk_129268.html

    Google Scholar 

  • Moore-Russo, D., & Weiss, M. (2011). Practical rationality, the disciplinary obligation, and authentic mathematical work: A look at geometry. The Mathematics Enthusiast, 8(3), 463–482.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • National Governors Association Center for Best Practices. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices, Council of Chief State School Officers.

    Google Scholar 

  • National Research Council. (2004). On evaluating curricular effects: Judging the quality of K-12 mathematics education. In J. Confrey & V. Stohl (Eds.). Washington, DC: National Academy Press.

    Google Scholar 

  • Olson, J. C., & Knott, L. (2013). When a problem is more than a teacher’s question. Educational Studies in Mathematics, 83, 27–36.

    Article  Google Scholar 

  • Pittalis, M., Christou, C., Mousoulides, N., & Pitta-Pantazi, D. (2004). A structural model for problem posing. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 49–56). Bergen, Norway: Bergen University College.

    Google Scholar 

  • Polya, G. (1957). How to solve it. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Rosenshine, B., Meister, C., & Chapman, S. (1996). Teaching students to generate questions: A review of the intervention studies. Review of Educational Research, 66(2), 181–221.

    Article  Google Scholar 

  • Santos-Trigo, M., & Diaz-Barriga, E. (2000). Posing questions from proposed problems: Using technology to enhance mathematical problem solving. Mathematics Teacher, 93(7), 578–580.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

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

    Google Scholar 

  • Silver, E. A. (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Mahwah, NJ: Erlbaum.

    Google Scholar 

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

    Google Scholar 

  • Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralbatt für Didaktik der Mathematik (ZDM), 97(3), 75–80.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135.

    Google Scholar 

  • Silver, E. A., Mamona-Downs, J., Leung, S. S., & Kenney, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27, 293–309.

    Article  Google Scholar 

  • Singer, F. M., & Moscovici, H. (2008). Teaching and learning cycles in a constructivist approach to instruction. Teaching and Teacher Education, 24(6), 1613–1634.

    Article  Google Scholar 

  • Stanic, G. M. A., & Kilpatrick, J. (1988). Historical perspectives on problem solving in mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), Research agenda for mathematics education: The teaching and assessing of mathematical problem solving (pp. 1–22). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

  • Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Traylor, K. C. (2005). Effect of problem posing on eighth grade students’ mathematical problem solving skills. Instructional Technology Monographs, 2(2). Retrieved March 11, 2013, from http://itm.coe.uga.edu/archives/fall2005/ktraylor.htm

  • van den Brink, J. F. (1987). Children as arithmetic book authors. For the Learning of Mathematics, 7, 44–48.

    Google Scholar 

  • Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students’ mathematical problem posing in China and USA. Educational Studies in Mathematics, 82(2), 201–221.

    Article  Google Scholar 

  • Voica, C., & Singer, F. M. (2012). Problem modification as an indicator of deep understanding. Paper presented at Topic Study Group 3, Activities and Programs for Gifted Students, ICME-12, Seoul, Korea.

    Google Scholar 

  • Voica, C., & Singer, F. M. (2013). Problem modification as a tool for detecting cognitive flexibility in school children. Zentralbatt für Didaktik der Mathematik (ZDM), 45, 267–279.

    Article  Google Scholar 

  • Wang, B., & Lu, C. (2000). Innovation and mathematical education of the primary and middle school [in Chinese]. Journal of Mathematics Education, 9(4), 34–37.

    Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.

    Article  Google Scholar 

  • Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem posing abilities. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5–28). Rotterdam, The Netherlands: Sense.

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Jinfa Cai, Stephen Hwang & Steven Silber

  2. Faculty of Education, University of Macau, Macau, China

    Chunlian Jiang

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  1. Jinfa Cai
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  2. Stephen Hwang
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  3. Chunlian Jiang
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Correspondence to Jinfa Cai .

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  1. Department of Educational Sciences, University of Ploiesti, Bucharest, Romania

    Florence Mihaela Singer

  2. Department of Mathematics, Illinois State University, Normal, Illinois, USA

    Nerida F. Ellerton

  3. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    Jinfa Cai

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Cai, J., Hwang, S., Jiang, C., Silber, S. (2015). Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_1

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