Persona-Based Journaling: Striving for Authenticity in Representing the Problem-Solving Process

  • Peter LiljedahlEmail author


Students’ mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students’ problem-solving journals, however, do not always reflect this rather organic process. Without proper guidance, some students tend to ‘smooth’ out their experiences and produce journal writing that is less reflective of the process and more representative of their product. In this article, I present research on the effectiveness of a persona-based framework for guiding students’ journaling to reflect the erratic to-and-fro of the problem-solving process more accurately. This framework incorporates the use of three personas—the narrator, the mathematician, and the participant—in telling the tale of the problem-solving process. Results indicate that this persona-based framework is effective in producing more representative journals.

Key Words

journaling persona problem solving 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Borwein, P. & Jörgenson, L. (2001). Visible structures in number theory. MAA Monthly, 2001.Google Scholar
  2. Burns, M. & Silbey, R. (2001). Math journals boost real learning. Instructor, 110(7), 18–20.Google Scholar
  3. Chapman, K. (1996). Journals: Pathways to thinking in second-year algebra. The Mathematics Teacher, 89(7), 588–590.Google Scholar
  4. Ciochine, J., & Polivka, G. (1997). The missing link? Writing in mathematics class! Mathematics Teaching in the Middle School, 2(5), 316–320.Google Scholar
  5. Dewey, J. (1938). Logic: The theory of inquiry. New York: Henry Holt.Google Scholar
  6. Dougherty, B. (1996). The write way: A look at journal writing in first-year algebra. The Mathematics Teacher, 89(7), 556–560.Google Scholar
  7. Fauvel, J. (1988). Cartesian and Euclidean rhetoric. For the Learning of Mathematics, 8(1), 25–29.Google Scholar
  8. Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, The Netherlands: Kluwer.Google Scholar
  9. Hadamard, J. (1945). The psychology of invention in the mathematical field. New York: Dover.Google Scholar
  10. Hofstadter, D. (1996). Discovery and dissection of a geometric gem. In J. King & D. Schattschneider (Eds.), Geometry turned on: Dynamic software in learning, teaching, and research (pp. 3–14). Washington, DC: The Mathematical Association of America.Google Scholar
  11. Liljedahl, P. (2004). The AHA! experience: Mathematical contexts, pedagogical implications. Doctoral Dissertation, Simon Fraser University, Burnaby, British Columbia, Canada.Google Scholar
  12. Liljedahl, P., Rösken, B. & Rolka, K. (2006). Documenting changes in pre-service elementary school teachers’ beliefs: Attending to different aspects. In S. Alatorre, J. L. Cortina, M. Sáiz, A. Méndez (Eds.), Proceedings of the 28th international conference for Psychology of Mathematics Education - North American Chapter (vol. 2, pp. 279–285). Mérida, Mexico: Universidad Pedagógica Nacional.Google Scholar
  13. Liljedahl, P., Rolka, K. & Rösken, B. (2007a). Affecting affect: The re-education of preservice teachers’ beliefs about mathematics and mathematics learning and teaching. In M. Strutchens & W. Martin (Eds.) 69th NCTM Yearbook (pp.319–330). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  14. Liljedahl, P., Rolka, K. & Rösken, B. (2007b). Thinking about belief change as conceptual change. Paper presented at the 5th congress of the European Society for Research in Mathematics Education, Larnaca, Cyprus.Google Scholar
  15. Mewborn, D. (1999). Reflective thinking among preservice elementary mathematics teachers. Journal for Research in Mathematics Education, 30(3), 316–341.CrossRefGoogle Scholar
  16. Miller, L. (1992). Teacher benefit from using impromptu writing in algebra classes. Journal of Mathematics Teacher Education, 23(4), 329–340.Google Scholar
  17. Poincaré, H. (1952). Science and method. New York: Dover.Google Scholar
  18. Rolka, K., Rösken, B. & Liljedahl, P. (2006). Challenging the mathematical beliefs of preservice elementary school teachers. Proceedings of the 30th international conference for Psychology of Mathematics Education (vol. 4, pp. 441–448). Prague, Czech Republic: Charles University.Google Scholar
  19. Waywood, A. (1992). Journal writing and learning mathematics. For the Learning of Mathematics, 12(2), 34–43.Google Scholar

Copyright information

© National Science Council, Taiwan 2007

Authors and Affiliations

  1. 1.Faculty of EducationSimon Fraser UniversityBurnabyCanada

Personalised recommendations