Abstract
This paper proposes to validate the structural relationships between the measurements of the academic agency components of student self-report and those observed in a mathematical learning episode, in order to provide evidence of how the metacognitive processes involved in success interact before and during an academic learning process. It is proposed to analyze the way in which learning styles, epistemic beliefs, and reading comprehension correlate with the degree of self-regulation and the ability to self-direct one’s cognitive resources in a conscious and voluntary way in the achievement of learning goals in tasks that involve solving mathematical problems around the notion of infinite process, mediated by the use of a computational tool. The findings underline the importance and role that the use of technology can play in developing teaching strategies and assessing learning outcomes that result in the promotion of metacognitive and self-regulated learning skills.
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Notes
- 1.
1, p. 21.
- 2.
The program can be downloaded for free from the following link: http://www.geogebra.org.
- 3.
ENLACE, an acronym for The National Evaluation of Academic Achievements in School Centers, was an exam that was applied each year in Mexico by the Secretary of Public Education (SEP) to all public and private elementary schools.
References
A. Bandura, Social cognitive theory: an agentic Albert Bandura. Asian J. Soc. Psychol. 2(1), 21–41 (1999). https://doi.org/10.1111/1467-839X.00024
Bentler, P.M. (2006). EQS Estructural Equations Program. Versión 6.2 [CD-ROM] Encino, CA: Multivariate Software, Inc
J. Bezuidenhout, Limits and continuity: some conceptions of first-year students. Int. J. Math. Educ. Sci. Technol. 32, 487–500 (2001)
Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.) Dordrecht, The Netherlands: Kluwer Academic
S.Y. Castañeda, E. Peñalosa, Validando constructos en epistemología personal. Revista Mexicana de Psicología 27(1), 65–75 (2010)
S. Castañeda, I. Pérez, Evaluando componentes de agencia académica en la WEB. Revista Mexicana de Psicología 22, 82–83 (2014)
S. Castañeda, M. Pineda, N. Somoza, E. Castro, Construcción de instrumentos de estrategias de estudio, autorregulación y epistemología personal. validación de constructo. Revista Mexicana de Psicología 27(1), 77–85 (2010)
S. Castañeda, E. Peñalosa, Y. Soto, Optimizando la Evaluación en Comprensión de Textos. Revista Mexicana de Psicología, 33, 1(January), 7–16 (2016)
B. Cornu, Limits, in Advanced mathematical thinking, ed. by D. Tall (Kluwer Academic, Dordrecht, The Netherlands, 1991), pp. 153–166
R.B. Davis, S. Vinner, The notion of limit: Some seemingly unavoidable misconception stages. J. Math. Behav. 5, 281–303 (1986)
E. de Corte, F. Depaepe, P.O.T. Eynde, L. Verschaffel, Students’ self-regulation of emotions in mathematics: An analysis of meta-emotional knowledge and skills. ZDM Int J Math Educ 43(4), 483–495 (2011). https://doi.org/10.1007/s11858-011-0333-6
P. Di Martino, R. Zan, Attitude towards mathematics: a bridge between beliefs and emotions. ZDM Int J Math Educ 43(4), 471–482 (2011). https://doi.org/10.1007/s11858-011-0309-6
Enlace (2014) http://www.enlace.sep.gob.mx/ms/informes_de_resultados/Geogebra
H.-Z. Ho, D. Senturk, A.G. Lam, J.M. Zimmer, S. Hong, Y. Okamoto, S.Y. Chiu, Y. Nakazawa, C.-P. Wang, The affective and cognitive dimensions of math anxiety: a cross-national study. J. Res. Math. Educ. 31(3), 362–379 (2000). http://doi.org/10.2307/749811
B.K. Hofer, P.R. Pintrich, The development of epistemological theories: beliefs about knowledge and knowing and their relation to learning. Rev. Educ. Res. 67(1), 88–140 (1997). https://doi.org/10.3102/00346543067001088
D.W.L. Hung, Meanings, contexts, and mathematical thinking: The meaning-context model. J. Math. Behav. 16(4), 311–324 (1997). https://doi.org/10.1016/S0732-3123(97)90010-9
M. Kawski, How CAS and visualization lead to a complete rethinking of an introduction to vector calculus, in Proceeding of the Third International Conference on Technology in Mathematics Teaching, ed. by W. Fraunholz (Koblenz, Germany, 1997)
D. Leclercq, A. Cabrera, Conceptos y modelos para concebir, analizar y evaluar innovaciones curriculares basadas en competencias. en: Redes de colaboración para la innovación en la docencia universitaria: II Encuentro de Centros de Apoyo a la Docencia: ECAD: 29 y 30 de septiembre, 2011, UCM, Talca (2011)
M. Pinto, D. Tall, Building formal mathematics on visual imagery: a case study and a theory. Learn. Math. 22, 2–10 (2002)
S. Papert, Microworlds: transforming education, in Artificial Intelligence and Education volumen one: Learning Environments and Turoring Systems, ed. by R. Lawler, M. Yazdani (Ablex Publishing, 355 Chestnut St. Norwood, NJ 07648, 1987)
R. Peñalva, Las matemáticas en el desarrollo de la metacognición. Política Y Cultura, (33), 135–151. Retrieved from http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0188-77422010000100008&lng=es&nrm=iso&tlng=es (2010)
K.H. Roh, Students’ images and their understanding of definitions of the limit of a sequence. Educ. Stud. Math. 69(3), 217–233 (2008). https://doi.org/10.1007/s10649-008-9128-2
D.M. Santos, S. Castañeda, Objetivación de información en aprendizaje matemático autorregulado. Revista Mexicana de Investigación …, 713–736. Retrieved from http://dialnet.unirioja.es/servlet/articulo?codigo=2748540 (2008)
D.M. Santos, Objetivar el conocimiento. Revista Mexicana de Psicología 27(1), 103–110. Retrieved from http://www.redalyc.org/articulo.oa?id=243016325011 (2010)
A.H. Schoenfeld, Mathematical Problem Solving (Academic Press, New York, 1985)
A.H. Schoenfeld, Learning to think mathematically: problem solving, metacongnition, and sense-making in mathematics, in Teaching and Learning, ed. by D. Grouws (MacMillan, New York, 1992), pp. 334–370
A. Sierpińska, Humanities students and epistemological obstacles related to limits. Educ. Stud. Math. 18, 371–397 (1987)
TECHSMITH, Camtasia Studio [CD-ROM]versión 6.0.0: TechSmith USA (2008)
S. Williams, Models of limit held by college calculus students. J. Res. Math. Educ. 22, 219–236 (1991)
B.J. Zimmerman, Becoming a self-regulated learner : an overview 41(2), 64–70 (2002). http://doi.org/10.1207/s15430421tip4102
A. Zuffianò, G. Alessandri, M. Gerbino, B.P. Luengo Kanacri, L. Di Giunta, M. Milioni, G.V. Caprara, Academic achievement: the unique contribution of self-efficacy beliefs in self-regulated learning beyond intelligence, personality traits, and self-esteem. Learn. Individ. Differ. 23(1), 158–162 (2013). https://doi.org/10.1016/j.lindif.2012.07.010
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Santos Melgoza, D.M., Landa Hernández, J.A., Ulloa González, F.A., Valdés Ramírez, A. (2021). Didactics for the Development of Mathematical Thinking and the Sense of Academic Agency. In: Tsihrintzis, G., Virvou, M. (eds) Advances in Core Computer Science-Based Technologies. Learning and Analytics in Intelligent Systems, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-41196-1_5
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