The Impact of Various Methods in Evaluating Metacognitive Strategies in Mathematical Problem Solving
Problem solving has been the theme of mathematics education in Singapore since the 1980s. For the past two decades, the Singapore mathematics curriculum has problem solving as its central focus and aims to prepare students to be competent problem solvers. Problem solving, as articulated by the Singapore Mathematics Curriculum Framework is supported by five inter-related components and Metacognition is one of the components. However, there are very few studies to find out how metacognition has worked through the Singapore classrooms and its impact on problem solving. This paper presents findings from a study on metacognitive strategies Singapore Secondary One (Year 7) students (N = 783) employed while solving mathematics problems. Discussion will center on the different methods used to investigate the nature of metacognition during mathematical problem solving, namely survey inventory, retrospective self-report and qualitative interview. Findings from this study suggest that results from different data collection instruments may lead to dissimilarities in the findings but provide a multi-facet perspective of metacognition in mathematical problem solving. As compared, findings based on data from a single instrument may only provide a skew perspective. Findings from this study bear important implications to the interpretation of research findings as well as the research designs for better insights to metacognition employed during mathematical problem solving.
- Adler, P. A., & Adler, P. (2012). How many qualitative interviews is enough? In S. E. Baker & R. Edwards (Eds.), How many qualitative interviews is enough? Expert voices and early career reflections on sampling and cases in qualitative research. Southampton, GB, National Centre for Research Methods, 43 pp. (National Centre for Research Methods Reviews). Retrieved http://eprints.ncrm.ac.uk/2273/4/how_many_interviews.pdf.
- Back, L. (2012). How many qualitative interviews is enough? In S. E. Baker & R. Edwards (Ed.), How many qualitative interviews is enough? Expert voices and early career reflections on sampling and cases in qualitative research (43 pp). National Centre for Research Methods: Southampton, GB. National Centre for Research Methods Reviews. Retrieved http://eprints.ncrm.ac.uk/2273/4/how_many_interviews.pdf.
- Biggs, J. B. (1987). Student approaches to learning and studying. Melbourne: Australian Council for Educational Research.Google Scholar
- Brown, A. (1987). Metacognition, executive control, self regulation and mysterious mechanisms. In Weinert and Klume (Eds.), Metacognition, motivation and understanding (pp. 65–117). New Jersery: Erlbaum Hillside.Google Scholar
- Chang, S. C. A., & Ang, W. H. (1999, July). Emotions, values, good thinking. Paper presented at the 8th International Conference on Thinking, Edmonton, Canada.Google Scholar
- Clarke, D. (1992). The role of assessment in determining mathematics performance. In G. Leder (Ed.), Assessment and learning in mathematics (pp. 145–168). Hawthorn, Victoria: ACER.Google Scholar
- Cohen, L., & Manion, L. (1994). Research methods in education (4th ed.). London: Routledge.Google Scholar
- Ericsson, K. A. (2006). Protocol analysis and expert thought: Concurrent verbalizations of thinking during experts’ performance on representative tasks. In K. A. Ericsson, N. Charness, P. J. Feltovich, & R. R. Hoffman (Eds.), The Cambridge handbook of expertise and expert performance (pp. 223–241). New York: Cambridge University Press.CrossRefGoogle Scholar
- Flick, U. (2012). How many qualitative interviews is enough? In S.E. Baker & R. Edwards (Eds.), How many qualitative interviews is enough? Expert voices and early career reflections on sampling and cases in qualitative research (43 pp). National Centre for Research Methods: Southampton, GB. National Centre for Research Methods Reviews. Retrieved http://eprints.ncrm.ac.uk/2273/4/how_many_interviews.pdf.
- Fortunato, I., Hecht, D., Kehr, C., Tittle, C., & Alvarex, L. (1991). Metacognition and problem solving. Arithmetic Teacher, 39(4), 38–40.Google Scholar
- Genest, M., & Turk, D. (1981). Think-aloud approaches to cognitive assessment. In T. V. Merluzzi, C. R. Glass, & M. Genest (Eds.), Cognitive assessment (pp. 233–269). New York: The Guilford Press.Google Scholar
- Ginsburg, H. P., Kossan, N. E., Schwartz, R., & Swanson, D. (1983). Protocol methods in research on mathematical thinking. In Ginsburg, H. (Ed.), The development of mathematical thinking (pp. 7–47). New York, Academic Press.Google Scholar
- Hacker, D. J. (1998). Metacognition in educational theory and practice. In D. J. Hacker, J. Dinlosky, & A. Graesser (Eds.), Definitions and empirical foundations (pp. 93–115). Greenrich, CT: Information Age Publishing.Google Scholar
- Lee, N. H. (2008). Enhancing Mathematical learning and achievement of secondary one normal (Academic) students using metacognitive strategies (Unpublished doctoral thesis). Nanyang Technological University, Singapore.Google Scholar
- Loh, M. Y. (2015). Metacognitive strategies secondary one students employed while solving mathematics problems (Unpublished doctoral thesis). Nanyang Technological University, Singapore.Google Scholar
- Ministry of Education. (2007). A guide to teaching and learning of primary mathematics. Singapore Curriculum Planning and Development Division, Ministry of Education.Google Scholar
- Ministry of Education. (2012). Primary mathematics teaching and learning syllabus. Singapore Curriculum Planning and Development Division, Ministry of Education.Google Scholar
- Moccoby, E. E., & Jacklin, C. N. (1974). Psychology of sex differences. Palo Alto, California: Stanford University Press.Google Scholar
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
- Nietfeld, J. L., Cao, L., & Osborne, J. W. (2005). Metacognitive monitoring accuracy and student performance in the postsecondary classroom. The Journal of Experimental Education, 74(1), 7–28.Google Scholar
- Pintrich, P. R., Wolters, C., & Baxter, G. (2000). Assessing metacognition and self-regulated learning. In G. Schraw & J. Impara (Eds.), Issues in the measurement of metacognition (pp. 43–97). Lincoln, NE: Buros Institute of Mental Measurements.Google Scholar
- Pólya, G. (1957). How to solve it. Princeton: Princeton University Press.Google Scholar
- Schoenfeld, A. H. (1982). Expert and novice mathematical problem solving. Final Project Report and Appendices B-H. MI: National Science Foundation, Washington, D.C. (ERIC Document Reproduction Service No. ED218124).Google Scholar
- Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic.Google Scholar
- Stacey, K. (1990). Making optimal use of mathematical knowledge. Australian Journal of Remedial Education, 22, 6–10.Google Scholar
- Veenman, M. V. J. (2005). The assessment of metacognitive skills: What can be learned from multi-method designs? In C. Artelt & B. Moschner (Eds.), Lernstrategien und Metakognition: Implikationen fÜr Forschung und Praxis (pp. 77–99). MÜnster: Waxmann.Google Scholar
- Webb, E., Campbell, D., Schwartz, R., & Sechrest, L. (1966). Unobtrusive measures. Chicago: Rand Mc Nally.Google Scholar
- Wilson, J. (1997). Beyond the basics: Assessing students’ metacognition. Paper presented at the Annual Meeting of the Hong Kong Educational Research Association, Hong Kong, 14 November 1997 (ERIC Document Reproduction Service ER415244).Google Scholar
- Wilson, J. (1998, June). The nature of metacognition: What do primary school problem solvers do? Paper presented at the National AREA Conference, Melbourne, Australia (ERIC Document Reproduction Service ER422315).Google Scholar
- Wilson, J. (2001, December). Methodological Difficulties of Assessing Metacognition: A New Approach. Paper presented at the Annual Meeting of the Australian Association for Research in Education, Fremantel, Western Australia, Australia.Google Scholar
- Wong, P. (1989, November). Students’ metacognition in mathematical problem solving. Paper presented at the Annual Meeting of the Australian Association for Research in Education (November 28–December 2).Google Scholar