Skip to main content
Log in

INTERLOCKED PROBLEM POSING AND CHILDREN’S PROBLEM POSING PERFORMANCE IN FREE STRUCTURED SITUATIONS

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

ABSTRACT

The aim of this study is to explore the mathematical problem posing performance of students in free structured situations. Two classes of fifth grade students (N  =  30) were randomly assigned to experimental and control groups. The categories of the problems posed in free structured situations by the 2 groups of students were studied through inductive and deductive content analysis and coded in categories before and after a 5-week treatment. The treatment for the experimental group was the Interlocked Problem Posing Instruction in which student cognitive engagement was emphasized, and for the control group, it was Traditional Problem Posing Instruction. The results revealed that the experimental group students posed more solvable, reasonable and start-unknown problems than the control group students after the treatment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baines, L. A. & Stanley, G. (2000). We want to see the teacher: Constructivism and the rage against expertise. Phi Delta Kappan, 82(4), 327–330.

    Google Scholar 

  • Biggs, J. B. & Telfer, P. J. (1998). The process of learning. Sydney: Prentice Hall.

    Google Scholar 

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

    Google Scholar 

  • Caplan, J. B. & Caplan, P. J. (2005). The perseverative search for sex differences in mathematics abilities. In A. M. Gallagher & J. C. Kaufman (Eds.), Gender differences in mathematics: An integrative psychological approach. Cambridge: Cambridge University Press.

    Google Scholar 

  • Carpenter, T. P., Kepner, H. S., Corbitt, M. K., Lindquist, M. & Reys, R. E. (1980). Solving verbal problems: Results and implications for national assessment. Arithmetic Teacher, 28(1), 8–12.

    Google Scholar 

  • Chang, N. (2007). Responsibilities of a teacher in a harmonic cycle of problem solving and problem posing. Early Childhood Education Journal, 34(4), 265–271.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dillon, J. T. (1982). Problem finding and solving. Journal of Creative Behaviour, 16, 97–111.

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • English, L. D. (1997a). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183–217.

    Article  Google Scholar 

  • English, L.D. (1997b). Development of seventh-grade students’ problem posing. In E. Pehkonen (Eds.), 21st Conference of the International Group for the Psychology of Mathematics Education. Lahti, Finland (volume 2, pp. 241–248).

  • 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 

  • English, L. D. (2003). Problem posing in elementary curriculum. In F. Lester & R. Charles (Eds.), Teaching mathematics through problem solving. Reston, Virginia: National Council of Teachers of Mathematics.

    Google Scholar 

  • English, L. D. & Halford, G. S. (1995). Mathematics education: Models and processes. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Fennema, E. & Carpenter, T. P. (1998). New perspectives on gender differences in mathematics: An introduction and a reprise. Educational Researcher, 27(5), 4–11. 19–22.

    Article  Google Scholar 

  • Fredricks, J. A., Blumenfeld, P. C. & Paris, A. H. (2004). School engagement: Potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59–109.

    Article  Google Scholar 

  • Gordon, M. (2009). Toward a pragmatic discourse of constructivism: Reflections on lessons from practice. Educational Studies, 45(1), 39–58.

    Article  Google Scholar 

  • Hinton, P. R. (1996). Statistics explained. New York: Routledge.

    Google Scholar 

  • Hyde, J. S., Fennema, E. & Lamon, S. J. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107(2), 139–155.

    Article  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). NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Knott, L. (2010). Problem posing from the foundations of mathematics. Montana Mathematics Enthusiast, 7(2&3), 413–432.

    Google Scholar 

  • Koedinger, K. R. & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13(2), 129–164.

    Article  Google Scholar 

  • Kojima, K. & Miwa, K. (2008). A system that facilitates diverse thinking in problem posing. International Journal of Artificial Intelligence in Education, 18(2), 209–236.

    Google Scholar 

  • Kong, Q., Wong, N. & Lam, C. (2003). Student engagement in mathematics: Development of instrument and validation of construct. Mathematics Education Research Journal, 15(1), 4–21.

    Article  Google Scholar 

  • Leung, S. K. (1996). Problem posing as assessment: Reflections and reconstructions. The Mathematics Educator, 1, 159–171.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Linnenbrink, E. A. & Pintrich, P. R. (2003). The role of self-efficacy beliefs in student engagement and learning in the classroom. Reading and Writing Quarterly, 19, 119–137.

    Article  Google Scholar 

  • Lowrie, T. (1998). The importance of visual processing in non-routine and novel problem solving situations. In A. McIntosh & N. Ellerton (Eds.), Research in mathematics education: Some current trends (pp. 186–210). Perth, Western Australia: MASTEC Publication.

    Google Scholar 

  • 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 (pp. 328–335). Panorama, South Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Lowrie, T. (2002a). Designing a framework for problem posing: Young children generating open-ended tasks. Contemporary Issues in Early Childhood, 3(3), 354–364.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lowrie, T. & Whitland, J. (2000). Problem posing as a tool for learning planning and assessment in the primary school. In T. Nakahara, T., Koyama (Eds.), Proceedings of the 24th International Conference for the Psychology of Mathematics Education. Hiroshima, Japan (pp. 247–254).

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

    Article  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: National Council of Teachers of Mathematics.

    Google Scholar 

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

    Google Scholar 

  • Newmann, F., Wehlage, G. G. & Lamborn, S. D. (1992). The significance and sources of student engagement. In F. Newmann (Ed.), Student engagement and achievement in American secondary schools (pp. 11–39). New York: Teachers College Press.

    Google Scholar 

  • Riley, M. S. & Greeno, J. G. (1988). Developmental analysis of understanding language about quantities and of solving problems. Cognition and Instruction, 5(1), 49–101.

    Article  Google Scholar 

  • Sheskin, D. J. (2004). Handbook of parametric and nonparametric statistical procedures (3rd ed.). New York: Chapman & Hall/CRC.

    Google Scholar 

  • Silver, E.A. (1993). On mathematical problem posing. In Hirabayasshi, N. Nohda, K. Shigematsu, & F.L Lin (Eds.), Proceedings of the Seventeenth International Conference for the Psychology of Mathematics Education. Tsukuba, Japan (vol. 1. pp. 66–85).

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

    Google Scholar 

  • Silver, E. A. (1995). The nature and use of open problems in mathematics education: Mathematical and pedagogical perspectives. International Reviews on Mathematical Education, 27, 67–72.

    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 

  • Sternberg, R. J. & O’Hara, L. A. (1999). Creativity and intelligence. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 251–272). Cambridge: Cambridge University Press.

    Google Scholar 

  • Stoyanova, E. (1998). Problem posing in mathematics analyses classrooms. In A. McIntosh & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp. 164–185). Perth, Western Australia: MASTEC, Edith Cowan University.

    Google Scholar 

  • Stoyanova, E. (2000). Empowering students’ problem solving via problem posing: The art of framing “good” questions. Australian Mathematics Teacher, 56(1), 33–37.

    Google Scholar 

  • Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32–40.

    Google Scholar 

  • Strauss, A. & Corbin, J. (1990). Basics of qualitative research. London, UK: Sage Publications.

    Google Scholar 

  • Wertheimer, M. (1959). Productive thinking. New York: Harper & Row.

    Google Scholar 

  • Willis, D. (1993). Academic involvement at university. Higher Education, 25, 133–150.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Osman Cankoy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cankoy, O. INTERLOCKED PROBLEM POSING AND CHILDREN’S PROBLEM POSING PERFORMANCE IN FREE STRUCTURED SITUATIONS. Int J of Sci and Math Educ 12, 219–238 (2014). https://doi.org/10.1007/s10763-013-9433-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-013-9433-9

KEY WORDS

Navigation