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Metacognition and errors: the impact of self-regulatory trainings in children with specific learning disabilities

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Abstract

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and performance. This assessment, in turn, can be helpful in the regulation of their own learning. In this regard, a body of literature suggests that the application of psychoeducational interventions that promote the development of mathematics-related metacognitive (e.g., control) processes, based on the analysis of the students’ errors, can successfully influence mathematics performance. The main objective of the current study was to investigate the impact of a metacognitive and cognitive training program developed to enhance various arithmetic skills (e.g., syntax, mental and written calculation), self-regulatory and control functions in primary and secondary school students exhibiting atypical mathematical development. Sixty-eight Italian children, 36 male and 32 female (mean age at pretest = 9.3 years, SD = 1.02 years), meeting the criteria for the diagnosis of dyscalculia or specific difficulties in mathematics, took part in the study. Of these, 34 children (i.e., experimental group) underwent the cognitive and self-regulatory intervention enhancing mathematics skills training for 16 weekly sessions. The remaining students were assigned to the control group. For a pre-test and post-test, a battery of standardized mathematical tests assessing different mathematics skills, such as written and mental operations, digit transcription and number ordering skills, was administered and provided a series of measures of calculation time and accuracy (i.e., number of errors). In the post-test, the experimental group exhibited better accuracy in written calculation and in digit transcription. Overall, the current outcomes demonstrate that psychoeducational interventions enriching metacognitive and mathematical achievements through error analysis may be an effective way to promote both the development of self-regulatory and control skills and mathematical achievement in children with atypical mathematical development.

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References

  • Ashcraft, M. A. (2016) Math anxiety: personal, educational, and cognitive consequences. Current Directions in Psychological Science 11(5):181–185

    Article  Google Scholar 

  • Baten, E., Praet, M., & Desoete, A. (2017). The relevance and efficacy of metacognition for instructional design in the domain of mathematics. ZDM Mathematics Education, 49, 613–623. https://doi.org/10.1007/s11858-017-0851-y.

    Article  Google Scholar 

  • Belacchi, C., Scalisi, T. G., Cannoni, E., & Cornoldi, C. (2008). Manuale CPM. Coloured progressive matrices. Standardizzazione Italiana [CPM manual. Coloured progressive matrices. Italian validation]. Firenze: Giunti O.S. Organizzazioni Speciali.

    Google Scholar 

  • Borkowski, J. G., & Muthukrishna, N. (1994). Lo sviluppo della metacognizione nel bambino: un modello utile per introdurre l’insegnamento metacognitivo in classe. Insegnare all’Handicappato, 8, 229–251.

    Google Scholar 

  • Cargnelutti, E., Tomasetto, C., & Passolunghi, M. C. (2016). How is anxiety related to math performance in young students? A longitudinal study of Grade 2 to Grade 3 children. Cognition and Emotion, 31, 755–764. https://doi.org/10.1080/02699931.2016.1147421.

    Article  Google Scholar 

  • Caviola, S., Mammarella, I., Cornoldi, C., & Lucangeli, D. (2009). A metacognitive visuospatial working memory training for children. International Electronic Journal of Elementary Education, 2(1), 122–136.

    Google Scholar 

  • Cornoldi, C. (Ed.). (2007). Difficoltà e disturbi dell’apprendimento [Learning difficulties and disabilities]. Bologna: Il Mulino.

    Google Scholar 

  • Cornoldi, C., Caponi, B., Focchiatti, R., Lucangeli, D., Todeschini, M., & Falco, G. (1995). Matematica e metacognizione [Mathematics and metacognition]. Trento: Edizioni Erickson.

    Google Scholar 

  • Cornoldi, C., Carretti, B., Drusi, S., & Tencati, C. (2015). Improving problem-solving in primary school students: the effect of a training program focusing on metacognition and working memory. British Journal of Educational Psychology, 85, 424–439. https://doi.org/10.1111/bjep.12083.

    Article  Google Scholar 

  • Cornoldi, C., & Cazzola, C. (2004). AC-MT 11–14. Test di valutazione delle abilità di calcolo e problem solving dagli 11 ai 14 anni Gruppo MT [AC-MT 11–14. Test for the assessment of calculation and problem solving skills from 11 to 14 years of age MT Group]. Trento: Edizioni Erickson.

    Google Scholar 

  • Cornoldi, C., Lucangeli, D., & Bellina, M. (2012). AC-MT 6–11. Test di valutazione delle abilità di calcolo e soluzione dei problemi Gruppo MT [AC-MT 6–11. Test for the assessment of calculation and problem solving skills from 6 to 11 years of age Gruppo MT]. Trento: Edizioni Erickson.

    Google Scholar 

  • Dennis, M. S., Sharp, E., Chovanes, J., Thomas, A., Burns, R. M., Custer, B., & Park, J. (2016). A meta-analysis of empirical research on teaching students with mathematics learning difficulties. Learning Disabilities Researche and Practice. https://doi.org/10.1111/ldrp.12107.

    Google Scholar 

  • Desoete, A., Roeyers, H., & De Clercq, A. (2003). Can off-line metacognition enhance mathematical problem solving? Journal of Educational Psychology, 95, 188–200. https://doi.org/10.1037/0022-0663.95.1.188.

    Article  Google Scholar 

  • Dinsmore, D. L., Alexander, P. A., & Loughlin, S. M. (2008). Focusing the conceptual lens on metacognition, self-regulation, and self-regulated learning. Educational Psychology Review, 20(4), 469–475.

    Article  Google Scholar 

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428.

    Article  Google Scholar 

  • Fastame, M. C., & Callai, D. (2015). Empowering visuo-spatial ability in primary school: Results from a follow-up study. Educational Psychology in Practice, 31, 86–98. https://doi.org/10.1080/02667363.2014.989315.

    Article  Google Scholar 

  • Flavell, J. H. (1979). Meta-cognitive and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 31, 906–911.

    Article  Google Scholar 

  • Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal of Research in Mathematics Education, 16, 163–176.

    Article  Google Scholar 

  • Geary, D. C., Hoard, M. K., & Bailey, D. H. (2012). Fact retrieval deficits in low achieving children and children with mathematical learning disability. Journal of Learning Disabilities, 45, 291–307. https://doi.org/10.1177/0022219410392046.

    Article  Google Scholar 

  • Hultsch, D. F., Herzog, C., Dixon, R. A., & Davidson, H. (1988). Memory self-knowledge and self-efficacy in the aged. In M. L. Howe e C. J. Brainerd (Eds.), Cognitive development in adulthood: Progress in developmental research (pp. 65–92). New York: Springer.

    Chapter  Google Scholar 

  • Jitendra, A. K., Lein, A. E., Im, S. H., Alghamdi, A. A., Hefte, S. B., & Mouanoutoua, J. (2018). Mathematical interventions for secondary students with learning disabilities and mathematics difficulties: A meta-analysis. Exceptional Children, 84(2), 177–196. https://doi.org/10.1177/0014402917737467.

    Google Scholar 

  • Lucangeli, D., Cornoldi, C., & Tessari, F. (1991). Bambini con disturbi di apprendimento in lettura e matematica: Aspetti comuni e specificità nei deficit cognitivi e di conoscenza metacognitiva. Psichiatria dell’Infanzia e dell’Adolescenza, 58(5–6), 629–664.

    Google Scholar 

  • Lucangeli, D., & Mammarella, I. (2010). Psicologia della cognizione numerica: Approcci teorici, valutazione e intervento [Numerical knowledge psychology: Theory, assessment and intervention]. Milan: Franco Angeli.

    Google Scholar 

  • Mevarech, Z., & Fridkin, S. (2006). The effects of IMPROVE on mathematical knowledge, mathematical reasoning and meta-cognition. Metacognition Learning. https://doi.org/10.1007/s11409-006-6584-x.

    Google Scholar 

  • Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34, 365–395. https://doi.org/10.3102/00028312034002365.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics (NCTM): Reston.

    Google Scholar 

  • Nelson, G., & Powell, S. R. (2017). A systematic review on longitudinal studies of mathematics difficulty. Journal of Learning Disabilities. https://doi.org/10.1177/0022219417714773.

    Google Scholar 

  • Orsini, A., Pezzuti, L., & Picone, L. (2011). WISC-IV. Contributo alla taratura Italiana. [WISC-IV Italian edition]. Firenze: Giunti, OS.

    Google Scholar 

  • Raven, J. C., & Court, J. H. (1998). Raven's progressive matrices and vocabulary scales. Oxford: Oxford Pyschologists Press.

    Google Scholar 

  • Re, A. M., Benavides-Varela, S., Pedron, M., De Gennaro, M. A., & Lucangeli, D. (submitted). Response to specific and digitally supported training for students with mathematical difficulties. 

  • Re, A. M., Pedron, M., Tressoldi, P. E., & Lucangeli, D. (2014). Response to specific training for students with different levels of mathematical difficulties: A controlled clinical study. Exceptional Children, 80(3), 337–352. https://doi.org/10.1177/0014402914522424.

    Google Scholar 

  • Rivera-Batiz, F. L. (1992). Quantitative literacy and the likelihood of employment among young adults in the United States. Journal of Human Resources, 27, 313–328. https://doi.org/10.2307/145737.

    Article  Google Scholar 

  • Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM The International Journal on Mathematics Education, 42, 149–161. https://doi.org/10.1007/s11858-010-0240-2.

    Article  Google Scholar 

  • Trainin, G., & Swanson, H. L. (2005). Cognition, metacognition, and achievement of college students with learning disabilities. Learning Disability Quarterly, 28, 261–272.

    Article  Google Scholar 

  • Veggetti, M. S. (1974). Storia dello sviluppo delle funzioni psichiche superiori. Firenze: Giunti-Barbera.

    Google Scholar 

  • Vygotskij, L. S. (1931). Istorija razvitija vysših psichi eskih funkcuj, in Sobrani so inenij, vol. 3 Moskva: Pedagogijka.

    Google Scholar 

  • Wang, A. H., Shen, F., & Byrnes, J. P. (2013). Does the opportunity-propensity framework predict the early mathematics skills of low-income pre-kindergarten children? Contemporary Educational Psychology, 38, 259–270. https://doi.org/10.1016/j.cedpsych.2013.04.004.

    Article  Google Scholar 

  • Wechsler, D. (2003). Wechsler intelligence scale for children: Fourth edition. San Antonio: Psychological Corporation.

    Google Scholar 

Download references

Acknowledgements

The authors thank the children who participated in the study and their families and the Polo Apprendimento Centres in Como, Fermo, Monselice, Padova, Porto Viro, Prato, Sardegna, Treviso and Vicenza.

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Authors and Affiliations

  1. Università degli Studi di Padova, Padua, Italy

    Daniela Lucangeli

  2. Università degli Studi di Cagliari, Cagliari, Italy

    Maria Chiara Fastame, Annamaria Porru & Maria Pietronilla Penna

  3. Polo Apprendimento, Padua, Italy

    Martina Pedron & Valeria Duca

  4. Università di Pisa, Pisa, Italy

    Paul Kenneth Hitchcott

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  1. Daniela Lucangeli
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  2. Maria Chiara Fastame
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  3. Martina Pedron
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  4. Annamaria Porru
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  5. Valeria Duca
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  6. Paul Kenneth Hitchcott
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  7. Maria Pietronilla Penna
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Correspondence to Martina Pedron.

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Lucangeli, D., Fastame, M.C., Pedron, M. et al. Metacognition and errors: the impact of self-regulatory trainings in children with specific learning disabilities. ZDM Mathematics Education 51, 577–585 (2019). https://doi.org/10.1007/s11858-019-01044-w

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