Abstract
Despite the importance of teachers’ conceptions of and competency in problem solving, limited attention is given to this area in the current literature. We examined 96 preservice elementary teachers’ problem-solving conceptions and performances by having them define and create metaphors for problem solving and then investigated the relationships between their conceptions and problem-solving performances. We found that a large majority defined problem solving as a means to a solution and created end-product metaphors and that their conceptions of problem solving were related to their performances. This study contributes to the current literature on problem solving and the knowledge base of teacher education.
Similar content being viewed by others
References
Antonietti, A., Ignazi, S., & Perego, P. (2000). Metacognitive knowledge about problem-solving methods. The British Journal of Educational Psychology, 70, 1–16.
Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90(4), 449–466.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.
Bruner, J. S. (1957). On perceptual readiness. Psychological Review, 64, 123–152.
Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving? Impact of early algebra learning and teachers’ beliefs. The Journal of Mathematical Behavior, 23, 135–167.
Cassel, D., & Vincent, D. (2011). Metaphors reveal preservice elementary teachers’ views of mathematics and science teaching. School Science and Mathematics, 111(7), 319–324.
Covington, M., & Crutchfield, R. (1965). Experiements in the use of programmed instruction for the facilitation of creative problem solving. Programed Instruction, 4, 3–10.
Depaepe, F., Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26, 152–160.
English, L. (1997). Analogies, metaphors, and images: Vehicles for mathematical reasoning. In L. English (Ed.), Mathematical reasoning: Analogies, metaphors and images (pp. 1–15). Mahwah, NJ: Lawrence Erlbaum Associates.
Foreman, L. C., & Bennett Jr., A. B. (1995). Visual mathematics: Course II, Lessons 1–10. Salem, MA: Math Learning Center.
Goldin, G. A., & McClintock, C. E. (1984). Task variables in mathematical problem solving. Philadelphia, PA: Franklin Institute Press.
Grbich, C. (2007). Qualitative data analysis: An introduction. Thousand Oaks, CA: Sage.
Hall, R. (1999). Following mathematical practices in design-oriented work. In C. Hoyles, C. Morgan, & G. Woodhouse (Eds.), Rethinking the mathematics curriculum (pp. 29–47). Philadelphia, PA: Falmer Press.
Kilpatrick, J. (2004). Variables and methodologies in research on problem solving. In T. P. Carpenter, J. A. Dossey, & J. L. Koehler (Eds.), Classics in mathematics education research (pp. 40–48). Reston, VA: National Council of Teachers of Mathematics.
Kilpatrick, J. (1985). A retrospective account of the past twenty-five years of research on teaching mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 1–16). Hillsdale, MI: Erlbaum.
Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, England: Cambridge University Press.
Lakoff, G., & Nunez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
Lee, M. Y., & Cross Francis, D. (2018). Investigating the relationship among elementary teachers’ perception about the use of students’ thinking, their professional noticing skills and their teaching practice. Journal of Mathematical Behavior, 51, 118-128.
Lee, M. Y., & Lee, J. (2019). Pre-service teachers’ perceptions of the use of representations and suggestions for students’ incorrect Use. Eurasia Journal of Mathematics, Science and Technology Education, 15(9), 1-21.
Lee, M. Y. (2017). Pre-service teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics, 96(3), 327-348.
Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Reston, VA: National Council of Teachers of Mathematics.
Lester, F. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25, 660–675.
Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 501–518). Mahwah, NJ: Erlbaum.
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. Cham, Switzerland: Springer.
Lortie, D. C. (1975). Schoolteacher: A sociological study. Chicago, IL: University of Chicago Press.
Markworth, K. (2010). Growing and growing: Promoting functional thinking with geometric growing patterns (Doctoral dissertation). Retrieved from ProQuest (Accession or Order No. 3418575).
Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1–2), 49–63.
Metallidou, P. (2009). Pre-service and in-service teachers’ metacognitive knowledge about problem-solving strategies. Teaching and Teacher Education, 25, 76–82.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Governors Association Center for Best Practices, Council of Chief State School Officers [NGA & CCSSO]. (2010). Common core state standards. Retrieved from http://corestandards.org
Newell, A., & Simon, H. A. (1972). Human problem solving. New Jersey: Prentice-Hall.
Pajares, M. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62, 307–332.
Polya, G. (1957). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.
Reeder, S., Utley, J., & Cassel, D. (2009). Using metaphors as a tool for examining preservice elementary teachers’ beliefs about mathematics teaching and learning. School Science and Mathematics, 109(5), 290–297.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan.
Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. New York, NY: Routledge.
Son, J. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49-70.
Son, J. (2016). Moving beyond a traditional algorithm in whole number subtraction: Preservice teachers’ responses to a student’s invented strategy. Educational Studies in Mathematics, 93(1), 105-129.
Son, J., & Crespo, S. (2009). Prospective teachers’ reasoning about students’ non-traditional strategies when dividing fractions, Journal of Mathematics Teacher Education, 12(4), 236-261.
Stanic, G., & Kilpatrick, J. (1989). Historical perspectives on problem solving in the mathematics curriculum. In R. Charles & E. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1–22). Reston, VA: National Council of Teachers of Mathematics.
Stein, M., Smith, M., Henningsen, M., & Silver, E. (2000). Implementing standards-based mathematics instruction. New York, NY: NCTM.
Steffe, L. P. (1983). Children’s counting types: Philosophy, theory, and application. New York, NY: Praeger.
van de Walle, J., Karp, K., & Bay-Williams, J. (2013). Elementary and middle school mathematics teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
Yee, S. P. (2017). Students’ and teachers’ conceptual metaphors for mathematical problem solving. School Science and Mathematics, 117(3–4), 146–157.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Son, JW., Lee, M.Y. Exploring the Relationship Between Preservice Teachers’ Conceptions of Problem Solving and Their Problem-Solving Performances. Int J of Sci and Math Educ 19, 129–150 (2021). https://doi.org/10.1007/s10763-019-10045-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10763-019-10045-w