The theory of problem posing in mathematics education suggests that there are motivational and cognitive benefits for students from creating their own problems, yet such activities are not typically integrated into the traditional classroom. A field study was conducted to learn if middle school students (N = 224) could successfully create math and science problems using a web-based content-authoring and sharing system, and if the activity could be successfully integrated into classroom instruction. Over the twelve-week activity, students created their own math and science problems, and solved problems authored by their peers. Results showed that students were able to create problems successfully, but that problem solving dominated problem posing activities. The process of reviewing and approving students’ work was also challenging for teachers. Both students and teachers reported strongly positive responses to the activity.
KeywordsMathematics EducationTechnology-Based InstructionMiddle School Students
Arroyo, I., & Woolf, B. P. (2003). Students in AWE: Changing their role from consumers to producers of ITS content. Proceedings of the 11th International Conference on Artificial Intelligence and Education, Sydney, 20-24 July 2003.
Arthur, C. (2006). What is the 1% rule? The Guardian, July 26, 2006. URL (last checked 1 May 2011). http://www.citeulike.org/group/2518/author/Arthur:C
Birch, M., & Beal, C. R. (2008). Problem posing in Animal Watch: An interactive system for student-authored content. Proceedings of the 21st International FLAIRS Conference, Coconut Grove, 15-17 May 2008.
Bonotto, C. (2010). Engaging students in mathematical modelling and problem posing activities. Journal of Mathematical Modelling and Application, 1, 18-32.
Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Hillsdale, NJ: Erlbaum.
Cai, J. (1998). An investigation of US and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10, 37-50. doi:10.1007/BF03217121
Cai, J., & Huang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401-421. doi:10.1016/S0732-3123(02)00142-6
Chi, M. T. H. (2009). Active-constructive-interactive: A conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1, 73-105. doi:10.1111/j.1756-8765.2008.01005.x
Chi, M. T. H., Roy, M., & Hausmann, R. G. M. (2008). Observing tutorial dialogues collaboratively: Insights about human tutoring effectiveness from vicarious learning. Cognitive Science, 32, 301-341. doi:10.1080/03640210701863396
Contreras, J. N. (2003). A problem-posing approach to specializing, generalizing and extending problems with interactive geometry software. The Mathematics Teacher, 96, 270-275.
Cotic, M., &Zuljan, M. V. (2009). Problem-based instruction in mathematics and its impact on the cognitive results of the students and on affective-motivational aspects. Educational Studies, 35, 297-310. doi:10.1080/03055690802648085
Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preserve teachers’ practices. Educational Studies in Mathematics, 52, 243-270. doi:10.1023/A:1024364304664
Davis, D. D. et al. (2006). An integrative model for enhancing inclusion in computer science education. In E. Trauth (Ed.), Encyclopedia of gender and information technology (pp. 269-275). Hershey, PA: Idea. doi:10.4018/978-1-59140-815-4.ch042
Education Development Corp. (2003). Making mathematics: Mentored research projects for young mathematicians. URL. http://www2.edc.org/makingmath/handbook/teacher/ProblemPosing/ProblemPosing.asp
English, L. (1997). Promoting a problem-posing classroom. Teaching Children Mathematics, 4, 172-179.
Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., & Brenwald, S. (2008). Highlights from TIMSS 2007: Mathematics and science achievement of US fourth and eighth grade students in an international context (NCES 2009-2011 Revised). Washington DC: National Center for Education Statistics, Institute of Education Sciences, US Department of Education.
Hausmann, R., & Van Lehn, K. (2007). Explaining self-explaining: A contrast between content and generation. Proceedings of the 13th International Conference on Artificial Intelligence and Education, Los Angeles, 9-13 July 2003.
Hirashima, T., Yokoyama, T., Okamoto, M., & Takeuchi, A. (2007). Learning by problem-posing as sentence-integration and experimental use. In R. Luckin, K. R. Koedinger, & J. Greer (Eds.), Artificial intelligence in education: Building technology rich contexts that work (pp. 254-261). Amsterdam: IOS Press.
King, A. (1992). Comparison of self-questioning, summarizing and note-taking review as strategies for learning from lectures. American Educational Research Journal, 29, 303-323.
Knuth, E. J. (2002). Fostering mathematical curiosity. The Mathematics Teacher, 95, 126-130.
Martinez-Cruz, A. M., & Contreras, J. N. (2002). Changing the goal: An adventure in problem solving, problem posing, and symbolic meaning with a TI-92. The Mathematics Teacher, 95, 592-597.
Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. Journal of Applied Developmental Psychology, 23, 9-50. doi:10.1016/S0193-3973(01)00101-0
Miller, L. (2006). Building confidence through math problem solving. URL (last checked 16 January 2006). http://www.nipissingu.ca/oar/archive-Vol2No1-V211E.htm
National Center for Education Statistics (2011). The Nation’s Report Card: Mathematics 2011 (NCES 2012-458). Washington DC: National Center for Education Statistics, Institute of Education Sciences, US Department of Education.
OCED (2010). PISA 2009 results: What students know and can do: Student performance in reading, mathematics and science. Paris: The Organisation for Economic Co-operation and Development.
Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving. New York: John Wiley.
Roscoe, R. D., & Chi, M. T. H. (2007). Understanding tutor learning: Knowledge building and knowledge telling in peer tutors’ explanations and questions. Review of Educational Research, 77, 534-574. doi:10.3102/0034654307309920
Roy, M., & Chi, M. T. H. (2005). The self-explanation principle. In R. E. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511816819.018
Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521-539. doi:10.2307/749846
Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1995). Thinking through mathematics. New York: College Board.
Simic-Mullter, K., Turner, E., & Varley, M. C. (2009). Math Club problem posing. Teaching Children Mathematics, 16, 206-212.
Verzoni, K. A. (1997). Turning students into problem solvers. Mathematics Teaching in the Middle School, 3, 102-107.
Whitin, P. (2004). Promoting problem posing explorations. Teaching Children Mathematics, 180, 7.
Wilson, J. M., Fernandez, M., & Hadaway, N. (2006). Mathematical problem solving. URL. http://jwilson.coe.uga.edu/emt725/PSsyn/PSsyn.html
Xia, X., Lu, C., & Wang, B. (2008). Research in mathematics instruction experiment based problem posing. Journal of Mathematics Education, 1, 153-163.