This article presents an overview of two studies that examined the relationship between metacognition and mathematical problem solving in 165 children with average intelligence in Grade 3 in order to help teachers and therapists gain a better understanding of contributors to successful mathematical performance. Principal components analysis on metacognition revealed that three metacognitive components (global metacognition, off-line metacognition, and attribution to effort) explained 66% to 67% of the common variance. The findings from these studies support the use of the assessment of off-line metacognition (essentially prediction and evaluation) to differentiate between average and above-average mathematical problem solvers and between students with a severe or moderate specific mathematics learning disability.
Get full access to this article
View all access options for this article.
References
1.
Allen, B.A., & Armour-Thomas, E. (1992). Construct validation of metacognition. The Journal of Psychology, 127, 203-211.
Boekaerts, M. (1999). Metacognitive experiences and motivational state as aspects of self-awareness: Review and discussion. European Journal of Psychology of Education, 14, 571-584.
4.
Borkowski, J.G. (1992). Metacognitive theory: A framework for teaching literacy, writing, and math skills. Journal of Learning Disabilities , 25, 253-257.
5.
Borkowski, J.G., Teresa Estrada, M., Milstead, M., & Hale, C.A. (1989). General problem-solving skills: Relations between metacognition and strategic processing. Learning Disability Quarterly, 12, 57-70.
6.
Brown, A.L. (1980). Metacognitive development and reading. In R. J. Spiro, B. C. Bruce, & W. F. Brewer (Eds.), Theoretical issues in reading comprehension: Perspectives from cognitive psychology, linguistics, artificial intelligence, and education (pp. 453-481). Hillsdale, NJ: Erlbaum.
7.
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: Erlbaum.
8.
Brus, B.T., & Voeten, M.J.M. (1999). Eén minuut test [One minute test]. Lisse, The Netherlands: Swets & Zeitlinger.
9.
Carr, M., Alexander, J., & Folds-Bennett, T. (1994). Metacognition and mathematics strategy use. Applied Cognitive Psychology, 8, 583-595.
10.
Carr, M., & Biddlecomb, B. (1998). Metacognition in mathematics from a constructivist perspective. In D. J. Hacker, J. Dunlosky, & A. C. Graesser (Eds.), Metacognition in educational theory and practice (pp. 69-91). Mahwah, NJ: Erlbaum.
11.
Carr, M., & Jessup, D.L. (1995). Cognitive and metacognitive predictors of arithmetics strategy use. Learning and Individual Differences, 7, 235-247.
12.
Cracco, J., Baudonck, M., Debusschere, A., Dewulf, B., Samyn, F., & Vercaemst, V. (1995). Kortrijkse rekentest [Kortrijk arithmetic test] . Kortrijk, Belgium: Revalidatiecentrum Overleie.
13.
Cross, D.R., & Paris, S.G. (1988). Development and instructional analyses of children's metacognition and reading comprehension. Journal of Educational Psychology, 80, 131-142.
14.
De Clercq, A., Desoete, A., & Roeyers, H. (2000). EPA 2000: A multilingual, programmable computer assessment of off-line metacognition in children with mathematical learning disabilities. Behavior Research Methods, Instruments, & Computers, 32, 304-311.
15.
De Corte, E., Verschaffel, L., & Greer, B. (1996). Mathematics, learning, and instruction. In E. De Corte & F. E. Weinert (Eds.), International encyclopedia of developmental and instructional psychology (pp. 535-538). Oxford, UK: Elsevier Science.
16.
De Corte, E., Verschaffel, L., & Op 't Eynde, P. (2000). Self-regulation: A characteristic and a goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687-726). San Diego: Academic Press.
17.
Desoete, A., & Roeyers, H. (2000). Rekenstoornissen bij negenjarigen: Bepalen de tests de diagnose? [Mathematics learning disabilities in nine year olds: Does the chosen test determine the diagnosis?]. Diagnostiek-wijzer , 4, 3-16.
18.
Desoete, A., Roeyers, H., & Buysse, A. (2000). Achtjarigen, waarbij rekenen nooit routine wordt: Rekenstoornissen in Vlaanderen [Eight-year-olds for whom arithmetic never becomes routine: Mathematics and learning disabilities in Flanders]. Tijdschrift voor Orthopedagogiek, 10, 430-441.
19.
Desoete, A., Roeyers, H., Buysse, A., & De Clercq, A. (in press). Dynamic assessment of metacognitive skills in young children with mathematics learning disabilities. In J. Carlson (Ed.), Potential assessment and cognitive training: Actual research and perspectives in theory-building and methodology. England: JAI Press.
20.
De Vos, T. (1992). Test voor het vaststellen van het rekenvaardigheidsniveau der elementaire bewerkingen (automatisering) voor het basis en voortgezet onderwijs: Handleiding [Test to determine the mathematics ability level for elementary operations (automatization) in primary and secondary education: Manual]. Nijmegen, The Netherlands: Berkhout.
21.
Dickson, S.V., Collins, V.L., Simmons, D.C., & Kameenui, E.J. (1998). Metacognitive strategies: Research bases. In D. C. Simmons & E. J. Kameenui (Eds.), What reading research tells us about children with diverse learning needs: Bases and basics (pp. 295-360). Mahwah, NJ: Erlbaum .
22.
Dudal, P. (1985). Vraagstukken 2de en 3de leerjaar [Word problems grades 2 and 3]. Torhout, Belgium: Mach.
23.
Flavell, J.H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231-236). Hillsdale, NJ: Erlbaum.
24.
Flavell, J.H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist , 34, 906-911.
25.
Flavell, J.H., Green, F.L., & Flavell, E.R. (1995). Young children's knowledge about thinking [Monographs of the Society for Research in Child Development, Serial No. 243]. Chicago: The University of Chicago Press .
Garcia, T., & Pintrich, P.R. (1994). Regulating motivation and cognition in the classroom: The role of self-schemes and self-regulatory strategies . In D. H. Schunk & B. J. Zimmerman (Eds.), Self-regulation of learning and performance: Issues and educational applications (pp.127-153). Hillsdale, NJ: Erlbaum.
28.
Geary, D. (1993). Mathematical disorders: Cognitive, neuropsychological and genetic components. Psychological Bulletin,114, 345-362.
29.
Ghesquière, P., & Ruijssenaars, A. (1994). Vlaamse normen voor studietoetsen rekenen en technisch lezen lager onderwijs [Flemish standards for study evaluation of mathematics and technical reading in primary schools]. Leuven, Belgium: Catholic University of Leuven, Center for Educational and Professional Guidance.
30.
Hacker, D., Dunlosky, J. , & Graesser, A. (Eds.). (1998). Metacognition in educational theory and practice: The educational psychology series. Mahwah, NJ: Erlbaum.
31.
Jacobs, J.E., & Paris, S.G. (1987). Children's metacognition about reading: Issues in definition, measurement, and instruction. Educational Psychologist , 22, 255-278.
32.
Lucangeli, D., & Cornoldi, C. (1997). Mathematics and metacognition: What is the nature of the relationship? MathematicalCognition, 3, 121-139.
33.
Lucangeli, D., Cornoldi, C., & Tellarini, M. (1998). Metacognition and learning disabilities in mathematics . In T. E. Scruggs & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities (pp. 219-244). Greenwich, CT: JAI Press.
34.
Masui, C., & De Corte, E. (1999). Enhancing learning and problem solving skills: orienting and self-judging, two powerful and trainable learning tools. Learning and Instruction, 9, 517-542.
35.
McLeod, D.B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 575-596). New York: Macmillan.
36.
Meltzer, L., Roditi, B., Houser, R.F., & Perlman, M. (1998). Perceptions of academic strategies and competence in students with learning disabilities. Journal of Learning Disabilities, 31, 437-451.
37.
Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25, 230-248.
38.
Montague, M. (1997). Cognitive strategy instruction on arithmetics for students with learning disabilities. Journal of Learning Disabilities, 30, 164-177.
39.
Montague, M. (1998). Research on metacognition in special education . In T. E. Scruggs & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities (pp. 151-183). Greenwich: JAI Press.
40.
Mora, J., & Saldana, D. (1995, August). Metacognitive assessment: An intervention oriented instrument. Paper presented at the VIIth European Conference on Developmental Psychology, Kraków , Poland.
41.
Myers, M., & Paris, S.G. (1978). Children's metacognitive knowledge about reading . Journal of Educational Psychology, 70, 680-690.
42.
Pintrich, P.R., & Anderman, E.M. (1994). Intra-individual differences and cognition in students with and without learning disabilities. Journal of Learning Disabilities, 27, 360-370.
43.
Reder, M., & Schunn, D. (1996). Metacognition does not imply awareness: Strategy choice is governed by implicit learning and memory. In L. Reder (Ed.), Implicit memory and metacognition (pp. 45-77). Mahwah, NJ: Erlbaum.
44.
Schoenfeld, A.H. (1992). Learning to think arithmetically: Problem solving, metacognition, and sense making in arithmetics. In D. A. Grouws (Ed.), Handbook of research on arithmetics teaching and learning: A project of the National Council of Teachers of Arithmetics (pp. 334-370). New York: Simon & Schuster.
45.
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, UK: Elsevier Science.
46.
Siegler, R.S. (1989). How domain-general and domain-specific knowledge interact to produce strategy choices. Merrill-Palmer Quarterly , 35, 1-26.
47.
Simons, P.R.J. (1996). Metacognition. In E. De Corte & F. E. Weinert (Eds.), International encyclopedia of developmental and instructional psychology (pp. 436-444). Oxford, UK: Elsevier Science.
48.
Tabachnick, B.G., & Fidell, L.S. (1996). Using multivariate statistics (3rd ed.). Northridge: California State University.
49.
Vander Steene, G., Van Haasen, P., De Bruyn, D., Coetsier, P., Pijl, Y. , Poortinga, Y., Spilberg, N., & Stinissen, J. (Eds.). (1986). Wechsler intelligence scale for children-Revised. WISC-R. Lisse, The Netherlands: Swets & Zeitlinger .
50.
Vermeer, H. (1997). Sixth-grade students' mathematical problem-solving behaviour: Motivational variables and gender differences. Leiden, The Netherlands : Leiden University.
51.
Vermunt, J.D.H.M. (1996). Metacognitive, cognitive, and affective aspects of learning styles and strategies: A phenomenographic analysis. Higher Education, 31, 25-50.
52.
Verschaffel, L. (1999). Realistic mathematical modelling and problem solving in the upper elementary school: Analysis and improvement. In J. H. M. Hamers, J. E. H. Van Luit, & B. Csapo (Eds.), Teaching and learning thinking skills: Contexts of learning (pp. 215-240). Lisse, The Netherlands: Swets & Zeitlinger .
53.
Winne, P.H., & Perry, N.E. (2000). Measuring self-regulated learning. In M. Boekaerts, P. E. Pintrich , & M. Zeidner (Eds.), Handbook of self-regulation (pp. 531-566). San Diego: Academic Press.
54.
Wong, B.Y.L. (1996). Metacognition and learning disabilities. In B. Y. L. Wong (Ed.), The ABCs of learning disabilities (pp. 120-139). San Diego, CA : Academic Press.
