Abstract
Metacognition is a powerful predictor for learning performance, and for problem-solving. But how metacognition works for cognitive strategies and learning performance is not clear. The present study was designed to explore how metacognition affected the cognition (learning strategies and problem solving strategies) and different kinds of learning performance involving the development of metacognition for adolescents. In a first study, we explored the structure of metacognition by examining multiple theoretical frameworks and the psychometric characteristics of metacognition. The Bifactor model confirmed the two processes modeling of domain-general versus domain-specific monitoring for different tasks in reading and mathematics. In a second study, a path model was used to explore the effect of metacognition on learning strategies, problem-solving strategies, and performance of reading and mathematics. The relationships in the model were tested controlling gender and age. Results showed that problem-solving was the only mediator between general metacognition and learning performance. It is suggested that the subcomponents of metacognition be involved in future studies.
Similar content being viewed by others
References
Aghaie, R., & Zhang, L. J. (2012). Effects of explicit instruction in cognitive and metacognitive reading strategies on Iranian EFL students’ reading performance and strategy transfer. Instructional Science, 40(6), 1063–1081. https://doi.org/10.1007/s11251-011-9202-5.
Alcock, J. (2009). Animal behavior: An evolutionary approach (9th ed.). Sunderland: Sinauer. https://doi.org/10.1086/650244.
Artelt, C., & Schneider, W. (2015). Cross-country generalizability of the role of metacognitive knowledge in students’ strategy use and reading competence. Teachers College Record, 117(1), 51–60. http://www.tcrecord.org/Content.asp?ContentId=17695.
Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), 1173–1182. https://doi.org/10.1037/0022-3514.51.6.1173.
Bentler, P. M. (2009). Alpha, dimension-free, and model-based internal consistency reliability. Psychometrika, 74(1), 137–143. https://doi.org/10.1007/s11336-008-9100-1.
Brophy, J. (1986). Teaching and learning mathematics: Where research should be going. Journal for Research in Mathematics Education, 17(5), 323–346. https://doi.org/10.2307/749326.
Brown, A. L. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation and understanding (pp. 65–116). Hillsdale, NJ: Lawrence Erlbaum Associates.
Brown, A. L., & Smiley, S. S. (1977). Rating the importance of structural units of prose passages: a problem of metacognitive development. Child Development, 48(1), 1–8.
Carr, M., & Jessup, D. L. (1997). Gender differences in first-grade mathematics strategy use: Social and metacognitive influences. Journal of Educational Psychology, 89(2), 318–328. https://doi.org/10.1037/0022-0663.89.2.318.
Chen, F. F., Hayes, A., Carver, C. S., Laurenceau, J., & Zhang, Z. (2012). Modeling general and specific variance in multifaceted constructs: A comparison of the bifactor model to other approaches. Journal of Personality, 80(1), 219–251. https://doi.org/10.1111/j.1467-6494.2011.00739.x.
Chen, F. F., West, S. G., & Sousa, K. A. (2006). A comparison of bifactor and second-order models of the quality of life. Multivariate Behavioral Research, 41, 189–225. https://doi.org/10.1207/s15327906mbr4102_5.
Chiappe, D., & MacDonald, K. (2005). The evolution of domain-general mechanisms in intelligence and learning. The Journal of General Psychology, 132(1), 5–40. https://search.proquest.com/docview/213646995?accountid=8554.
Christoph, L. H. (2006). The role of metacognitive skills in learning to solve problems. School Science & Mathematics, 56(9), 701–707. https://doi.org/10.1111/j.1949-8594.1956.tb16904.x.
Chrysikou, E. G. (2006). When shoes become hammers: Goal-derived categorization training enhances problem-solving performance. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32(4), 935–942. https://doi.org/10.1037/0278-7393.32.4.935.
Cohen, A. D., & Macaro, E. (2007). Language learner strategies: Thirty years of research and practice. Oxford: Oxford University Press.
Confer, J. C., Easton, J. A., Fleischman, D. S., Goetz, C. D., Lewis, D. M. G., Perilloux, C., et al. (2010). Evolutionary psychology: Controversies, questions, prospects, and limitations. American Psychologist, 65(2), 110–126. https://doi.org/10.1037/a0018413.
Desoete, A., Roeyers, H., & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities, 34(5), 435. https://doi.org/10.1177/002221940103400505.
Dignath, C., & Büttner, G. (2008). Components of fostering self-regulated learning among students. A meta-analysis on intervention studies at primary and secondary school level. Metacognition & Learning, 3(3), 231–264. https://doi.org/10.1007/s11409-008-9029-x.
Efklides, A. (2006). Metacognition and affect: What can metacognitive experiences tell us about the learning process? Educational Research Review, 1, 3–14. https://doi.org/10.1016/j.edurev.2005.11.001.
Efklides, A. (2008). Metacognition: Defining its facets and levels of functioning in relation to self-regulation and co-regulation. European Psychologist, 13(4), 277–287. https://doi.org/10.1027/1016-9040.13.4.277.
Erbas, A. K., & Okur, S. (2012). Researching students’ strategies, episodes, and metacognitions in mathematical problem solving. Quality & Quantity, 46(1), 89–102. https://doi.org/10.1007/s11135-010-9329-5.
Fitzgerald, L. M., Arvaneh, M., & Dockree, P. M. (2017). Domain-specific and domain-general processes underlying metacognitive judgments. Consciousness and Cognition: An International Journal, 49, 264–277. https://doi.org/10.1016/j.concog.2017.01.011.
Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–235). New York: Nova Science Publishers.
Flavell, J. H. (1978). Metacognitive development. In C. J. Brainerd (Ed.), Scandura JM. Alphen a. d. Rijn: Structural/process theories of complex human behavior. Sijthoff & Noordhoff.
Flavell, J. H., Miller, P. H., & Miller, S. A. (2002). Cognitive development (4th ed.). Upper Saddle River, NJ: Prentice Hall.
Flavell, J. H., & Wellman, H. M. (1977). Metamemory. In R. V. Kail & J. W. Hagen (Eds.), Perspectives on the development of memory and cognition. Hillsdale: Lawrence Erlbaum Associates.
Fleming, S. M., Ryu, J., Golfinos, J. G., & Blackmon, K. E. (2014). Domain-specific impairment in metacognitive accuracy following anterior prefrontal lesions. Brain A Journal of Neurology, 137(10), 2811–2822. https://doi.org/10.1093/brain/awu221.
Frost, R., Armstrong, B. C., Siegelman, N., & Christiansen, M. H. (2015). Domain generality versus modality specificity: The paradox of statistical learning. Trends in Cognitive Sciences, 19(3), 117–125. https://doi.org/10.1016/j.tics.2014.12.010.
Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176. https://doi.org/10.2307/748391.
Gaultney, J. F. (1995). The effect of prior knowledge and metacognition on the acquisition of a reading comprehension strategy. Journal of Experimental Child Psychology, 59(1), 142–163. https://doi.org/10.1006/jecp.1995.1006.
Georghiades, P. (2004). Making pupils’ conceptions of electricity more durable by means of situated metacognition research report. International Journal of Science Education, 26(1), 85–99.
Gick, M. L. (2013). Problem-solving strategies. Educational Psychologist, 21(1–2), 99–120. https://doi.org/10.1080/00461520.1986.9653026.
Heppner,P.P. (1988). The problem-solving inventory (PSI) Research manual. Counsukting Psychologist Press.
Holzinger, K. J., & Swineford, F. (1937). The bi-factor method. Psychometrika, 2, 41–54. https://doi.org/10.1007/BF02287965.
Jonassen, D. H., & Cpt, E. R. G. (2010). Learning to solve problems. Performance Improvement, 44(9), 45–47. https://doi.org/10.1002/pfi.4140440909.
Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of, cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281–310. https://doi.org/10.3102/00028312040001281.
Künsting, J., Kempf, J., & Wirth, J. (2013). Enhancing scientific discovery learning through metacognitive support. Contemporary Educational Psychology, 38(4), 349–360. https://doi.org/10.1016/j.cedpsych.2013.07.001.
Mccurdy, L. Y., Maniscalco, B., Metcalfe, J., Liu, K, Y., de lange, F. P., & Lau, H. (2013). Anatomical coupling between distinct metacognitive systems for memory and visual perception. Journal of Neuroscience, 33(5), 1897–1906. https://doi.org/10.1523/JNEUROSCI.1890-12.2013.
Meijer, J., & Veenman, M. V. J. (2006). Metacognitive activities in text-studying and problem-solving: development of a taxonomy. Educational Research & Evaluation, 12(3), 209–237. https://doi.org/10.1080/13803610500479991.
Mevarech, Z., & Fridkin, S. (2006). The effects of improve on mathematical knowledge, mathematical reasoning and meta-cognition. Metacognition & Learning, 1(1), 85–97. https://doi.org/10.1007/s11409-006-6584-x.
Mohammadi, Y., Kaykha, K., Sadeghi, A., Kazemi,S., & Raeisoon, M. R. (2015). Relationship of metacognition learning strategy and locus of control with academic achievement of students. Bimonthly of Education Strategies in Medical Sciences, 8(5), 323–328. http://edcbmj.ir/article-1-892-en.html.
OECD. (2010). PISA 2009 Assessment framework: Key competencies in reading, mathematics and science. Paris: OECD Publishing. https://doi.org/10.1787/9789264062658-en.
OECD. (2013). PISA 2012 Assessment and analytical framework: Mathematics, reading, science, problem solving and financial literacy. Paris: OECD Publishing. https://doi.org/10.1787/9789264190511-en.
Opstal, M. T. V., & Daubenmire, P. L. (2015). Extending students’ practice of metacognitive regulation skills with the science writing heuristic. International Journal of Science Education, 37(7), 1089–1112. https://doi.org/10.1080/09500693.2015.1019385.
Oxford, R. L. (2011). Teaching and researching language learning strategies. Harlow: Longman. https://doi.org/10.4324/9781315838816.
Pehkonen, E., Näveri, L., & Laine, A. (2013). On teaching problem solving in school mathematics. CEPS Journal: Center for Educational Policy Studies Journal, 3(4), 9–23. https://doi.org/10.1002/dir.4000010209.
Pishghadam, R., & Khajavy, G. H. (2013). Intelligence and metacognition as predictors of foreign language achievement: a structural equation modeling approach. Learning & Individual Differences, 24(2), 176–181. https://doi.org/10.1016/j.lindif.2012.12.004.
Pugalee, D. K. (2010). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science & Mathematics, 101(5), 236–245. https://doi.org/10.1111/j.1949-8594.2001.tb18026.x.
Reise, S. P., Moore, T. M., & Haviland, M. G. (2010). Bifactor models and rotations: Exploring the extent to which multidimensional data yield univocal scale scores. Journal of Personality Assessment, 92(6), 544. https://doi.org/10.1080/00223891.2010.496477.
Riding, R., & Rayner, S. (2000). Cognitive styles and learning strategies. Understanding style differences in learning and behaviour. London: David Fulton Publishers.
Rios, J., & Wells, C. (2014). Validity evidence based on internal structure. Psicothema, 26(1), 108–116. https://doi.org/10.7334/psicothema2013.260.
Satorra, A., & Bentler, P. M. (2010). Ensuring positiveness of the scaled difference Chi square test statistic. Psychometrika, 75(2), 243–248. https://doi.org/10.1007/s11336-009-9135-y.
Schellings, G. L. M., van Hout-Wolters, B. H. A. M., Veenman, M. V., & Meijer, J. (2013). Assessing metacognitive activities: The in-depth comparison of a task-specific questionnaire with think-aloud protocols. European Journal of Psychology of Education, 28(3), 963–990. https://doi.org/10.1007/s10212-012-0149-y.
Scherer, R., & Tiemann, R. (2012). Factors of problem-solving competency in a virtual chemistry environment: The role of metacognitive knowledge about strategies. Computers & Education, 59(4), 1199–1214. https://doi.org/10.1016/j.compedu.2012.05.020.
Schoenfeld, A. H. (1983). Episodes and executive decisions in mathematical problem solving. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 345–395). New York: Academic Press.
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: A project of the National Council of Teachers of Mathematics (pp. 334–370). New York, NY: Macmillan Publishing Co.
Schraw, G., Dunkle, M. E., Bendixen, L. D., & Roedel, T. D. (1995). Does a general monitoring skill exist? Journal of Educational Psychology, 87(3), 433–444. https://doi.org/10.1037/0022-0663.87.3.433.
Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational Psychology Review, 7(4), 351–371. https://doi.org/10.1007/BF02212307.
Sperling, R. A., Howard, B. C., Staley, R., & DuBois, N. (2004). Metacognition and self-regulated learning constructs. Educational Research and Evaluation, 10, 117–139. https://doi.org/10.1076/edre.10.2.117.27905.
Stel, M. V. D., & Veenman, M. V. J. (2014). Metacognitive skills and intellectual ability of young adolescents: A longitudinal study from a developmental perspective. European Journal of Psychology of Education, 29(1), 117–137. https://doi.org/10.1007/s10212-013-0190-5.
Taasoobshirazi, G., & Farley, J. (2013). Construct validation of the physics metacognition inventory. International Journal of Science Education, 35(3), 447. https://doi.org/10.1080/09500693.2012.750433.
Thiessen, V., & Blasius, J. (2008). Mathematics achievement and mathematics learning strategies: Cognitive competencies and construct differentiation. International Journal of Educational Research, 47(6), 362–371. https://doi.org/10.1016/j.ijer.2008.12.002.
Thorpe, K., & Satterly, D. J. H. (1990). The development and inter-relationship of metacognitive components among primary school children. Educational Psychology: An International Journal of Experimental Educational Psychology, 10(1), 5–21. https://doi.org/10.1080/0144341900100102.
Veenman, M. V. J. (2011). Alternative assessment of strategy use with self-report instruments: a discussion. Metacognition and Learning, 6(2), 205–211. https://doi.org/10.1007/s11409-011-9080-x.
Veenman, M. V. J., & Spaans, M. A. (2005). Relation between intellectual and metacognitive skills: Age and task differences. Learning & Individual Differences, 15(2), 159–176. https://doi.org/10.1016/j.lindif.2004.12.001.
Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3–14. https://doi.org/10.1007/s11409-006-6893-0.
Veenman, M. V. J., & Verheij, J. (2003). Technical students’ metacognitive skills: Relating general vs specific metacognitive skills to study success. Learning & Individual Differences, 13(3), 259–272. https://doi.org/10.1016/S1041-6080(02)00094-8.
Vista, A. (2012). The role of problem solving ability and reading comprehension skill in predicting growth trajectories of mathematics achievement between ESB and BESB students. Melbourne Graduate School of Education. http://hdl.handle.net/11343/37570.
Vrugt, A., & Oort, F. J. (2008). Metacognition, achievement goals, study strategies and academic achievement: pathways to achievement. Metacognition & Learning, 3(2), 123–146. https://doi.org/10.1007/s11409-008-9022-4.
Wang, M. C., Haertel, G. D., & Walberg, H. J. (1990). What influences learning? A content analysis of review literature. Journal of Educational Research, 84(1), 30–43. https://doi.org/10.1080/00220671.1990.10885988.
Youngju, J., & Dongsim, K. (2015). The structural relationship among metacognition, interactions, problem solving ability and achievement in gifted students through the 3p model. Journal of Gifted/talented Education, 25(1), 161–177. https://doi.org/10.9722/JGTE.2015.25.1.161.
Yüksel, İ., & Yüksel, İ. (2012). Metacognitive awareness of academic reading strategies. Procedia-Social and Behavioral Sciences, 31, 894–898. https://doi.org/10.1016/j.sbspro.2011.12.164.
Zhao, N., Valcke, M., Desoete, A., Zhu, C., Sang, G., & Verhaeghe, J. (2014). A holistic model to infer mathematics performance: The interrelated impact of student, family and school context variables. Scandinavian Journal of Educational Research, 58(1), 1–20. https://doi.org/10.1080/00313831.2012.696210.
Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ω h: Their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 123–133. https://doi.org/10.1007/s11336-003-0974-7.
Zohar, A., & David, A. B. (2008). Explicit teaching of meta-strategic knowledge in authentic classroom situations. Metacognition & Learning, 3(1), 59–82. https://doi.org/10.1007/s11409-007-9019-4.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhao, N., Teng, X., Li, W. et al. A path model for metacognition and its relation to problem-solving strategies and achievement for different tasks. ZDM Mathematics Education 51, 641–653 (2019). https://doi.org/10.1007/s11858-019-01067-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11858-019-01067-3