Metacognitive strategies in mathematical modelling activities: structuring an identification instrument

Authors

  • Lourdes Maria Werle De Almeida Universidade Estadual de Londrina
  • Élida Maiara Velozo de Castro Universidade Estadual de Londrina

https://doi.org/10.17583/redimat.12926

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Abstract

The paper aims to propose an instrument to identify students’ metacognitive strategies in mathematical modelling activities. The items were designed from a review regards metacognition and instrumensts already recognised in literature. This design comprises an instrument that differs from others in which the data were the self-reported students’ use of metacognitive strategies. The instrument we propose is aimed at the teacher and it is he/she who, based on an analytical process, will infer whether the students use metacognitive strategies in modelling activities. An empirical research was realized and five modelling problems were solved by students of a mathematics degree. The analysis addressed the groups actions and the individual behaviour within the group when working on modelling processes. The results allow to conclude working successfully and in a goal-oriented manner on modelling problems requires metacognitive strategies and the instrument seems to be adequate for the teacher to identify these students' strategies.

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References

Almeida, L. M. W. (2018). Considerations on the use of mathematics in modeling activities.

Google Scholar Crossref

ZDM, 50(1), 19-30.

Google Scholar Crossref

Blum, W. (2009). Can modelling be taught and learnt? Some answers from empirical

Google Scholar Crossref

research. Journal of Mathematical Modelling and Application. 1(1) 45-58

Google Scholar Crossref

Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can

Google Scholar Crossref

we do? In The proceedings of the 12th international congress on mathematical education

Google Scholar Crossref

pp. 73-96. Springer, Cham.

Google Scholar Crossref

Brown, A. (1987). Metacognition, executive control, self-regulation, and other more

Google Scholar Crossref

mysterious mechanisms. In: F. E. Weinert & R. Kluwe (Orgs.) Metacognition, motivation,

Google Scholar Crossref

and understanding, pp. 1-16.

Google Scholar Crossref

Carreira, S., Baioa, A. M., & Almeida, L. M. W. (2020). Mathematical models and meanings

Google Scholar Crossref

by school and university students in a modelling task. Avances de investigación en

Google Scholar Crossref

educación matemática, 17(1), 67-83.

Google Scholar Crossref

Castro, E. M. V. & Almeida, L. M. W. (2023). Estratégias metacognitivas de estudantes

Google Scholar Crossref

brasileiros em atividades de modelagem matemática. Revista Actualidades Investigativas

Google Scholar Crossref

en Educación, 23(1), 1-26. Doi. https://doi.org/10.15517/aie.v23i1.51512

Google Scholar Crossref

Cevikbas, M.; Kaiser, G. & Schukajlow, S. (2022). A systematic literature review of the

Google Scholar Crossref

current discussion on mathematical modelling competencies: state-of-the-art developments

Google Scholar Crossref

in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 109(2),

Google Scholar Crossref

-236.

Google Scholar Crossref

Desoete, A. & De Craene, B. (2019). Metacognition and mathematics education: an

Google Scholar Crossref

overview. ZDM, 51(4), 565–575. https://doi.org/10.1007/s11858-019-01060-w

Google Scholar Crossref

Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The

Google Scholar Crossref

nature of intelligence. Hillsdale, NJ: Erlbaum, (pp. 231-235), 1976.

Google Scholar Crossref

Fredj, P. & Vos, P. (2022). A commentary on the Special Issue “Innovations in measuring

Google Scholar Crossref

and fostering mathematical modelling competencies”. Educational Studies in

Google Scholar Crossref

Mathematics, 109 (2), 455-468.

Google Scholar Crossref

Frenken, L. (2021). Measuring students’ metacognitive knowledge of mathematical

Google Scholar Crossref

modelling. In: Mathematical modelling education in east and west. Springer, Cham. pp.

Google Scholar Crossref

-225.

Google Scholar Crossref

Harris, K. R., Santangelo, T., & Graham, S. (2010). Metacognition and strategies instruction

Google Scholar Crossref

in writing. Metacognition, strategy use, and instruction, 226-256.

Google Scholar Crossref

Hidayat, R., Zamri, S. N. A. S., Zulnaidi, H., & Yuanita, P. (2020). Meta-cognitive behaviour

Google Scholar Crossref

and mathematical modelling competency: mediating effect of performance goals. Heliyon,

Google Scholar Crossref

(4), e03800.

Google Scholar Crossref

Hidayat, R., Zulnaidi, H., & Syed Zamri, S. N. A. (2018). Roles of metacognition and

Google Scholar Crossref

achievement goals in mathematical modelling competency: A structural equation

Google Scholar Crossref

modeling analysis.PloS one, 13(11), e0206211.

Google Scholar Crossref

Kim, Y. R., Park, M. S., Moore, T. J., & Varma, S. (2013). Multiple levels of metacognition

Google Scholar Crossref

and their elicitation through complex problem-solving tasks. The Journal of Mathematical

Google Scholar Crossref

Behavior, 32(3), 377-396.

Google Scholar Crossref

REDIMAT – Journal of Research in Mathematics Education, 12(3)

Google Scholar Crossref

Magiera, M. T., & Zawojewski, J. S. (2019). Principles for Designing Research Settings to

Google Scholar Crossref

Study Spontaneous Metacognitive Activity. In Affect in Mathematical Modeling (pp. 53-

Google Scholar Crossref

. Springer, Cham.

Google Scholar Crossref

Mahdavi, M. (2014). An overview: Metacognition in education. International Journal of

Google Scholar Crossref

Multidisciplinary and current research, 2(6), 529-535.

Google Scholar Crossref

Paris, S. G., Cross, D. R., & Lipson, M. Y. (1983). Informed strategies for learning: A

Google Scholar Crossref

program to improve children's reading awareness and comprehension. Journal of

Google Scholar Crossref

Educational psychology, 76(6), 1239.

Google Scholar Crossref

Pollak, H. (2015). Where Does Mathematical Modeling Begin? A Personal Remark. In

Google Scholar Crossref

Werner Blum und seine Beiträge zum Modellieren im Mathematikunterricht (pp. 277-279).

Google Scholar Crossref

Springer Spektrum, Wiesbaden.

Google Scholar Crossref

Pressley, M., Forrest-Pressley, D. L., Elliott-Faust, D., & Miller, G. (1985). Children’s use of

Google Scholar Crossref

cognitive strategies, how to teach strategies, and what to do if they can’t be taught. In

Google Scholar Crossref

Cognitive learning and memory in children (pp. 1-47). Springer, New York, NY.

Google Scholar Crossref

Price-Mitchell, M. (2020). Millenials reflect on social networking. Psychology Today.

Google Scholar Crossref

Marilyn Price-Mitchell. https://www. psychologytoday. com/us/blog/themomentyouth/201406/millennials-reflect-social-networking. Accessed, 1. Accessed

Google Scholar Crossref

september 10, 2021.

Google Scholar Crossref

Rosa, C. T. W. (2017). Instrumento para avaliação do uso de estratégias metacognitivas nas

Google Scholar Crossref

atividades experimentais de Física. Revista Thema, 14(2), 182-193.

Google Scholar Crossref

Sharma, S. (2013). Qualitative approaches in mathematics education research: Challenges

Google Scholar Crossref

and possible solutions. Education Journal, 2(2), 50-57. doi: 10.11648/j.edu.20130202.14

Google Scholar Crossref

Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational psychology review,

Google Scholar Crossref

(4), 351-371.

Google Scholar Crossref

Schraw, G., & Dennison, R. S. (1994). Assesing Metacognitive Awareness. Contemporary

Google Scholar Crossref

Educational Pschology, 19, 460–475.

Google Scholar Crossref

Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM, 42(2),

Google Scholar Crossref

-161.

Google Scholar Crossref

Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and

Google Scholar Crossref

modelling tasks at secondary school. Trends in teaching and learning of mathematical

Google Scholar Crossref

modelling, 165-180.

Google Scholar Crossref

Torregrosa, A., Deulofeu Piquet, J., & Albarracin Gordo, L. (2020). Caracterización de

Google Scholar Crossref

procesos metacognitivos en la resolución de problemas de numeración y patrones

Google Scholar Crossref

matemáticos. Educacion Matematica, 32(3), 0002.

Google Scholar Crossref

Vertuan, R. E., & Almeida, L. M. W. D. (2016). Práticas de monitoramento cognitivo em

Google Scholar Crossref

atividades de modelagem Matemática. Bolema, 30(1), 1070-1091.

Google Scholar Crossref

Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling

Google Scholar Crossref

competencies: Empirical verification of theoretical assumptions. Zdm, 50(1), 343-354.

Google Scholar Crossref

Vorhölter, K. (2019). Enhancing metacognitive group strategies for modelling. ZDM, 51(4),

Google Scholar Crossref

-716.

Google Scholar Crossref

Vorhölter, K. (2017). Measuring metacognitive modelling competencies. In Mathematical

Google Scholar Crossref

Modelling and Applications (pp. 175-185). Springer, Cham.

Google Scholar Crossref

Werle de Almeida & Velozo de Castro – Metacognitive Strategies 228

Google Scholar Crossref

Vorhölter, K., & Kaiser, G. (2016). Theoretical and pedagogical considerations in promoting

Google Scholar Crossref

students' metacognitive modeling competencies. National Council of Teachers of

Google Scholar Crossref

Mathematics.

Google Scholar Crossref

Vorhölter, K., & Krüger, A. (2021). Metacognitive strategies in modeling: Comparison of the

Google Scholar Crossref

results achieved with the help of different methods. Quadrante, 30(1), 178-197.

Google Scholar Crossref

Vorhölter, K., Krüger, A., & Wendt, L. (2020). Metacognition in mathematical modeling–An

Google Scholar Crossref

overview. In: S. A. Chamberlin; B. Sriraman (Org). Affect in mathematical modeling,

Google Scholar Crossref

Springer, Cham, 29-51.

Google Scholar Crossref

Vygotsky, L. S. (1997). Educational psychology (R. Silverman, Trans.). Boca Raton, FL: St.

Google Scholar Crossref

Lucie, 173.

Google Scholar Crossref

Yildirim, T. P. (2010). Understanding the Modeling Skill Shift in Engineering: The Impace of

Google Scholar Crossref

Self-Efficacy, Epistemology, and Metacognition. Doctoral Dissertation, University of

Google Scholar Crossref

Pittsburgh.

Google Scholar Crossref

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Published

2023-10-24

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