Educational Studies in Mathematics

, Volume 30, Issue 3, pp 229–260 | Cite as

Do it this way! Metacognitive strategies in collaborative mathematical problem solving

  • Merrilyn Goos
  • Peter Galbraith


Recent years have seen increasing interest in the role of metacognition in mathematical problem solving, and in the use of small group work in classroom settings. However, little is known about the nature of secondary students' metacognitive strategy use, and how these strategies are applied when students work together on problems. The study described in this paper investigated the monitoring behaviour of a pair of senior secondary school students as they worked collaboratively on problems in applied mathematics. Analysis of verbal protocols from think aloud problem solving sessions showed that, although the students generally benefited from adopting complementary metacognitive roles, unhelpful social interactions sometimes impeded progress. The findings shed some light on the nature of individual and interactive metacognitive strategy use during collaborative activity.


Social Interaction Small Group Group Work Applied Mathematic Mathematical Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. BransfordJ., SherwoodR., VyeN. and ReiserJ.: 1986, ‘Teaching thinking and problem solving’, American Psychologist 41, 1078–1089.Google Scholar
  2. CampioneJ. C., BrownA. L. and ConnellM. L.: 1989. ‘Metacognition: On the importance of understanding what you are doing’, in R. I.Charles and E. A.Silver (eds.), ‘The Teaching and Assessing of Mathematical Problem Solving’, Reston, Virginia, Erlbaum, NCTM, 93–114.Google Scholar
  3. CobbP.: 1986, ‘Contexts, goals, beliefs and learning mathematics’, For the Learning of Mathematics 6(2), 2–9.Google Scholar
  4. CollinsA., BrownJ. S. and NewmanS. E.: 1987, ‘Cognitive apprenticeship: Teaching the craft of reading, writing and mathematics’. Technical Report No. 403. Bolt, Beranek and Newman, Inc., Cambridge, Massachusetts; Illinois University, Urbana. Centre for the Study of Reading. (ED 284 181).Google Scholar
  5. EricssonK. A. and SimonH. A.: 1980, ‘Verbal reports as data’, Psychological Review 87, 215–251.Google Scholar
  6. EricssonK. A. and SimonH. A.: 1984, ‘Protocol Analysis’, Cambridge, Massachusetts, MIT Press.Google Scholar
  7. FlavellJ. H.: 1976, ‘Metacognitive aspects of problem solving’, in L. R.Resnick (ed.), ‘The Nature of Intelligence’, Hillsdale, New Jersey, Erlbaum, 231–235.Google Scholar
  8. FormanE.: 1989, ‘The role of peer interaction in the social construction of mathematical knowledge’, International Journal of Educational Research 13, 55–70.Google Scholar
  9. GalbraithP. L. and ClatworthyN. J.: 1990, ‘Beyond standard models — Meeting the challenge of modelling’, Educational Studies in Mathematics 21, 137–163.Google Scholar
  10. GarofaloJ.: 1987, ‘Metacognition and school mathematics’, Arithmetic Teacher 34(9), 22–23.Google Scholar
  11. GarofaloJ.: 1989, ‘Beliefs and their influence on mathematical performance’, Mathematics Teacher 82, 502–505.Google Scholar
  12. GarofaloJ. and LesterF. K.Jr.: 1985, ‘Metacognition, cognitive monitoring, and mathematical performance’, Journal for Research in Mathematics Education 16, 163–176.Google Scholar
  13. GenestM. and TurkD.: 1981, ‘Think-aloud approaches to cognitive assessment’, in T. V.Merluzzi, C. R.Glass and M.Genest (eds.), ‘Cognitive Assessment’, New York, The Guilford Press, 233–269.Google Scholar
  14. GinsburgH. P., KossanN. E., SchwartzR. and SwansonD.: 1983, ‘Protocol methods in research on mathematical thinking’, in H.Ginsburg (ed.), ‘The Development of Mathematical Thinking’, New York, Academic Press, 7–47.Google Scholar
  15. GlaserR.: 1984, ‘Education and thinking: The role of knowledge’, American Psychologist 39, 93–104.Google Scholar
  16. Kroll, D. L.: 1988, ‘Cooperative problem solving and metacognition: A case study of three pairs of women’. Doctoral dissertation, Indiana University. Dissertation Abstracts International, 49, 2958A. (University Microfilms No. 8902580).Google Scholar
  17. LaveJ., SmithS. and ButlerM.: 1989, ‘Problem solving as everyday practice’, in R. I.Charles and E. A.Silver (eds.), ‘The Teaching and Assessing of Mathematical Problem Solving’, Reston, Virginia, Erlbaum, NCTM, 61–81.Google Scholar
  18. LesterF. K.Jr.: 1989, ‘Reflections about mathematical problem solving research’, in R. I.Charles and E. A.Silver (eds.), ‘The Teaching and Assessing of Mathematical Problem Solving’, Reston, Virginia, Erlbaum, NCTM, 115–124.Google Scholar
  19. LesterF. K.Jr. and others: 1989, ‘The role of metacognition in mathematical problem solving: A study of two grade seven classes’. Final Report. Indiana University, Bloomington: Mathematics Education Development Centre. (ED 314 255).Google Scholar
  20. LewisA. B.: 1989, ‘Training students to represent arithmetic word problems’, Journal of Educational Psychology 81, 521–531.Google Scholar
  21. MasonJ., BurtonL. and StaceyK.: 1985, Thinking Mathematically (Revised ed.), Wokingham, Addison-Wesley.Google Scholar
  22. MayerR.: 1983, ‘Thinking, Problem Solving, Cognition’, New York, W. H. Freeman and Co.Google Scholar
  23. McLeodD. B.: 1988, ‘Affective issues in mathematical problem solving: Some theoretical considerations’, Journal for Research in Mathematics Education 19, 134–141.Google Scholar
  24. NewellA. and SimonH. A.: 1972, ‘Human Problem Solving’, Englewood Cliffs, New Jersey, Prentice-Hall.Google Scholar
  25. NisbettR. E. and WilsonT. D.: 1977, ‘Telling more than we can know: Verbal reports on mental processes’, Psychological Review 84, 231–259.Google Scholar
  26. PerkinsD. N., SimmonsR. and TishmanS.: 1990, ‘Teaching cognitive and metacognitive strategies’, Journal of Structural Learning 10, 285–303.Google Scholar
  27. SchoenfeldA. H.: 1985a, ‘Mathematical Problem Solving’, Orlando, Florida, Academic Press.Google Scholar
  28. SchoenfeldA. H.: 1985b, ‘Making sense of “out loud” problem-solving protocols’, Journal of Mathematical Behavior 4, 171–191.Google Scholar
  29. SchoenfeldA. H.: 1987a, ‘Confessions of an accidental theorist’, For the Learning of Mathematics 7(1), 30–38.Google Scholar
  30. SchoenfeldA. H.: 1987b, ‘What's all the fuss about metacognition?’, in A. H.Schoenfeld (ed.), ‘Cognitive Science and Mathematics Education’, Hillsdale, New Jersey, Erlbaum, 189–215.Google Scholar
  31. SchoenfeldA. H.: 1988, ‘When good teaching leads to bad results: The disasters of “well-taught” mathematics courses’, Educational Psychologist 23, 145–166.Google Scholar
  32. SchoenfeldA. H.: 1989, ‘Explorations of students' mathematical beliefs and behaviour’, Journal for Research in Mathematics Education 20, 338–355.Google Scholar
  33. SilverE. A.: 1982, ‘Knowledge organization and mathematical problem solving’, in F. K.LesterJr. and J.Garofalo (eds.), ‘Mathematical Problem Solving: Issues in Research’, Philadelphia, The Franklin Instutute Press, 15–25.Google Scholar
  34. SilverE. A.: 1987, ‘Foundations of cognitive theory and research for mathematics problem-solving instruction’, in A. H.Schoenfeld (ed.), ‘Cognitive Science and Mathematics Education’, Hillsdale, New Jersey, Erlbaum, 33–60.Google Scholar
  35. ThomasD. A.: 1988, ‘Reading and reasoning skills for math problem solvers’, Journal of Reading 32, 244–249.Google Scholar
  36. VenezkyR. L. and BregarW. S.: 1988, ‘Different levels of ability in solving mathematical word problems’, Journal of Mathematical Behavior 7, 111–134.Google Scholar
  37. VygotskyL. S.: 1978, ‘Mind in Society’, Cambridge, Massachusetts, Harvard University Press.Google Scholar
  38. WertschJ. V.: 1985, ‘Vygotsky and the Social Formation of Mind’, Cambridge, Massachusetts, Harvard University Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Merrilyn Goos
    • 1
  • Peter Galbraith
    • 1
  1. 1.The University of Queensland Graduate School of EducationBrisbane 233Australia

Personalised recommendations