Skip to main content

Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School

  • Conference paper
  • First Online:
Trends in Teaching and Learning of Mathematical Modelling

Abstract

The importance of reflective metacognitive activity during mathematical modelling activity has been recognised by scholars and researchers over the years. The metacognitive activity (or lack of it) of secondary students associated with transitions between stages in the modelling process – especially in relation to the identification and release of blockages to progress – is considered. Productive metacognitive acts are identified as occurring at three levels. Routine metacognition together with metacognitive responses to Goos’ red flag situations are elaborated together with the notion of meta-metacognition being engaged in by teachers trying to foster students’ development of independent modelling competencies especially their metacognitive competencies.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Blum, W., & Kaiser, G. (1984). Analysis of applications and of conceptions for an application oriented mathematics instruction. In J. S. Berry, D. N. Burghes, I. D. Huntley, D. J. G. James, & A.O. Moscardini (Eds.), Teaching and applying mathematical modelling (pp. 201–214). Chichester: Ellis Horwood.

    Google Scholar 

  • Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 260–270). Chichester: Horwood.

    Google Scholar 

  • Carlson, R.A., Khoo, B. H., Yaure, R. G., & Schneider, W. (1990). Acquisition of a problem-solving skill: Levels of organisation and use of working memory. Journal of Experimental Psychology: General, 119(2), 193–214.

    Article  Google Scholar 

  • Carlson, R. A., Sullivan, M. A., & Schneider, W. (1989). Practice and working memory effects in building procedural skill. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 517–526.

    Article  Google Scholar 

  • Efklides, A. (2002). The systemic nature of metacognitive experiences: Feelings, judgements, and their interactions. In M. Izaute, P. Chambres, & P.-J. Marescaux (Eds.), Metacognition: Process, function, and use (pp. 19–34). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Efklides, A., Kiorpelidou, K., & Kiosseoglou, G. (2006). Worked-out examples in mathematic: Effects on performance and metacognitive experiences. In A. Desoete & M. Veenman (Eds.), Metacognition in mathematics education (pp. 11–33). New York: Nova Science.

    Google Scholar 

  • Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–235). Hillsdale: Erlbaum.

    Google Scholar 

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

    Article  Google Scholar 

  • Galbraith, P., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 130–140). Chichester: Horwood.

    Google Scholar 

  • Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176.

    Article  Google Scholar 

  • Goos, M. (1998). ‘I don’t know if I’m doing it right or I’m doing it wrong!’ unresolved uncertainty in the collaborative learning of mathematics. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching mathematics in new times. (Proceedings of the Twenty-first annual conference of the Mathematics Education Research Group of Australasia) (Vol. 1, pp. 225–232). Gold Coast: MERGA.

    Google Scholar 

  • Kluwe, R. H. (1987). Executive decisions and regulation of problem solving behaviour. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation and understanding. Hillsdale: Erlbaum.

    Google Scholar 

  • Maaß, K. (2007). Modelling in class: What do we want the students to learn? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 63–78). Chichester: Horwood.

    Google Scholar 

  • Oke, K. H., & Bajpai, A. C. (1986). Formulation – Solution processes in mathematical modelling. In J. S. Berry, D. N. Burghes, I. D. Huntley, D. J. G. James, & A. O. Moscardini (Eds.), Mathematical modeling methodology, models and micros (pp. 61–79). Chichester: Ellis Horwood & Wiley.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic.

    Google Scholar 

  • Schoenfeld, A. H. (1987). Cognitive science and mathematics education. Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • 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 (pp. 334–370). New York: Macmillan.

    Google Scholar 

  • Stillman, G.A. (1998). The emperor’s new clothes? Teaching and assessment of mathematical applications at the senior secondary level. In P. Galbraith, W. Blum, G. Booker, & I. D. Huntley (Eds.), Mathematical modelling: Teaching and assessment in a technology-rich world (pp. 243–253). Chichester, UK: Horwood.

    Google Scholar 

  • Stillman, G. A. (2002). Assessing higher order mathematical thinking through applications. Unpublished Doctor of Philosophy thesis, Brisbane, Australia: University of Queensland.

    Google Scholar 

  • Stillman, G. A. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications tasks. Mathematics Education Research Journal, 16(1), 41–70.

    Google Scholar 

  • Stillman, G. A., & Galbraith, P. L. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157–195.

    Article  Google Scholar 

  • Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice. (Proceedings of the 30th annual conference of the Mathematics Research Group of Australasia (MERGA)) (Vol. 2, pp. 688–707). Adelaide: MERGA.

    Google Scholar 

  • Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at Year 9. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modelling students’ mathematical modeling competencies ICTMA13 (pp. 385–398). New York: Springer.

    Google Scholar 

Download references

Acknowledgement

Examples used in this chapter are from research that was funded by the Australian Research Council linkage project, RITEMATHS (LP0453701), industry partner secondary schools and Texas Instruments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gloria Stillman .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this paper

Cite this paper

Stillman, G. (2011). Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School. In: Kaiser, G., Blum, W., Borromeo Ferri, R., Stillman, G. (eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_18

Download citation

Publish with us

Policies and ethics