Problem-posing research in mathematics education: New questions and directions

Educational Studies in Mathematics

Volumn 83, Issue 1, 2013, Pages 1-7

  Singer, Florence Mihaela ^a   Ellerton, Nerida ^b   Cai, Jinfa ^c  

^a PETROLEUM GAS UNIVERSITY OF PLOIESTI   (Romania)

^b ILLINOIS STATE UNIVERSITY   (United States)

^c UNIVERSITY OF DELAWARE   (United States)

Author keywords

Field of mathematics education research; Instruction; Problem posing; Problem solving

Indexed keywords

EID: 84876197001     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-013-9478-2     Document Type: Article

References (44)

1. Brown, S., & Walter, M. (1983/2005). The art of problem posing (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
2. 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.
3. Cai, J., & Cifarelli, V. (2005). Exploring mathematical exploration: how do two college students formulate and solve their own mathematical problems? Focus on Learning Problems in Mathematics, 27(3), 43-72.
4. Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt für Didaktik der Mathematik, 37(3), 149-158.
5. Cifarelli, V., & Cai, J. (2005). The evolution of mathematical explorations in open ended problem solving situations. The Journal of Mathematical Behavior, 24, 302-324.
6. 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.
7. Einstein, A., & Infeld, L. (1938). The evolution of physics. New York: Simon & Schuster.
8. Ellerton, N. F. (1986). Children's made-up mathematics problems-a new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261-271.
9. Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 987-1053). Netherlands: Kluwer.
10. English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
11. English, L. D. (2003). Problem posing in the elementary curriculum. In F. K. Lester Jr. & R. I. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten-grade 6 (pp. 187-198). Reston: NCTM.
12. Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42-53). Dordrecht: Kluwer.
13. Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field. Princeton: Princeton University Press (page ref. are to Dover edition, New York 1954).
14. Harel, G., Koichu, B., & Manaster, A. (2006). Algebra teachers' ways of thinking characterizing the mental act of problem posing. In I. J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 241-248). Prague: Charles University.
15. 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: Lawrence Erlbaum Associates.
16. 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.
17. Kuhn, T. S. (1962/1969). The structure of scientific revolutions. International Encyclopedia of Unified Science. Volume 2, no. 2. Retrieved from http://turkpsikiyatri. org/arsiv/kuhn-ssr-2nded. pdf.
18. Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In Proceedings of the International Group for the Psychology of Mathematics Education, Seoul, Korea, 8-13 July 2007 (pp. 161-168). Seoul, Korea: The Korea Society of Educational Studies in Mathematics.
19. Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralblatt für Didaktik der Mathematik, 97(3), 81-85.
20. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.
21. Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24, 385-401.
22. Nohda, N. (1995). Teaching and evaluating using "open-ended problems" in the classroom. Zentralblatt für Didaktik der Mathematik, 27(2), 57-61.
23. Ponte, J. (2007). Investigations and explorations in the mathematics classroom. ZDM, 39, 419-430.
24. Ponte, J., & Matos, J. F. (1992). Cognitive processes and social interactions in investigation activities. In J. Ponte et al. (Eds.), Mathematical problem solving and new information technologies: Research in contexts of practice (pp. 239-254). Berlin: Springer.
25. Popper, K. R., & Eccles, J. A. (1977). The self and its brain: An argument for interactionism. Berlin: Springer.
26. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
27. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75-80.
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.
29. Silver, E. A., & Cai, J. (2005). Assessing students' mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
30. Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1990). Thinking through mathematics: Fostering inquiry and communication in mathematics classrooms. New York: The College Board.
31. Silver, E. A., Mamona-Downs, J., Leung, S., & Kenney, P. A. (1996). Posing mathematical problems: an exploratory study. Journal for Research in Mathematics Education, 27(3), 293-309.
32. Singer, F. M. (2007). Beyond conceptual change: Using representations to integrate domain-specific structural models in learning mathematics. Mind, Brain, and Education, 1(2), 84-97.
33. Singer, F. M. (2008). Enhancing transfer as a way to develop creativity within the dynamic structural learning. In R. Leikin (Ed.), Proceedings of the 5th International Conference on Creativity in Mathematics and the Education of Gifted Students (pp. 223-230). Tel Aviv: CET.
34. Singer, F. M. (2009). The dynamic infrastructure of mind-a hypothesis and some of its applications. New Ideas in Psychology, 27, 48-74.
35. Singer, F. M. (2010). Children's cognitive constructions: From random trials to structures. In J. A. Jaworski (Ed.), Advances in sociology research (Vol. 6, pp. 1-35). Hauppauge: Nova.
36. Singer, F. M. (2012). Boosting the young learners' creativity: Representational change as a tool to promote individual talents (plenary lecture). In The 7th International Group for Mathematical Creativity and Giftedness (MCG) International Conference Proceedings (pp. 3-26). Busan, South Korea: MCG.
37. Singer, F. M., Ellerton, N., Cai, J., Leung, E. (2011). Problem posing in mathematics learning and teaching: A research agenda. In B. Ubuz (Ed.), Developing mathematical thinking. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 137-166). Ankara, Turkey: PME.
38. Singer, F. M., & Moscovici, H. (2008). Teaching and learning cycles in a constructivist approach to instruction. Teaching and Teacher Education, 24(6), 1613-1634.
39. Singer, F. M., Pelczer, I., & Voica, C. (2011). Problem posing and modification as a criterion of mathematical creativity. In T. Rowland & E. Swoboda (Eds.) Proceedings of the 7th Conference of the European Society for Research in Mathematics Education (CERME 7) University of Rzeszów, Poland, 9-13 February, 2011.
40. 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). Melbourne: Mathematics Education Research Group of Australasia.
41. Torrance, E. P. (1974). Torrance tests of creative thinking: Norms and technical manual. Bensenville: Scholastic Testing Services.
42. Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modeling in the elementary school. A teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28, 577-601.
43. Voica, C., & Singer, M. (2012). Creative contexts as ways to strengthen mathematics learning. In M. Aniţei, M. Chraif & C. Vasile (guest Eds.), Procedia-Social and Behavioral Sciences, PSIWORLD 2011 (vol. 33, 538-542). Available at http://www. sciencedirect. com/science/article/pii/S1877042812001875. Accessed 3 Oct 2013.
44. Yuan, X., & Sriraman, B. (2010). 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: Sense Publishers.