Abstract
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 (Nā=ā783) 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.
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References
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, 43Ā 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 (43Ā 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.
Brown, A. (1987). Metacognition, executive control, self regulation and mysterious mechanisms. In Weinert and Klume (Eds.), Metacognition, motivation and understanding (pp. 65ā117). New Jersery: Erlbaum Hillside.
Chang, S. C. A., & Ang, W. H. (1999, July). Emotions, values, good thinking. Paper presented at the 8th International Conference on Thinking, Edmonton, Canada.
Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13, 145ā182.
Clarke, D. (1992). The role of assessment in determining mathematics performance. In G. Leder (Ed.), Assessment and learning in mathematics (pp. 145ā168). Hawthorn, Victoria: ACER.
Cohen, L., & Manion, L. (1994). Research methods in education (4th ed.). London: Routledge.
Cromley, J., & Azevedo, R. (2011). Measuring strategy use in context with multiple-choice items. Metacognition and Learning, 6, 155ā177.
Crouch, M., & McKenzie, H. (2006). The logic of small samples in interview based qualitative research. Social Science Information, 45(4), 483ā499.
Efklides, A. (2006). Metacognitive and affect: What can metacognitive experiences tell us about the learning process? Educational Research Review, 1, 3ā14.
Ericsson, K. A. (2006). Protocol analysis and expert thought: Concurrent verbalizations of thinking during expertsā 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. 223ā241). New York: Cambridge University Press.
Ericsson, K. A., & Simon, H. (1980). Verbal reports as data. Psychological Review, 87, 215ā251.
Flavell, J. H. (1979). Metacognitive and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906ā911.
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 (43Ā 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), 38ā40.
Garofalo, J., & Lester, F. K., Jr. (1985). Metacognition, cognitive monitoring and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163ā176.
Genest, M., & Turk, D. (1981). Think-aloud approaches to cognitive assessment. In T. V. Merluzzi, C. R. Glass, & M. Genest (Eds.), Cognitive assessment (pp. 233ā269). New York: The Guilford Press.
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. 7ā47). New York, Academic Press.
Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30, 229ā260.
Hacker, D. J. (1998). Metacognition in educational theory and practice. In D. J. Hacker, J. Dinlosky, & A. Graesser (Eds.), Definitions and empirical foundations (pp. 93ā115). Greenrich, CT: Information Age Publishing.
Jacobse, A. E., & Harskamp, E. G. (2012). Towards efficient measurement of metacognition in mathematical problem solving. Metacognition Learning, 7, 133ā149.
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.
Loh, M. Y. (2015). Metacognitive strategies secondary one students employed while solving mathematics problems (Unpublished doctoral thesis). Nanyang Technological University, Singapore.
Ministry of Education. (2007). A guide to teaching and learning of primary mathematics. Singapore Curriculum Planning and Development Division, Ministry of Education.
Ministry of Education. (2012). Primary mathematics teaching and learning syllabus. Singapore Curriculum Planning and Development Division, Ministry of Education.
Moccoby, E. E., & Jacklin, C. N. (1974). Psychology of sex differences. Palo Alto, California: Stanford University Press.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
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), 7ā28.
OāNeil, H. F., Jr., & Abedi, J. (1996). Reliability and validity of a state metacognitive inventory: Potential for alternate assessment. Journal of Education Research, 89, 234ā245.
OāNeil, H. F., Jr., & Brown, R. S. (1998). Differential effects of question formats in math assessment on metacognition and affect. Applied Measurement in Education, 11(4), 331ā351.
Pintrich, P. R., & De Groot, E. V. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82, 33ā40.
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. 43ā97). Lincoln, NE: Buros Institute of Mental Measurements.
PĆ³lya, G. (1957). How to solve it. Princeton: Princeton University Press.
Pugalee, D. K. (2001). Writing mathematics, and metacognition: Looking for connections through studentsā work in mathematical problem solving. School Science and Mathematics, 101(5), 236ā245.
Schellings, G., & Van Hout-Wolters, B. H. A. M. (2011). Measuring strategy use with self-report instruments: Theoretical and empirical considerations. Metacognition and Learning, 6, 83ā90.
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).
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic.
Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19, 460ā475.
Schraw, G., & Moshman, D. (1995). Metacognition theories. Educational Psychological Review, 7, 351ā371.
Solas, J. (1992). Investigating teacher and student thinking about the process of teaching and learning using autobiography and repertory grid. Review of Educational Research, 62, 205ā225.
Sperling, R., Howard, L., & Murphy, C. (2002). Measures of childrenās knowledge and regulation of cognition. Contemporary Educational Psychology, 27, 51ā79.
Stacey, K. (1990). Making optimal use of mathematical knowledge. Australian Journal of Remedial Education, 22, 6ā10.
Thorpe, K., & Satterly, D. (1990). The development and interrelationship of metacognitive components among primary school children. Educational Psychology, 10(1), 5ā21.
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 fĆr Forschung und Praxis (pp. 77ā99). MĆnster: Waxmann.
Webb, E., Campbell, D., Schwartz, R., & Sechrest, L. (1966). Unobtrusive measures. Chicago: Rand Mc Nally.
Wilson, J. (1997). Beyond the basics: Assessing studentsā metacognition. Paper presented at the Annual Meeting of the Hong Kong Educational Research Association, Hong Kong, 14 November 1997 (ERIC Document Reproduction Service ER415244).
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).
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.
Wong, P. (1989, November). Studentsā metacognition in mathematical problem solving. Paper presented at the Annual Meeting of the Australian Association for Research in Education (November 28āDecember 2).
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Loh, M.Y., Lee, N.H. (2019). The Impact of Various Methods in Evaluating Metacognitive Strategies in Mathematical Problem Solving. In: Liljedahl, P., Santos-Trigo, M. (eds) Mathematical Problem Solving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-10472-6_8
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