Mathematical Problem-Solving Heuristics Among Student Teachers

Authors

  • Melanie Gurat Saint Mary’s University

DOI:

https://doi.org/10.7160/eriesj.2018.110302

Keywords:

cognitive, critical thinking, elaboration, metacognitive, organization, rehearsal, self-regulation

Abstract

The main purpose of the study is to understand the mathematical problem-solving strategies among student teachers. This study used both quantitative and qualitative type of research. Aside from the semi-structured interviews, data were gathered through participant's actual mathematical problem-solving outputs and the videotaped interviews. Findings revealed that the problem-solving strategies among student teachers in the Problem-Solving subject are cognitive, metacognitive and other strategies. The cognitive strategies used by the student teachers are rehearsal, elaboration, and organization. The metacognitive strategies are critical thinking and self-regulation. Other strategies are overlapping the cognitive and metacognitive strategies. These are prediction/orientation, planning, monitoring, and evaluating. The findings also suggest a significant influence of the strategies to the academic performance of the student teachers. 

References

Akyol, G., Sungur, S. and Tekkaya, C. (2010) ‘The contribution of cognitive and metacognitive strategy use to students' science achievement’, Educational Research and Evaluation, Vol. 16 No. 1, pp. 1-21. https://doi.org/10.1080/13803611003672348

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, [Online], Available: http://www.eric.ed.gov/PDFS/ED146562.pdf [7 Jun 2011].

Carson, J. (2007) ‘A problem with problem-solving: teaching thinking without teaching knowledge’, The Mathematics Educator, Vol. 17, No. 2, pp. 7–14.

Cockcroft, W. (1982) Mathematics counts. Report of the committee of inquiry into the teaching of mathematics in schools, London: Her Majesty's Stationery Office, (ED.), [Online], Available: http://www.educationengland.org.uk/documents/cockcroft/ [10 Jul 2011].

Dendane, A. (2009) ‘Skills needed for mathematical problem solving’, [Online], Available: http://www.analyzemath.com/math_problems/paper_7.html [3 Apr 2011].

Dewey, J. (1933). ‘How we think’, Boston: D.C. Heath.

Glaser, B.G., and Strauss, A.L. (1967) ‘The discovery of grounded theory: Strategies for qualitative research’, Chicago: Aldine.

Goldman, S. and Booker, A. (2009) ‘Making math a definition of the situation: Families as sites for mathematical practices’, Anthropology and Education Quarterly, Vol. 40, No. 4, pp. 369-387. https://doi.org/10.1111/j.1548-1492.2009.01057.x 

Gurat, M. and Medula, C. Jr. (2016) ‘Metacognitive strategy knowledge use through mathematical problem solving amongst student teachers’, American Journal of Educational Research, Vol. 4, No. 2, pp. 170-189. https://doi.org/10.12691/education-4-2-5

Halmos, P. (1980) ‘The heart of mathematics’, American Mathematical Monthly, Vol. 87, No. 7, pp. 519-524. https://doi.org/10.2307/2321415

Hoon, T., Kee K. and Singh, P. (2013) ‘Learning mathematics using heuristics approach’, Procedia - Social and Behavioral Sciences, Vol. 90, pp. 862-869. http://dx.doi.org/10.1016/j.sbspro.2013.07.162

Koichu, B., Berman, A. and Moore, M. (2004) ‘Promotion of heuristic literacy in a regular mathematics classroom’, For the Learning of Mathematics, Vol. 24, No. 1, pp. 33-39. 

Krawec, J., Huang, J., Montague, M., Kressler, B. and de Alba, A. (2012) ‘The effects of cognitive strategy instruction on knowledge of problem-solving processes of middle school students with learning disabilities’, Learning Disability Quarterly, Vol. 36, No. 2, pp. 80-92. http://dx.doi.org/10.1177/0731948712463368

Krulik, S., and Rudnick, J.A. (1987) ‘Problem solving: A handbook for teachers’, (2nd ed.). Boston: Allyn and Bacon.

Liu, E. and Lin C. (2010) ‘The survey study of mathematics motivated strategies for learning questionnaire (MMSLQ) for grade 10-12 Taiwanese’, The Turkish Online Journal of Educational Technology, Vol. 9, No.  2, pp. 221-223. 

Novotná, J., Eisenmann, P., Přibyl, J., Ondrušová, J. and Břehovský, J.  (2014) ‘Problem solving in school mathematics based on heuristic strategies’, Journal on Efficiency and Responsibility in Education and Science, Vol. 7, No. 1, pp. 1-6. https://doi.org/10.7160/eriesj.2013.070101

Polya, G. (1988) ‘How to solve it: A new aspect of mathematical method’, (2nd ed.), Princeton, NJ: Princeton University Press.

Reiss, K. and Renkl, A. (2002) ‘Learning to prove: The idea of heuristic examples’, Zentralblatt für Didaktik der Mathematik (ZDM), Vol. 34, No. 1, pp. 29-35. https://doi.org/10.1007/BF02655690

Reys, E, Lindquist, Lambdin D.V., Smith, N.L. and Suydam, M.N. (2001) ‘Helping children learn mathematics’, (6th ed.), John Wiley and Sons, Inc., New York.

Schoen, H.L. and Charles, R. I. (2003) ‘Teaching mathematics through problem solving’, National Council of Teachers of Mathematics (NCTM) catalog.

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.

Schurter, W. (2002) ‘Comprehension monitoring: an aid to mathematical problem solving’, Journal of Developmental Education, Vol. 26, No. 2, pp. 22-33. 

Simsek, A. and Balaban, J. (2010) ‘Learning strategies of successful and unsuccessful university students’, Contemporary Educational Technology, Vol. 1. No. 1, pp. 36-45. 

Simsek, A. (2006) ‘Bilissel stratejilerin ogretimi [Teaching cognitive strategies]’, In A. Simsek (Ed.), Icerik turlerine dayali ogretim (pp.181-208). Ankara: Nobel.

Stacey, K. (2005) ‘The place of problem solving in contemporary mathematics curriculum documents’, The Journal of Mathematical Behavior, Vol. 24, pp. 341. https://doi.org/10.1016/j.jmathb.2005.09.004

Stanic, G. and Kilpatrick, J. (1989) ‘Historical Perspective on Problem Solving in the Mathematics Curriculum’, In R. Charles and E. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1-22), Reston, VA: National Council of Teachers of Mathematics.

Strauss, A., and Corbin, J. (1998) ‘Basics of Qualitative Research: Grounded theory procedures and techniques’, (2nd ed.). London: Sage.

Wilson J., Fernandez M. and Hadaway, N. (2011) ‘Mathematical problem solving’, [Online], Available: http://jwilson.coe.uga.edu/emt725/PSsyn/Pssyn.html [8 Aug 2011].

Additional Files

Published

2018-10-01

How to Cite

Gurat, M. (2018) ’Mathematical Problem-Solving Heuristics Among Student Teachers’, Journal on Efficiency and Responsibility in Education and Science, vol. 11, no. 3, pp. 53–64. https://doi.org/10.7160/eriesj.2018.110302

Issue

Vol. 11 No. 3 (2018)

Section

Research Paper

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