Educational Studies in Mathematics

, Volume 49, Issue 2, pp 225–250 | Cite as

The effects of metacognitive instruction on solving mathematical authentic tasks

  • Bracha Kramarski
  • Zemira R. Mevarech
  • Marsel Arami


The present study investigates the differential effects of cooperative-learning with or without metacognitive instruction on lower and higher achievers' solutions of mathematical authentic tasks. Participants were 91 seventh graders who studied in three classrooms. Data were analyzed by using qualitative and quantitative methods. Results indicated that students who were exposed to the metacognitive instruction within cooperative learning (COOP+META) significantly outperformed their counterparts who were exposed to cooperative learning with no metacognitive instruction (COOP). The positive effects of COOP+META were observed on both authentic and standard tasks. In addition, the findings show the positive effects of COOP+META method on lower and higher achievers. The practical implications of the study are discussed.

authentic tasks cooperative learning metacognition problem solving 


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  1. Anderson, J.R.: 1990, Cognitive Psychology and Its Implications, (3rd ed.), Freeman, New York.Google Scholar
  2. Brown, A.L., Bransford, J.D. Ferrara, R.A. and Campione, J.C.: 1983, 'Learning, remembering, and understanding', in J.H. Flavell and E.M. Markman (eds.), Handbook of Child Psychology: Vol. 3, Cognitive Development, Wiley, New York, pp. 77–166.Google Scholar
  3. Cai, J.: 2000, Problem-Based Mathematics Instruction: Promises and Challenges, Paper presented at the ICME-9 Congress in Makuhari, Japan, in Topic Group 11, Problem Solving in Mathematics.Google Scholar
  4. Cardelle-Elawar, M.: 1995, 'Effects of metacognitive instruction on low achievers in mathematics problems', Teaching and Teacher Education 11(1), 81–95.CrossRefGoogle Scholar
  5. Cobb, P.: 1994, 'Where is the mind? Constructivist and sociocultural perspectives on mathematical development', Educational Researcher 23, 13–20.Google Scholar
  6. Cohen, E.G.: 1996, A Sociologist Looks at Talking and Working Together in the Mathematics Classroom, Paper presented at the American Educational Research Association, NY.Google Scholar
  7. Cross, D.R. and Paris, S.C.: 1988, 'Developmental and instrumental analysis of children's metacognition and reading comprehension', Journal of Educational Psychology 80, 131–142.CrossRefGoogle Scholar
  8. Darling-Hammond, L.: 1992, Reforming the School Reform Agenda: Developing Capacity for School Transformation, Eric ED. 347656.Google Scholar
  9. Davidson, N.: 1990, Cooperative Learning in Mathematics, Academic Press, New York.Google Scholar
  10. Flavell, J.H.: 1978, 'Metacognitive development', in J.M. Scandura and C.J. Brainerd (eds.), Structural Process Theories of Complex Human Behavior, Sijtoff & Noordhoff, Alphen a/d Rijn, The Netherlands, pp. 213–245.Google Scholar
  11. Forman, S.L. and Steen, L.A.: 2000, Making Authentic Mathematics Work for all Students, Eric ED. 440848.Google Scholar
  12. Fry, S.M.: 1987, 'The NCTM standards: Challenges for all classrooms', Mathematics Teacher 2, 313–317.Google Scholar
  13. Fuchs, L.S., Fuchs, D., Hamlett, C.L. and Karns, K.: 1998, 'High-achieving students' interactions and performance on complex mathematical tasks as a function of homogeneous and heterogeneous pairings', American Educational Research Journal 35(2), 227–267.Google Scholar
  14. Hattie, J., Biggs, J. and Purdie, N.: 1996, 'Effects of learning skills interventions on students learning: a meta-analysis', Review of Educational Research 66, 99–136.Google Scholar
  15. Hembree, R.: 1992, 'Experiments and relational studies in problem solving: A metaanalysis', Journal for Research in Mathematics Education 23(3), 242–273.Google Scholar
  16. Hegarty, M., Mayer, R.E. and Monk, C.A.: 1995, 'Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers', Journal of Educational Psychology 87, 18–32.CrossRefGoogle Scholar
  17. Hoek, D., Eden, P. and Terwel, J.: 1999, 'The effects of integrated social and cognitive strategy instruction on the mathematics achievement in secondary education', Learning and Instruction 9, 427–448.CrossRefGoogle Scholar
  18. Jacobs, J. and Paris, S.: 1987, 'Children's metacognition, measurement, and instruction', Educational Psychologist 22, 255–278.Google Scholar
  19. King, A.: 1989, 'Effects of self-questioning training on college students' comprehension of lectures', Contemporary Educational Psychology 14, 366–381.CrossRefGoogle Scholar
  20. King, A.: 1991, 'Effects of training in strategic questioning on children's problem-solving performance', Journal of Educational Psychology 83, 307–317.CrossRefGoogle Scholar
  21. King, A.: 1994, 'Guiding knowledge construction in the classroom: Effects of teaching children how to question and how to explain', American Educational Research Journal 31, 338–368.Google Scholar
  22. Kramarski, B.: 2000, 'The effects of different instructional methods on the ability to communicate mathematically', in Tadao Nakahara and Masataka Koyama (eds.), Education, Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Mathematical Reasoning, Hiroshima University, Hiroshima, Japan, 1, pp. 167–171.Google Scholar
  23. Kramarski, B., Mevarech, Z.R. and Liberman, A.: 2001, 'The effects of multilevel - versus unilevel-metacognitive training on mathematical reasoning', Journal for Educational Research 94(5), 292–300.Google Scholar
  24. Kramarski, B., and Mevarech, Z.R.: in press, 'Enhancing mathematical reasoning in the classroom; Effects of cooperative learning and metacognitive training', American Educational Research Journal.Google Scholar
  25. Lampert, L.: 1990, 'When the problem is not the question and the solution is not the answer: Mathematical; knowing and teaching', American Educational Research Journal 27(1), 29–63.Google Scholar
  26. Lester, F.K.: 1994, 'Musing about mathematical problem solving research: 1970-1994', Journal for Research in Mathematical Education 25(6), 660–675.Google Scholar
  27. Lester, F.K., Garofalo, J. and Kroll, D.L.: 1989, The Role of Metacognition in Mathematical Problem Solving: A Study of Two Grade Seven Classes, (Final Report), Indiana University, Mathematics Education Development Center, Bloomington.Google Scholar
  28. Mayer, E.R.: 1987, Educational Psychology, Little Brown, Boston.Google Scholar
  29. Mevarech, Z.R: 1999, 'Effects of metacognitive training embedded in cooperative settings on mathematical problem solving', The Journal of Educational Research 92(4), 195–205.Google Scholar
  30. Mevarech, Z.R. and Kramarski, B.: 1997, 'IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms', American Educational Research Journal 34(2), 365–395.Google Scholar
  31. National Council of Teacher of Mathematics: 2000, Principles and Standards for School Mathematics, Author, Reston, VA.Google Scholar
  32. OECD: 2000, Measuring Students Knowledge and Skills, The PISA 2000 assessment of reading, mathematical and scientific literacy.Google Scholar
  33. Prawat, R.S.: 1998, 'Current self-regulation views of learning and motivation viewed through a Deweyan lens: The problems with dualism', American Educational Research Journal 35(2), 199–224.Google Scholar
  34. Pressley, M., Borkowski, J.G. and O'sullivan, J.T.: 1985, 'Children metamemory and the teaching of memory strategies', in D.L. Forest-Pressley, G.E. Mackinnon and T.G. Waller (eds.), Metacognition, cognition, and human performance, Academic Press, New York.Google Scholar
  35. Qin, Z., Johnson, D.W. and Johnson, R.T.: 1995, 'Cooperative versus competitive efforts and problem solving', Review of Educational Research 65, 129–144.Google Scholar
  36. Rose, T. and Schuncke, G.M.: 1997, 'Problem solving. The link between social studies and mathematics', Cleaning House 70(3), 137–140.Google Scholar
  37. Salomon, G., Globerson, T., and Guterman, E.: 1989, 'The computer as a zone of proximal development: Internalizing reading-related metacognition from a reading partner', Journal of Educational Psychology 81, 620–627.CrossRefGoogle Scholar
  38. Schoenfeld, A.H.: 1987, 'What's all the fuss about metacognition?' in A.H. Schoenfeld (ed.), Cognitive Science and Mathematics Education, Erlbaum, Hillsdale, NJ, pp. 19–216.Google Scholar
  39. 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, MacMillan, New York, pp. 165–197.Google Scholar
  40. Silver.: 1994, 'Mathematics thinking and reasoning for all students: moving from rhetoric to reality', in D. Robitaille, D. Wheeler and C. Kieran (eds.), Selected Lectures from the 7th International Congress on Mathematical Education, Le presse de l'universite Lavel, Sainte-Foy, Quebec, Canada, pp. 311–326.Google Scholar
  41. Stacey and Kay: 1992, 'Mathematical problem solving in groups - Are two heads better than one?' Journal of Mathematical Behavior 11(3), 261–275.Google Scholar
  42. Symons, S. and Greene, C.: 1993, 'Elaborative interrogation and children's learning of unfamiliar facts', Applied Cognitive Psychology 7, 219–228.Google Scholar
  43. Swanson, H.L.: 1990, 'Influence of metacognitive knowledge and aptitude on problem solving', Journal of Educational Psychology 82(2), 306–314.CrossRefGoogle Scholar
  44. TIMSS: 1999, Third International Mathematics and Science Study, The International Study Center, Lynch School of Education, Boston College.Google Scholar
  45. Verschaffel, L., Greer, B. and De Corte, E.: 2000, Making Sense of Word Problems, Swets and Zeitlinger, Lisse, ISBN 90-265-1628-2.Google Scholar
  46. Webb, N.M.: 1989, 'Peer interaction and learning in small groups', International Journal of Educational Research 13, 21–40.CrossRefGoogle Scholar
  47. Webb, N.M.: 1991, 'Task-related verbal interaction and mathematics learning in small groups', Journal for Research in Mathematics Education 22, 366–389.Google Scholar
  48. Webb, N. and Farivar, S.: 1994, 'Promoting helping behavior in cooperative small groups in middle school mathematics', American Educational Research Journal 31, 369–396.Google Scholar
  49. Wittrock, M.C.: 1986, 'Students' thought processes', in M.C. Wittrock (ed.), Handbook of Research on Teaching, (3rd ed.), Macmillan, New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Bracha Kramarski
    • 1
  • Zemira R. Mevarech
    • 1
  • Marsel Arami
    • 1
  1. 1.School of EducationBar-Ilan UniversityRamat-GanIsrael

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