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Metacognition in Mathematics: Does The Research Evidence Confirm Its Significance?

Metacognition is often defined as "thinking about thinking"; metacognitive pedagogies focus on the planning, monitoring, evaluation and regulation of cognition. Definitions range in their breadth with some definitions being narrow (referring to task-specific activities) whilst others referring to more generalised forms of reflection and self-regulation. Metacognition can be explained as individuals’ use of information while they are learning or fulfilling a task and a deliberate organisation in cognitive processes (Brown, Bransford, Ferrara & Campione, 1983); metacognition occurs as a result of one’s individual evaluation and observation of their cognitive behaviour in a learning environment (Ayersman, 1995).


In ‘How People Learn, the National Academy of Sciences’ synthesis of decades of research on the science of learning, one of the three key findings of this work is the effectiveness of a “‘metacognitive’ approach to instruction” (Bransford, Brown, & Cocking, 2000, p. 18): metacognition, especially the ability for students to evaluate their own level of understanding, is an essential component of self-regulated learning. An Analysis of Research on Metacognitive Teaching Strategies (Ellis et al 2014) concludes metacognition to be an effective strategy especially when used regularly and accompanied by effective teacher modelling.

The following article provides a summary of recent peer reviewed research evidencing the benefits of metacognition in primary and secondary mathematics classrooms:


• Desoete et al. (2019) showed that the metacognitive skills of Belgian children were related to accuracy in mathematics during the whole elementary school period. With R2 varying from 0.03 (in Grade 2 about 4% explained variance) to 0.16 (in Grade 6 about 16% explained variance), metacognitive skills were significant predictors of mathematical accuracy in all grades.


• Faradiba et al (2019) explored the concept of 'metacognitive blindness' in the mathematics learning process. They refer two three 'red flags' that can help teachers identify metacognitive blindness: e lack of progress (LP), error detection (ED), and anomalous results (AR). The results of the analysis show that students who experience math anxiety can experience metacognitive blindness during the problem-solving process. Red flag, which is dominant in metacognitive blindness, is error detection. This red flag occurs because subjects with mathematics anxiety pay less attention to the details of the problem, so they miss a lot of important information. This research also points to the need for a focus on emotional self-regulation training in the classroom.


• Hidayat et al (2018) investigated the relationship between metacognition and achievement goals which may influence mathematical modelling competency in students (aged 18-21) of mathematics education programs. Studying 538 students of mathematics education program the researchers found that indicate that achievement goals and metacognition positively influence mathematical modelling competency. Moreover, four metacognition dimensions including awareness, planning, cognitive strategy and self-checking are positive partial mediators because they increase the association between achievement goals and mathematical modelling competency.


• Baten et al. (2019) confirmed this parallel relationship between the metacognitive post-diction skills of Belgian elementary school children from Grades 4 to 6 and their mathematical accuracy and speed. This may suggest that teachers ought to pay attention to the componential nature of mathematics and to the accuracy of self-judgments of children when they analyse metacognition in mathematics education. Using the metacognitive awareness inventory may be useful towards this end.


• Özcan et a. (2019) investigate the direct and indirect effects of a number non-cognitive constructs such as mathematics self-efficacy, mathematics anxiety, and metacognitive experience on the mathematical problem solving of middle-school students. Metacognitive experience was found to be the only non-cognitive construct, which had a direct effect on mathematical problem-solving performance; it also mediated the effects of self-efficacy, motivation, and mathematics anxiety on performance.


• Hacker et al. (2019) highlighted how through a metacognitive intervention students improvement in the accuracy of fraction calculations and of the confidence in those calculations. Their intervention shows that metacognitive interventions helped the children become more self-regulated learners.


• Ismirawati et al. (2020) investigated the significanc of metacognitive skills in distance-learning (e-learning in this case) procedures: they found a significant correlation between metacognitive skills and cognitive learning results, with the influence of 85.6% and the linear regression equation is Y = 0.880X + 13.11.


• Trigueros et al. (2020) found that metacognition plays a vital role in increasing student motivation in both the Mathematics and English classroom. In their analysis of over 200 students and the teaching behaviours of 32 teachers they found that motivation showed a positive relationship with metacognition strategies and academic performance. Similarly, metacognition strategies showed a positive relationship with academic achievement. The authors explained this in terms of the fact that metacognitive strategies are procedures that facilitate information processing by selecting, organizing, and regulating cognitive processes


• Veenman et al. (2019) confirmed the findings of their previous (2006) study: that metacognitive skills accounted for about 40% of the variance in mathematics performance. Their more recent study showed a significant correlation between mathematics problem solving and the systematic observation measure (r = 0.52) as well as with the think-aloud protocol (r = 0.71) and the retrospective questionnaire (r = 0.34) for secondary-school students (aged 14–15 years old) in the Netherlands.


• Lucangeli et al. (2019) reached the conclusion that psycho-educational interventions that enrich metacognitive and mathematical success through error analysis may be an effective way to develop self-regulatory and control skills and mathematical achievement in children from Grade 2 of elementary school till Grade 1 of secondary school. Their research focused on students with learning-disabilities and suggests that error-analysis is of particular relevance to such students.


• Muhali et al. (2020) investigated the content and construct validity of the Reflective-Metacognitive Learning (RML) Model, and the effectiveness of the RML Model in comparison with Cognitive-Metacognitive Learning (CML) Model in improving students’ metacognitive knowledge, skills, and awareness after the learning process. The results showed that the Reflective-Metacognitive Learning Model [which is marked by the reflection of thinking processes as the core] was highly valid in terms of content validity and construct validity, Metacognitive knowledge increased to a high degree, while metacognitive skills and awareness increased to a medium degree. Based on the results, it was concluded that the RML Model was valid and more effective than the Cognitive-Metacognitive Learning Model in terms of improving students’ metacognitive ability.



An Overview of Meta-Analyses into the Impact of Metacognition in Mathematics Education


Dignath & Büttner (2008) conducted two meta-analyses separately, one for primary and one for secondary school level to allow for comparisons between both school levels. The meta-analyses included 49 studies conducted with primary school students and 35 studies conducted with secondary school students; analyzing 357 effect sizes altogether. The potential effects of training characteristics were investigated by means of meta-analytic multiple regression analyses. The average effect size was 0.69. For both school levels, effect sizes were higher when the training was conducted by researchers instead of regular teachers. Moreover, interventions attained higher effects when conducted in the scope of mathematics than in reading/writing or other subjects.


Metacognitive strategies in the mathematics classroom were found to have a similar impact in a subsequent meta-analysis from Donker et al (2014): based on a total of 95 interventions and 180 effect sizes demonstrated substantial effects in the domains of writing (Hedges’ g = 1.25), science (.73), mathematics (.66) and comprehensive reading (.36).



Teaching Resources for Metacognition in the Secondary Mathematics Classroom


If you are an educator hoping to use new metacognitive strategies in your lessons, have a look at our 'Metacognition in Mathematics Toolkit': it contains a wide selection of teaching tools and resources that will help you to bring metacognition into your maths lessons!


References


Ayersman, D. J. (1995). Effects of Knowledge Representation Format and Hypermedia Instruction on Metacognitive Accuracy. Computers in Human Behavior, 11(3-4), 533-555.


Baten, E., & Desoete, A. (2019). Metacognition and motivation in school-aged children with and without learning disabilities in Flanders. ZDM Mathematics Education, 51 (4), this issue. https://doi.org/10.1007/s11858-018-01024-6


Bransford, John D., Brown Ann L., and Cocking Rodney R. (2000). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.


Brown, A. L., Bransford, J. D., Ferrara, R. A. and Campione, J. C. (1983). “Learning, Remembering, and Understanding”. In P. H. Mussen (Ed.). Handbook of Child Psychology (pp.77-166). New York: John Wiley.


Desoete, A., Baten, E., Vercaemst, V. De Busschere, A., Baudonck, M., & Vanhaeke, J. (2019). Metacognition and motivation as predictors for mathematics performance of Belgian elementary school children. ZDM Mathematics Education, 51 (4), this issue. https://doi.org/10.1007/s11858-018-01020-w.


Donker,A.S., H. de Boer, D. Kostons, C.C. Dignath van Ewijk, M.P.C. van der Werf, Effectiveness of learning strategy instruction on academic performance: A meta-analysis, Educational Research Review, Volume 11, 2014, Pages 1-26, ISSN 1747-938X,https://doi.org/10.1016/j.edurev.2013.11.002.


Ellis, Arthur & Denton, David & Bond, John. (2014). An Analysis of Research on Metacognitive Teaching Strategies. Procedia - Social and Behavioral Sciences. 116. 10.1016/j.sbspro.2014.01.883.


Faradiba (2019) Looking Without Seeing: The Role Of Metacognitive Blindness Of Student With High Math AnxietY Surya Sari Faradiba; Cholis Sa'dijah, Prof , M A; Nengah Parta, M Si; Swasono Rahardjo, M Si.International Journal of Cognitive Research in Science, Engineering and Education; Vranje Vol. 7, Iss. 2, (2019): 53-65. DOI:10.5937/IJCRSEE1902053F


Hacker, D. J., Kiuhara, S. A., & Levin, J. R. (2019). Project FACT+R2C2: Developing proficiency with fractions and literacy for students with mathematics learning disabilities. ZDM Mathematics Education, 51 (4), this issue.


Hidayat R, Zulnaidi H, Syed Zamri SNA (2018) Roles of metacognition and achievement goals in mathematical modeling competency: A structural equation modeling analysis. PLoS ONE 13(11): e0206211. https://doi.org/10.1371/journal.pone.0206211


Ismirawati, Nur & Corebima Aloysius, Duran & Zubaidah, Siti & Ristanto, Rizhal & Nuddin, Andi. (2020). Implementing ERCoRe in Learning: Will Metacognitive Skills Correlate to Cognitive Learning Result?. 8. 51-58. 10.13189/ujer.2020.081808.


Lucangeli, D., Penna, M. P., Fastame, M. C., Pedron, M., Porru, A., & Duca, V. (2019). Metacognition and errors: The impact of self-regulatory trainings in children with specific learning disabilities. ZDM Mathematics Education, 51 (4), this issue.


Muhali; YUANITA, Leny; IBRAHIM, Muslimin. The Validity and Effectiveness of the Reflective-Metacognitive Learning Model to Improve Students’ Metacognition Ability in Indonesia. Malaysian Journal of Learning and Instruction, [S.l.], v. 16, n. 2, p. 33-74, dec. 2019. ISSN 2180-2483. Available at: <http://e-journal.uum.edu.my/index.php/mjli/article/view/mjli2019.16.2.2>. Date accessed: 23 nov. 2020. doi: https://doi.org/10.32890/mjli2019.16.2.2.


Özcan ZÇ, Eren Gümüş A. A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety. Australian Journal of Education. 2019;63(1):116-134. doi:10.1177/0004944119840073


Trigueros Ruben, Aguilar-Parra José M., Lopez-Liria Remedios, Cangas Adolfo J., González Jerónimo J., Álvarez Joaquín F. 2020 Front. Psychol., 09 January 2020 | https://doi.org/10.3389/fpsyg.2019.02794 The Role of Perception of Support in the Classroom on the Students’ Motivation and Emotions: The Impact on Metacognition Strategies and Academic Performance in Math and English Classes


Veenman, M. V. J., & van Cleef, D. (2019). Measuring metacognitive skills for mathematics: Students’ self-reports vs. online assessment methods. ZDM Mathematics Education, 51 (4), this issue.