Metacognitive Strategy Knowledge Use through Mathematical Problem Solving amongst Pre-service Teachers

Melanie G. Gurat^1, and Cesar T. Medula Jr.²

¹Mathematics Department, Saint Mary’s University, Nueva Vizcaya, Philippines

²Institutional Development and Quality Assurance Office, Saint Mary’s University, Nueva Vizcaya, Philippines

Cite this paper:
Melanie G. Gurat and Cesar T. Medula Jr.. Metacognitive Strategy Knowledge Use through Mathematical Problem Solving amongst Pre-service Teachers. American Journal of Educational Research. 2016; 4(2):170-189. doi: 10.12691/education-4-2-5

Abstract

Metacognition-related studies do often give focus on the regulation or experience components but little on the knowledge component. In particular and especially within the Philippine context, not much focus is given with regards to a clear and coherent academic framework that fortifies the metacognitive strategy knowledge in mathematical problem solving amongst students. Using an evolved grounded theory, the purpose of this study is to look closely into the metacognitive strategy knowledge of preservice teacher education students. Twenty-three students participated and initial data were collected using the prepared problem solving test. Subsequently, interviews were conducted to supplement the initial data. Pandit’s grounded theory methodology and the constant comparison method were used to analyze the data collected. Findings revealed an emerging three-phased categorization of metacognitive strategy knowledge thru problem solving: preparatory, production, and evaluation. The multi-distinct yet related categorization were neither linear nor just cyclic in nature but is experienced and underwent by problem solvers with varying degree of creativity and flexibility depending on the problem at hand, beliefs, attitudes, and learning style. The findings shed some light on the distinct role of metacognitive strategy knowledge and some ensuing factors during authentic problem solving.

Keywords:
metacognition metacognitive strategy knowledge preservice teacher education mathematical problem solving

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References:

[1]	Brown, A.L. & Day, J.D. (1983). Macrorules for summarizing texts. The development of expertise. Journal of Verbal Learning and Verbal Behavior, 22, 1-14.
[2]	Brown, A.L. (1978). Knowing when, where, and how to remember: A problem of metacognition. In Glaser, R. (ed) Advances in Instructional Psychology (Vol.1). Hillsdale, NJ: Lawrence Erlbaum Associates. Retrieved June 2011 from http://www.eric.ed.gov/PDFS/ED146562.pdf.
[3]	Brown, A. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. E. Weinert & R. H. Kluwe, (Eds.) Metacognition, motivation, and understanding (pp. 65-116). Hillsdale, NJ: Lawrence Erlbaum.
[4]	Campione, J. C., Brown, A. L., & Connell, M. L. (1989). Metacognition: On the importance of understanding what you are doing. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 93-114).Reston, VA: Lawrence Erlbaum Associates.
[5]	Strauss, A., & Corbin, J. (1998). Basics of Qualitative Research: Grounded theory procedures and techniques (2nd ed.). London: Sage.
[6]	Desoete, A. (2007). Evaluating and Improving Mathematics Teaching-learning Process through Metacognition. Electronic Journal of Research in Psychology, N.13 Vol 5(3), 2007. ISSN: 1696-2095. pp705-730.
[7]	Edwards, B.P. (2008). "The Interplay among Prospective Secondary Mathematics Teachers' Affect, Metacognition, and Mathematical Cognition in a Problem-Solving Context" Middle-Secondary Education and Instructional Technology Dissertations. Paper 63. http://digitalarchive.gsu.edu/msit_diss/63.
[8]	Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231-235). Hillsdale, NJ: Lawrence Erlbaum.
[9]	Garofalo, J. & Lester, F.K. (1985). Metacognition, Cognitive Monitoring, and Mathematical performance. Journal for Research in Mathematics Education, 16 (3), 163-176.
[10]	Glaser, B.G., & Strauss, A.L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine.
[11]	Laguda, R., FCS. (2007). Being called to mission for stakeholders in educational setting. Unpublished doctoral dissertation. De La Salle University, Manila Lesh, R. & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Handbook of research on mathematics teaching and learning (2nd ed., pp. 763{804). Charlotte, NC: Information Age.
[12]	Lester, F. K. (1994). Musings about mathematical problem solving research: 1970-1994. Journal for Research in Mathematics Education, 25 (6), 660-675.
[13]	Liu, E. and Lin C. (2010). The Turkish Online Journal of Educational Technology. April 2010, Volume 9 Issue 2 pp221-223. Retrieved April 2011 From www.tojet.net/articles/9223.pdf
[14]	National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
[15]	Pandit, N.R. (1996). The creation of a theory. A recent application of the grounded theory method. The Qualitative Report, 2(4). Retrieved June 200, from http://www.nova.edu.sss/QR/QR2-4/pandit.html.
[16]	Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press. Retrieved April 2011 from http://books.google.com.ph/books?id=X3xsgXjTGgoC&printsec=frontcover&dq=How+to+solve+it+by+polya(1945)&hl=tl&sa=X&ei=gNasT4n7Ks2biQezm4mPCQ&ved=0CDEQ6AEwAA#v=onepage&q=How%20to%20solve%20it%20by%20polya(1945)&f=false.
[17]	Schoenfeld, A. (1985). Mathematical Problem Solving. San Diego, CA: Academic Press.
[18]	Schoenfeld, A.H. (1987). What's all the fuss about metacognition ? In Schoenfeld, A.H. (ed.), Cognitive Science and Mathematics Education, chapter 8, 189-215. Lawrence Erlbaum Associates
[19]	Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 165-197). MacMillan, New York
[20]	Strauss, A., & Corbin, J. (1998). Basics of Qualitative Research: Grounded theory procedures and techniques (2nd ed.). London: Sage.
[21]	Victor, A.M. (2004). The effects of metacognitive instruction on the planning and academic achievement of first and second grade children. (Doctoral Thesis). Chicago, IL: Graduate College of the Illinois Istitute of Technology.
[22]	Weinstein, C.E., & Mayer, R. (1986). The teaching of learning strategies. In M.C. Wittrock (Ed.), Handbook of research on teaching (pp. 315-327). New York: Macmillan.
[23]	Wellman, H. (1985). The child’s theory of mind: The development of conscious cognition. The growth of reflection in children. San Diego, Academic Press.
[24]	Wilson J.W, Fernandez M.L., and Hadaway, N. (2011). Mathematical Problem Solving. Retrieved August 2011from http://jwilson.coe.uga.edu/emt725/PSsyn/Pssyn.html.