Meta-cognitive Skills and Strategies Application: How this Helps Learners in Mathematics Problem-solving
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School of Mathematics, Natural Science and Technology Education, Bloemfontein, SOUTH AFRICA
Online publish date: 2019-03-05
Publish date: 2019-03-05
EURASIA J. Math., Sci Tech. Ed 2019;15(5):em1702
Learners’ problem-solving in mathematics is often problematic for both the learners and teachers and this needs to be addressed by applying relevant skills and strategies in the teaching and learning of mathematics. Meta-cognitive skills and strategies acquisition is vital for a learner’s academic success and particularly in mathematics problem-solving. The paper investigates the relevance of learners’ use of meta-cognitive skills and strategies in mathematics problem-solving. A qualitative approach was used, including a case-study design; observation and semi-structured interviews were used to collect data. Four rural schools, four mathematics teachers and four learners from different schools (one from each school) were selected for the study. Content analysis was used to analyze the data together with verbal quotes that supported themes that emerged. The aim was to obtain condensed and broad descriptions of the phenomena. The findings revealed that learners’ use of meta-cognitive skills and strategies, such as task analysis, planning, monitoring, checking and reflection, self and group-monitoring skills, reading and writing skills, self-regulation skills (SR) and self-assessment (SA) helped them in mathematics problem-solving. The learners could also solve problems more easily through group discussions and thinking about their own thinking. Recommendations were made to benefit learners and further improve their use of meta-cognition for successful problem-solving.
Ahuja, O. P. (2006). World‐class high quality mathematics education for all K‐12 American students. The Montana Mathematics Enthusiast, 3(2), 223‐248.
Amin, I., & Sukestiyarno, Y. L. (2015). Analysis metacognitive skills on learning mathematics in high school. International journal education and research, 3(3).
Ataman, A., & Özsoy, G. (2009). The effect of meta-cognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67-82.
Bormotova, L. S. (2010). A qualitative study of meta-cognitive reflection: the beliefs, attitudes and reflective practices of developing professional educators (PhD Dissertation). Indiana University of Pennsylvania.
Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.
Bruner, J. S., & Haste, H. (Ed.). (1987). Making sense: The child’s construction of the world. New York: Methuen.
Cecez-Kecmanovic, D. (2011). ‘On Methods, Methodologies and How They Matter’, in Proceedings of the 19th European Conference on Information Systems (ECIS 2011), Association for Information Systems, USA, presented at 19th European Conference on Information Systems (ECIS 2011), Helsinki, Finland, June 9-11, 2011,
Christiansen, B., Howson, A. G., & Otte, M. 1984. Perspectives on mathematics education. Dordrecht: D. Reidel.
Cooperstein, S. E., & Kocevar-Weidinger, E. (2004). Beyond active learning: A constructivist approach to learning. Reference Services Review, 32(2), 141–148.
Coskun, A. (2010). The effect of meta-cognitive strategy trading on the listening performance of beginner students. Novitas-ROYAL (Research on Youth and Language), 4(1), 35-50.
Department of Basic Education (DBE). (2011a). Curriculum and Assessment Policy Statement (CAPS) Grades 1-3 Mathematics. Pretoria. Retrieved on 4 August 2014 from
Department of Education (DoE). (2002). Draft education for all status report 2002. South Africa.
Department of Education (DoE). (2003). Revised National Curriculum Statement grade R-9 (schools) Mathematics. Sol Plaatje House. Pretoria: Government Printer.
Department of Education (DoE). (2010). Curriculum and Assessment Policy Statement. Grade 10-12 Mathematics. Pretoria: Government Printer.
Dewey, J. (1933). How we think: a statement of the relation of reflective thinking to the educative process. Boston: Heath.
Dewey, J. (1998). How we think: A restatement of the relation of reflective thinking to the education process. Boston: Houghton Mifflin.
Dolya, G. (2010). Vygotsky in action in the early years.The ‘key to learning’ curriculum. London: Routledge.
Ebrahim, A. (2010). Mathscitech. Retrieved on 23 April 2012 from
Engelbrecht, P., Green, L., Naicker, S., & Engelbrecht, L. (2004). Inclusive Education in Action in South Africa. Pretoria: Van Schaik.
English, L. D. (2007). Cognitive psychology and Mathematics education: reflections on the past and future. The Montana Mathematics Enthusiast, 4(2), 119–126.
Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany: State University of New York Press.
Feza-Piyose, N. (2012). Language: A cultural capital for conceptualizing mathematics knowledge. International Electronic Journal of Mathematics Education, 7(2), 62-79.
Fischer, G. (1998). “Making Learning a Part of Life—Beyond the ‘Gift-Wrapping’ Approach of Technology.” In P. Alheit, & E. Kammler (Eds.), Lifelong Learning and Its Impact on Social and Regional Development, Donat Verlag, Bremen, pp. 435-462.
Flavell, J. H. (1976). Meta-cognition and cognitive monitoring: a new area of cognitive-development inquiry. American Psychologist, 34, 906–911.
Gningue, S. M., Peach, R., & Schroder, B. (2013). Developing Effective Mathematics Teaching: Assessing Content and Pedagogical Knowledge, Student‐Centered Teaching, and Student Engagement.
Gok, T. (2010). The general assessment of problem solving processes in physics education. Eurasian Journal of Physics and Chemistry Education, 2(2), 110-122.
Goos, M. (2004). Learning mathematics a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.
Henson, K. T. (2004). Constructivist teaching strategies for diverse middle-level classroom. Boston: Pearson.
Jagals, D. (2013). Dissertation submitted for the degree Magister Education is in the Faculty of Educational Sciences at the North-West University Potchefstroom Campus (Unpublished dissertation).
Johnson, C. J., & Kritsonis, W. (2006). A national dilemma: African American student’s underrepresented in advanced mathematics courses. Doctoral Forum: National Journal for Publishing and Mentoring Doctoral Student Research, 20(3), 7.
Joseph, N. (2010). Metacognition needed: Teaching middle and high school students to develop strategic learning skills. Preventing School Failure: Alternative Education for Children and Youth, 54(2), 99-103.
Kayashima, M., & Inaba, A. (2014). The Model of Meta-cognitive Skills and How to Facilitate Development of the Skill. Retrieved on 7 August 2014 from
Kim, B. (2001). Social Constructivism. In M Orey (ed). Emerging perspectives on learning, teaching, and technology. Retrieved on 11 May 2013 from
Knox, H. (2017). Using Writing Strategies in Math to Increase Metacognitive Skills for the Gifted Learner. Gifted Child Today, 40(1), 43-47.
Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281-310.
Lai, E. R. (2011). Meta-cognition: A literature review. Retrieved on 15 October 2011 from http://www.pearsonassessments.....
Lerman, S. (2001). Cultural, Discursive Psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46, 87-113.
Livingston, J. A. (1997). Metacognition: An overview. Retrieved on 6 April 2010 from
Maree, J. G., Olivier, E. C., & Swanepoel, A. C. (2004). Die senior Harmony Suid-Afrikaanse Wiskunde-olimpiade: ‘n analise van die resultate van die senior groep, tweede rondte. SA Tydskrif vir Natuurwetenskap en Tegnologie, 23(3), 52–60.
Mayaba, N. (2009). The effect of a scientific literacy strategy on grade 6 and 7 learners general literacy skills (Unpublished MEd dissertation). Port Elizabeth: Nelson Mandela Metropolitan University.
Mokhaba, M. B. (1993). The application of the activity principle in mathematics teaching – A strategy for teacher training (Unpublished PhD Thesis). Pretoria: University of South Africa.
Muis, K. R. (2008). Epistemic profiles and self-regulated learning: Examining relations in the context of mathematics problem solving. Educational Psychology, 33, 177–208.
Nieuwenhuis, J. (2007). Introducing qualitative research. In Maree, K. ed., First steps in research. Pretoria: Van Schaik.
Oxford English Dictionary. (1989). Oxford University Press.
Panaoura, A., & Philippou, G. (2007). The developmental change of young pupils’ metacognitive ability in mathematics in relation to their cognitive abilities. Cognitive Development, 22, 149-164.
Piaget, J. (1973). The child and reality: Problems of genetic psychology. New York: Grossman.
Posthuma, A. (2011). The nature of mathematics teachers’ reflective practice (Unpublished Thesis), University of Pretoria.
Posthuma, B., Human, A., & Van der Walt, A. (2015). International comparisons of Foundation Phase number domain mathematics knowledge and practice standards. South African Journal of Education, 35(1), 1-13.
Rylands, L. J., & Coady, C. (2008). Performance of students with week mathematics in first-year mathematics and science. International journal of mathematics education in Science and Technology, 40(6), 741-753.
Schraw, G., & Graham, T. (1997). Helping gifted students develop metacognitive awareness. Roeper Review, 20, 4-8.
Sepeng, J. P. (2010). Grade 9 Second-Language Learners in Township Schools: Issues of Language and Mathematics when solving word problems (Unpublished Thesis). Port Elizabeth: Nelson Mandela Metropolitan University.
Setati, M., & Barwell, R. (2008). Making mathematics accessible for multilingual learners. Pythagoras, 67, 2-4.
Strawderman, V. W. (2010). Mathematics anxiety model. Retrieved on 5 Octover 2010 from anxiety model.html.
Van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46, 59-85.
Veenman, M. V. J. (2006). The role of intellectual and metacognitive skills in math problem-solving. In A. Desoete & M. V. J. Veenman (Eds.), Metacognition in mathematics education. New York: Nova Science Publishers.
Veenman, M., Van Hout-Wolters, B., & Afflerbach, P. (2006). Metacognition and learning: conceptual and methodological considerations. Metacognition and Learning, 1(1), 3-14.
Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press.
Webb, L., & Webb, P. (2008a). Introducing Discussion into Multilingual Mathematics Classrooms: An Issue of Code Switching. Pythagoras: Journal of the Association for Mathematics Education of South Africa, 67, 26-32.
Webb, P., & Austin, P. (2009). The family maths programme: parents’ perceptions of what influences their engagement, enjoyment and confidence within a complex learning community. Education as Change, 13(1), 27-44.
White, D. (2003). Promoting productive mathematical classroom discourse. Journal of Mathematical Behavior, 22, 37-53.
Whitebread, D., Coltman, P., Pasternak, D. P., Sangster, C., Grau, V., Bingham, S., Almeqdad, Q., & Demetriou, D. (2009). The development of two observational tools for assessing metacognition and self-regulated learning in young children. Metacognition and Learning, 4(1), 63-85.
Witterholt, M., Goedhart, M., & Suhre, C. (2016). The impact of peer collaboration on teachers’ practical knowledge. European Journal of Teacher Education, 39(1), 126-1243.
Yoong, W. K., (2002). Helping Your Students to Become Metacognitive in Mathematics: A Decade Later. Mathematics Newsletter, 12(5).
Zimmerman, B. J. (2000). Attaining self-regulation: a social cognitive perspective. In Boekarts, M., Pintrich, P. R., & Zeidner, M. (Eds.). Handbook of Self-regulation. San Diego, CA: Academic Press.