Skip to main content

Advertisement

Log in

Metacognition and mathematics education: an overview

  • Survey Paper
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

This special issue includes contributions discussing the assessment and training of metacognition that appear promising for the purpose of positively influencing the learning process of students’ learning of mathematics. More specifically, contributors explore, illustrate and scrutinize available research evidence for its relevance and effectiveness in the specific curricular field of mathematics education. After an introduction and discussion of the individual input, we explore the scientific progress in the area of the theoretical framework and conceptualizations of metacognition, the relationships between metacognition and mathematics performance, the various effects upon ability levels, the measures to assess metacognition, and the interventions that aim to improve mathematics performance. This special issue ends with a reflection on practical suggestions for mathematics education.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adagideli, F. H., Saraç, S., & Ader, E. (2015). Assessing preschool teachers’ practices to promote self-regulated learning. International Electronic Journal of Elementary Education, 7(3), 423–439.

    Google Scholar 

  • Ader, E. (2019). What would you demand beyond mathematics? Investigating teachers’ promotion of students’ self-regulated learning and metacognition. ZDM Mathematics Education, 51 (4), this issue.

  • Baten, E., & Desoete, A. (2019). Metacognition and motivation in school-aged children with and without learning disabilities in Flanders. ZDM Mathematics Education, 51 (4), this issue. https://doi.org/10.1007/s11858-018-01024-6.

  • Baten, E., Praet, M., & Desoete, A. (2017). The relevance and efficacy of metacognition for instructional design in the domain of mathematics. ZDM Mathematics Education, 49, 613–623. https://doi.org/10.1007/s11858-017-0851-y.

    Article  Google Scholar 

  • Brown, A. L. (1978a). Knowing when, where, and how to remember: A problem of metacognition. In R. Glaser (Ed.), Advances in Instructional Psychology (Vol. 1, pp. 77–165). Hillsdale: Erlbaum.

    Google Scholar 

  • Brown, A. L. (1978b). Knowing when, where, and how to remember. A problem of metacognition. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 1, pp. 77–165). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Brown, A. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. Reiner & R. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 65–116). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Byrnes, J. P., & Miller, D. C. (2007). The relative importance of predictors of math and science achievement: An opportunity-propensity analysis. Contemporary Educational Psychology, 32, 599–629. https://doi.org/10.1016/j.cedpsych.2006.09.002.

    Article  Google Scholar 

  • Byrnes, J. P., & Miller, D. C. (2016). The growth of mathematics and reading skills in segregated and diverse schools: An opportunity-propensity analysis of a national database. Contemporary Educational Psychology, 46, 34–51. https://doi.org/10.1016/j.cedepsych.2016.04.002.

    Article  Google Scholar 

  • Cornoldi, C., Carretti, B., Drusi, S., & Tencati, C. (2015). Improving problem-solving in primary school students: The effect of a training program focusing on metacognition and working memory. British Journal of Educational Psychology, 85, 424–439. https://doi.org/10.1111/bjep.12083.

    Article  Google Scholar 

  • De Boer, H., Donker, A. S., Kostons, D. D. N. M., & Van der Werf, G. P. C. (2018). Thematic review. Long-term effects of metacognitive strategy instruction on student academic performance: A meta-analysis. Educational Research Review, 24, 98–115. https://doi.org/10.1016/j.edurev.2018.03.002.

    Article  Google Scholar 

  • Dennis, M. S., Sharp, E., Chovanes, J., Thomas, A., Burn, R. M., Custer, B., et al. (2016). A meta-analysis of empirical research of teaching students with mathematics learning difficulties. Learning Disabilities Research and Practice, 31, 156–168. https://doi.org/10.1111/ldrp.12107.

    Article  Google Scholar 

  • Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ metacognitive and heuristic approaches to word problem solving: Analysis and impact on students’ beliefs and performance. ZDM Mathematics Education, 42, 205–218. https://doi.org/10.1007/s11858-009-0221-5.

    Article  Google Scholar 

  • Desoete, A., Baten, E., Vercaemst, V. De Busschere, A., Baudonck, M., & Vanhaeke, J. (2019). Metacognition and motivation as predictors for mathematics performance of Belgian elementary school children. ZDM Mathematics Education, 51 (4), this issue. https://doi.org/10.1007/s11858-018-01020-w.

  • Desoete, A., & Veenman, M. (2006). Metacognition in mathematics: Critical issues on nature, theory, assessment and treatment. In A. Desoete & M. Veenman (Eds.), Metacognition in mathematics education (pp. 1–10). New York: Nova Science Publishers.

    Google Scholar 

  • Dignath, C., & Büttner, G. (2018). Teachers’ direct and indirect promotion of self-regulated learning in primary and secondary school mathematics classes—Insights from video-based classroom observations and teacher interviews. Metacognition and Learning, 13, 127–157. https://doi.org/10.1007/s11409-018-9181-x.

    Article  Google Scholar 

  • Donker, A. S., de Boer, H., Kostons, D., Dignath van Ewijk, C. C., & van der Werf, M. P. C. (2014). Effectiveness of learning strategy instruction on academic performance: A meta-analysis. Educational Research Review, 11, 1–26. https://doi.org/10.1016/j.edurev.2013.11.002.

    Article  Google Scholar 

  • Dowker, A. (2015). Individual differences in arithmetical abilities. The componential nature of arithmetic. In The Oxford handbook of mathematical cognition (pp. 862–878). Oxford: Medicine UK.

  • Flavell, J. H. (1971). First discussant's comments. What is memory development the development of? Human Development, 14, 272–278.

    Article  Google Scholar 

  • Flavell, J. H. (1976). Metacognitive aspects of problem-solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–236). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Flavell, J. H. (1978). Metacognitive development. In J. M. Scandura & C. J. Brainerd (Eds.), Structural/process theories of complex human behavior. Alphen a. d. Rijn, The Netherlands: Sijthoff & Noordhoff.

  • Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34, 906–911.

    Article  Google Scholar 

  • Flavell, J. H. (1987). Speculations about the nature and development of metacognition. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 20–29). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Gascoine, L., Higgins, S., & Wall, K. (2017). The assessment of metacognition in children aged 4–16 years: A systematic review. Review of Education, 5, 3–57. https://doi.org/10.1002/rev3.3077.

    Article  Google Scholar 

  • Hacker, D. J., Kiuhara, S. A., & Levin, J. R. (2019). Project FACT+R2C2: Developing proficiency with fractions and literacy for students with mathematics learning disabilities. ZDM Mathematics Education, 51 (4), this issue.

  • Hidayat, R., Zulnaida, H., & Syed Zamri, S. N. A. (2018). Roles of metacognition and achievement goals in mathematical modelling competency: A structural equation modelling analysis. PLoS One, 13(11), e0206211. https://doi.org/10.1371/journal.pone.0206211.

    Article  Google Scholar 

  • Kuzle, A. (2018). Assessing metacognition of grade 2 and grade 4 students using an adaptation of multi-method interview approach during mathematics problem-solving. Mathematics Education Research Journal, 30, 185–207. https://doi.org/10.1007/s13394-017-0227-1.

    Article  Google Scholar 

  • Lingel, K., Lenhart, J., & Schneider, W. (2019). Metacognition in mathematics: Do different metacognitive monitoring measures make a difference? ZDM Mathematics Education, 51 (4), this issue.

  • Lucangeli, D., Penna, M. P., Fastame, M. C., Pedron, M., Porru, A., & Duca, V. (2019). Metacognition and errors: The impact of self-regulatory trainings in children with specific learning disabilities. ZDM Mathematics Education, 51 (4), this issue.

  • Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in hetereogeneous classrooms. American Education Research Journal, 34, 365–394. https://doi.org/10.3102/00028312034002365.

    Article  Google Scholar 

  • Nelson, G., & Powell, S. R. (2017). A systematic review on longitudinal studies of mathematics difficulty. Journal of Learning Disabilities, 51, 523–539. https://doi.org/10.1177/0022219417714773.

    Article  Google Scholar 

  • Ohtani, K., & Hisasaka, T. (2018). Beyond intelligence: A meta-analytic review of the relationship among metacognition, intelligence, and academic performance. Metacognition Learning, 13, 179–212. https://doi.org/10.1007/s11409-018-9183-8.

    Article  Google Scholar 

  • Pieters, S., Roeyers, H., Rosseel, Y., Van Waelvelde, H., & Desoete, A. (2015). Identifying subtypes among children with developmental coordination disorder and mathematical learning disabilities, using model-based clustering. Journal of Learning Disabilities, 48(1), 83–95. https://doi.org/10.1177/0022219413491288.

    Article  Google Scholar 

  • Robson, S. (2010). Self-regulation and metacognition in young children’s self-initiated play and reflective dialogue. International Journal of Early Years Education, 18, 227–241. https://doi.org/10.1080/09669760.2010.521298.

    Article  Google Scholar 

  • Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM Mathematics Education, 42, 149–161. https://doi.org/10.1007/s11858-010-0240-2.

    Article  Google Scholar 

  • Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26(1–2), 113–125. https://doi.org/10.1023/a:1003044231033.

    Article  Google Scholar 

  • Shilo, A., & Kramarski, B. (2019). Mathematical-metacognitive discourse: How can it be developed among teachers and their students? Empirical evidence from a videotaped lesson and two case studies. ZDM Mathematics Education, 51 (4), this issue.

  • Shute, V. J. (1996). Learning processes and learning outcomes. In E. De Corte & F. E. Weinert (Eds.), International encyclopedia of developmental and instructional psychology (pp. 409–418). Oxford: Elsevier Science.

    Google Scholar 

  • Spruce, R., & Bol, L. (2015). Teacher beliefs, knowledge, and practice of self-regulated learning. Metacognition and Learning, 10, 245–277. https://doi.org/10.1007/s11409-014-9124-0.

    Article  Google Scholar 

  • Stillman, G., & Mevarech, Z. (2010). Metacognition research in mathematics education: From hot topic to mature field. ZDM Mathematics Education, 42, 145–148. https://doi.org/10.1007/s11858-010-0245-x.

    Article  Google Scholar 

  • Temur, O. D., Ozsoy, G., Turgut, S., & Kuruyer, H. G. (2019). Metacognitive instructional behaviors of preschool teachers in mathematical activities. ZDM Mathematics Education, 51 (4), this issue.

  • Veenman, M. V. J. (2006). The role of intellectual and metacognitive skills in math problem solving. In A. Desoete & M. Veenman (Eds.), Metacogniton in mathematics education (pp. 35–50). Haupauge, NY: Nova Science.

    Google Scholar 

  • Veenman, M. V. J. (2013). Training metacognitive skills in students with availability and production deficiencies. In H. Bembenutty, T. Cleary, & A. Kitsantas (Eds.), Applications of self-regulated learning across diverse disciplines: A tribute to Barry J. Zimmerman (pp. 299–324). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Veenman, M. V. J. (2017). Learning to self-monitor and self-regulate. In R. Mayer & P. Alexander (Eds.), Handbook of research on learning and instruction, 2nd revised edition (pp. 233–257). New York: Routledge.

    Google Scholar 

  • Veenman, M. V. J., Elshout, J. J., & Meijer, J. (1997). The generality vs. domain-specificity of metacognitive skills in novice learning across domains. Learning and Instruction, 7, 187–209. https://doi.org/10.1016/S0959-4752(96)00025-4.

    Article  Google Scholar 

  • Veenman, M. V. J., & van Cleef, D. (2019). Measuring metacognitive skills for mathematics: Students’ self-reports vs. online assessment methods. ZDM Mathematics Education, 51 (4), this issue.

  • Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition Learning, 1, 3–14. https://doi.org/10.1007/s11409-006-6893-0.

    Article  Google Scholar 

  • Veenman, M. V. J., Wilhelm, P., & Beishuizen, J. J. (2004). The relation between intellectual and metacognitive skills from a developmental perspective. Learning and Instruction, 14, 89–109. https://doi.org/10.1016/j.learninstruc.2003.10.004.

    Article  Google Scholar 

  • Verschaffel, L., Van Dooren, W., & Start, J. (2017). Applying cognitive psychology based instructional design principles in mathematics teaching and learning: Introduction. ZDM Mathematics Education, 49, 491–496. https://doi.org/10.1007/s11858-017-0861-9.

    Article  Google Scholar 

  • Vorhölter, K. (2019). Structure of modelling specific metacognitive strategies of small groups. ZDM Mathematics Education, 51 (4), this issue.

  • Wang, A. H., Shen, F., & Byrnes, J. P. (2013). Does the opportunity-propensity framework predict the early mathematics skills of low-income pre-kindergarten children? Contemporary Educational Psychology, 38, 259–270. https://doi.org/10.1016/j.cedpsych.2013.04.004.

    Article  Google Scholar 

  • Whitebread, D., Coltman, P., Anderson, H., Mehta, S., & Pasternak, D. P. (2005). Metacognition in young children: Evidence form a naturalistic study of 3–5 year olds. Paper presented at 11th EARLI International Conference. Cyprus: University of Nicosia.

  • Zhao, N., Teng, S., Li, Y., Wang, S., Li, W., Wen, H., & Mengya, Y. (2019). A path model for metacognition and its relation to problem-solving strategies and achievement for different tasks. ZDM Mathematics Education, 51 (4), this issue.

  • Zimmerman, B. J. (2008). Investigating self-regulation and motivation: Historical background, methodological development, and future prospects. American Educational Research Journal, 45, 166–183. https://doi.org/10.3102/0002831207312909.

    Article  Google Scholar 

  • Zohar, A. (2012). Explicit teaching of metastrategic knowledge: Definitions, students’ learning, and teachers’ professional development. In A. Zohar & Y. J. Dori (Eds.), Metacognition in science education: Trends in current research (pp. 197–223). New York: Springer.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Brigitte De Craene.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Desoete, A., De Craene, B. Metacognition and mathematics education: an overview. ZDM Mathematics Education 51, 565–575 (2019). https://doi.org/10.1007/s11858-019-01060-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-019-01060-w

Keywords

Navigation