Exploring the Metacognitive Skills of Secondary School Students’ Use During Problem Posing

Authors

  • Tony Karnain Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Md Nor Bakar Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Seyed Yaser Mousavi Siamakani Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Hossein Mohammadikia Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Muhammad Candra Universitas Maritim Raja Ali Haji Kepulauan Riau Indonesia

DOI:

https://doi.org/10.11113/jt.v67.1847

Keywords:

Metacognitive skill, problem posing, secondary school students

Abstract

The purpose of our study was to explore students’ use of metacognitive skills during problem posing activities. This qualitative research explored the metacognitive skill of 21 secondary school students in a rural Anambas Indonesia while posing individually mathematical problems. Thinking-Aloud protocol was conducted during the problem posing activities. The audio recordings of Thinking-Aloud protocol for the students provided the data to address this question. Analysis of their written work and Thinking-Aloud protocols provided evidence of how students used metacognitive skills while problem posing and revealed different levels of these skills. Analyses of the Thinking-Aloud protocol also provided evidence for the metacognitive skills associated with planning, monitoring, and evaluation. The students used planning and monitoring skills equally. Furthermore, different levels of sophistication of planning were apparent. Students who combined these metacognitive skills demonstrated a higher level of monitoring. However, from our analyses that there was considerable overlap in the metacognitive activities associated with monitoring and evaluation.

Author Biography

  • Tony Karnain, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
    Faculty of Education (Mathematics Education)

References

Akay, H., and Boz, N. 2010. The Effect of Problem Posing Oriented Analyses-II Course on the Attitudes Toward Mathematics and Mathematics Self-Efficacy of Elementary Prospective Mathematics Teachers. Australian Journal of Teacher Education. 3(2): 59–75.

Ashman, A., & Conway, R. 1993. Using Cognitive Methods in the Classroom. London: Routledge.

Barlow, A. T., and Cates, J. M. 2006. The Impact of Problem Posing on Elementary Teacher’s Beliefs About Mathematics and Mathematics Teaching. School Science and Mathematics. 106: 64–73.

Brown, S., and Walter, M. 1983. The Art of Problem Posing. Philadelphia: Franklin Press.

Brown, S., and Walter, M. 2005. The Art of Problem Posing. 3rd Ed. Hillsdale, NJ: Lawrence Erlbaum.

De Corte, E. & Verschaffel, L. 1996. An Empirical Test of The Impact of Primitive Intuitive Models of Operations on Solving Word Problems With a Multiplicative Structure. Learning and Instruction. 6(3): 219–242.

Delvecchio, F. 2011. Students’ Use of Metacognitive Skills While Problem Solving in High School Chemistry. Doctoral Dissertation, Queen’s University. Kingston, Ontario, Canada.

Dweck, C. S. 2002. The Development of Ability Conceptions. In A. Wigfield & J. Eccles (Eds.), The Development of Achievement Motivation. New York: Academic Press.

Ellerton, N. F., and Clarkson, P. C. 2007. Language Factors in Mathematics Teaching. In: Bishop A.J et al., International Handbook of Mathematics Education. Kluwer Academic Publishers, Netherlands.

Ericsson, K. Anders, & Herbert, A. Simon, 1993. Completeness of Reports. In Protocol Analysis: Verbal Reports As Data, MIT Press.

Ernest, P. 1991. The Philosophy of Mathematics Education. London: Falmer Press.

Everson, H. and Tobias, S. 2001. The Ability to Estimate Knowledge and Performance in College: A Metacognitive Analysis. In H.J. Hartman (Ed.). Metacognition in Learning and Instruction. The Netherlands: Kluwer Academic Publishers. 69–83.

Flavell, J. H. 1976. Metacognitive Aspects of Problem Solving. In L.B. Resnick (Ed.). The Nature of Intelligence. Hillsdale, NJ: Lawrence Erlbaum Associates.

Foong, P. Y. 1993. Development of a Framework for Analyzing Mathematical Problem Solving Behaviours. Singapore Journal of Education.13(1): 61–75.

Gourgey, A. F. 1998. Metacognition in Basic Skills Instruction. Instructional Science. 26: 81–96.

Gourgey, A. F. 1998. Metacognition in Basic Skills Instruction. Instructional Science. 26(1–2): 81–96.

Hammouri, H. A . 2003. An Investigation of Undergraduates‘ Transformational Problem Solving Strategies: Cognitive/Metacognitive Processes as Predictors of Holistic/Analytic Strategies. Assessment & Evaluation in Higher Education. 28: 571–586.

Hartman, H. J. 2001. Developing Students’ Metacognitive Knowledge and Strategies. In H. J. Hartman (Ed.). Metacognition in Learning and Instruction: Theory, Research, and Practice. Dordrecht, The Netherlands: Kluwer Academic Publishers. 33–68.

Heyworth, R. M. 1999. Procedural and Conceptual Knowledge of Expert and Novice Students for the Solving of a Basic Problem In Chemistry. International Journal of Science Education. 21: 195–211.

Holistic Education Network. 2004. Metacognition-Thinking About Thinking -Learning to Learn. Holistic Education Network Tasmania, Australia.

Jager, B., Jansen, M., & Reezigt, G. 2005. The Development of Metacognition in Primary School Learning Environments. School Effectiveness and School improvement. 16: 179–196.

Kaberman, Z. & Dori, Y. J. 2009. Metacognition in Chemical Education: Question Posing in the Case-based Computerized Learning Environment. Instructional Science. 37: 403–436.

Kilpatrick, J. 1987. Problem formulating: Where Do Good Problems Come From? In A. H. Schoenfeld (Ed), Cognitive Science and Mathematics Education. Hilsdale, NJ: Lawrence Erlbaum. 123–147.

Kramarski, B., and Zoldan, S. 2008. Using Errors as Springboards for Enhancing Mathematical Reasoning with Three Metacognitive Approaches. Journal of Educational Research. 102: 137–151.

Krutetskii,V. A. 1976. The Psychology of Mathematical Abilities in School Children. (J. Teller, trans. & J. Kilpatrick & I. Wirszup, Eds.). Chicago: University of Chicago Press.

Kwakwa, A. 2012. Teachers Asked to Adopt Problem Posing. GNA. http;//ghananewsagency.devonet.com/details/education/teachers-asked-to-adopt-problem-posing-approach/?ci=9&ai=36707.

Lai, R. E. 2011. Metacognition: A Literature Review. Research Report. TMRS Staff.

Lave, J. 1988. Cognition in Practice: Mind, Mathematics, and Culture in Everyday Life. Cambridge, England: Cambridge University Press.

Leung, S. S., & Silver, E. A. 1997. The Role of Task Format, Mathematics Knowledge, and Creative Thinking on the Arithmetic Problem Posing of Prospective Elementary School Teachers. Mathematics Education Research Journal. 9(1): 5–24.

Lin, p. 2004. Supporting Teachers on Designing Problem-Posing Tasks as a Tool of Assessment to Understand Students' Mathematical Learning. PME 28, Bergen, Norway, July 14–18.

Lipman, M. 1985. Thinking Skills Fostered by Philosophy for Children. In, Segal, J. W., Chipman, S. F. & Glaser, R. (Eds.). Thinking and Learning Skills: Volume 1: Relating Instruction To Research. London; Lawrence Erlbaum Associates.

Matanzo, J. B. & Harris, D. L. 1999. Encouraging Metacognitive Awareness in Pre-Service Literacy Courses: Advancing the World of Literacy. Florida: Florida Atlantic University.

Nelson, T. 2012. The Effectiveness of Metacognitive Strategies on 8th Grade Students In Mathematical Achievements and Problem Solving Skills. Doctoral Dissertation. Faculty of the Graduate School. Southern University and A&M College.

Nelson, T. O., & Narens, L. 1990. Metamemory: A Theoretical Framework And New Findings. The Psychology of Learning and Motivation. 26: 125–141.

O'Malley, J. M., Chamot, A. U., Stewner-Manzanares, G., Russo, R. P., and Kupper, L. 1985. Learning Strategy Applications with Students of English as a Second Language. TESOL Quarterly. 19(3): 557–584.

Paris, S. G., & Paris, A. H. 2001. Classroom Applications of Research on Self-Regulated Learning. Educational Psychologist. 36(2): 89–101.

Patton, M. Q. 1990. Qualitative Research and Evaluation Methods. 2nd ed. Newbury Park, CA: Sage.

Patton, M. Q. 2002. Qualitative Research and Evaluation Methods. Thousand Oaks, CA: Sage.

Roth, W. M. & McGinn, M. K. 1997. Graphing: Cognitive Ability or Practice? Science Education. 81: 91–106.

Schoenfeld, A. H. 1985. Mathematical Problem Solving. San Diego: Academic Press.

Schoenfeld, A. H. Teaching Mathematical Thinking and Problem Solving. In L. B. Resnick and L. Klopfer (Eds.). Toward the Thinking Curriculum: Current Cognitive Research (1989 Yearbook of the Association for Supervision and Curriculum Development). Washington, DC: Association for Supervision and Curriculum Development 1989. 83–103.

Schoenfeld, A. H. 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. New York, NY: Macmillan Publishing.

Schraw, G., Crippen, K. J., & Hartley, K. 2006. Promoting Self-regulation in Science Education: Metacognition as Part of a Broader Perspective in Learning. Research in Science Education. 36(1–2): 111–139.

Schunk, D. H. & Zimmerman, B. J. 1997. Social Origins of Self-regulatory Competence. Educational Psychologist. 32: 195–208.

Semadeni, W. 1986. Verbal Problems in Arithmetic Teaching. Proceedings of the International Congress of Mathematicians Berkeley, California, USA.

Silver, Edward, A., Down, J. M., Leung, S. S., and Kenny, P. A. 1996. Posing Mathematical Problems: An Exploratory Study. Journal for Research in Mathematics Education. 27(3): 293–309.

Singer, F. M., Ellerton, N., & Cai, J. F. 2013. Problem-Posing Research in Mathematics Education: New Questions and Directions. Educational Studies in Mathematics. 83(1): 1–7. doi: DOI 10.1007/s10649-013-9478-2.

Stickles, P. R. 2006. An Analysis of Secondary and Middle School Teachers’ Mathematical Problem Posing. Doctoral Dissertation. University of Indiana.

Stillman, G. A., & Galbraith, P. L. 1998. Applying Mathematics with Real World Connections: Metacognitive Characteristics Of Secondary Students. Educational Studies in Mathematics. 36: 157–195.

Swanson, H. L. 1990. Influence of Metacognitive Knowledge and Aptitude on Problem Solving. Journal of Educational Psychology. 82(2): 306–314.

Tobin, K., & Gallagher, J. J. 1987. What Happens in High School Science Classrooms? Journal of Curriculum Studies. 19: 549–560.

Toluk-Ucar, Z. 2009. Developing Preservice Techers Understanding of Fractions Through Problem Posing. Teacher and Teacher Education. 25: 166–75.

Zimmerman, B. J., & Bandura, A. 1994. Impact of Self-regulatory Influences on Writing Course Attainment. American Educational Research Journal. 31: 845–862.

Downloads

Published

2014-04-13

Issue

Section

Social Sciences

How to Cite

Exploring the Metacognitive Skills of Secondary School Students’ Use During Problem Posing. (2014). Jurnal Teknologi, 67(1). https://doi.org/10.11113/jt.v67.1847