Affective pathways and interactive visualization in the context of technological and professional mathematical knowledge

Authors

  • Inés Ma Gómez-Chacón

DOI:

https://doi.org/10.7146/nomad.v17i3-4.148474

Abstract

This article reports the findings for a qualitative study on the use of dynamic geometry systems (DGS) and their impact on students’ affective pathways. The approach adopted is to view affect through the lens of a representational system. The participants, mathematics teacher trainees, were asked to solve geometric locus exercises using GeoGebra software. The results reveal a number of features that characterize subjects’ local and global affect. Future teachers’ local affect when using imagery in computerized environments was found to be impacted by the balance between their analytical-algebraic and graphic reasoning and their understanding of the tools at their avail and their use in the instrumental deconstruction of geometric figures. Evidence was observed that linked student teachers’ global affect, in turn, to their motivation as defined by their goals and self-concept.

References

Artigue, M. (2002). Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7 (3), 245-274. https://doi.org/10.1023/A:1022103903080

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52 (3), 215-24. https://doi.org/10.1023/A:1024312321077

Cobb, P. (1986). Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6 (2), 2-9.

Cobb, P., Cofrey, J., di Sessa, A., Lehrer, R. & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32 (1), 9-13. https://doi.org/10.3102/0013189X032001009

DeBellis, V. A. & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: a representational perspective. Educational Studies in Mathematics, 63 (2), 131-147. https://doi.org/10.1007/s10649-006-9026-4

Di Martino, P., & Zan, R. (2003). What does 'positive' attitude really mean? In N A. Pateman, B. J. Dougherty & J. T. Zilliox (Ed.), Proceedings of the 2003 joint meeting of PME and PMENA (Vol. 4, pp. 451-458). Honolulu: College of Education.

Duval, R. (1999). Representation, vision and visualization: cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 3-26). Columbus: ERIC.

Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131. https://doi.org/10.1007/s10649-006-0400-z

Eisenberg, T. (1994). On understanding the reluctance to visualize. Zentralblatt für Didaktik der Mathematik, 26, 109-113.

Forgasz, H. J. (2006b). Teachers, equity, and computers for secondary mathematics learning. Journal for Mathematics Teacher Education, 9 (5), 437-469. https://doi.org/10.1007/s10857-006-9014-8

Goldin, G.A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical thinking and learning, 2 (3), 209-219. https://doi.org/10.1207/S15327833MTL0203_3

Gómez-Chacón, I. Ma & Escribano, J. (2011). Teaching geometric locus using GeoGebra. An experience with pre-service teachers. GeoGebra The New Language For The Third Millennium, 2 (1), 209-224.

Gómez-Chacón, I. Ma & Joglar, N. (2010). Developing competencies to teach exponential and logarithmic functions using GeoGebra from a holistic approach. Educação Matemática Pesquisa, 12 (3), 485-513.

Gómez-Chacón, I. Ma (2000a). Matemática emocional. Los afectos en el aprendizaje matemático [Emotional mathematics. Affects in mathematics learning]. Madrid: Narcea.

Gómez-Chacón, I. Ma (2000b). Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43, 149-168. https://doi.org/10.1023/A:1017518812079

Gómez-Chacón, I. Ma (2011). Mathematics attitudes in computerized environments. A proposal using GeoGebra. In L. Bu & R. Schoen (Eds.), Model-centered learning: pathways to mathematical understanding using GeoGebra (pp. 147-170). Rotterdam: Sense Publishers. https://doi.org/10.1007/978-94-6091-618-2_11

Gómez-Chacón, I. Ma & Kuzniak, A. (2011). Les espaces de travail Géométrique de futurs professeurs en contexte de connaissances technologiques et professionnelles. Annales de Didactique et de Sciences Cognitives, 16, 187-216.

Guzmán, M. de (2002). The role of visualization in the teaching and learning of mathematical analysis. In D. H. Hallett & C. Tzanakis (Eds.),Proceedings of the 2nd international conference on the teaching of mathematics (at the undergraduate level). Hersonissos: University of Crete.

Hannula, M. S. (2002). Attitude towards mathematics: emotions, expectations and values. Educational Studies in Mathematics, 49, 25-46. https://doi.org/10.1023/A:1016048823497

Houdement, C. & Kuzniak, A. (2006). Paradigmes géométriques et enseignement de la géométrie. Annales de Didactique et de Sciences Cognitives, 11, 175-193.

Kortenkamp, U. (2007). Combining CAS and DGS - towards algorithmic thinking. In L. Shangzhi et al. (Eds.), Symbolic computation and education (pp. 150-173). Singapore: World Scientific Publication. https://doi.org/10.1142/9789812776006_0009

Mithalal, J. (2010). Déconstruction instrumentale et déconstruction dimensionnelle dans le contexte de la géométrie dynamique tridimensionnelle (Ph.D. thesis). Université de Grenoble.

McCulloch, A. W. (2011). Affect and graphing calculator use. Journal of Mathematical Behavior, 30, 166-179. https://doi.org/10.1016/j.jmathb.2011.02.002

Lagrange, J. B. (Ed.) (2009). Genèses d'usages professionnels des technologies chez les enseignants (GUPTEn Rapport final Septembre 2009). Paris: Université Paris-Diderot.

Presmeg, N. C. & Balderas-Cañas, P. E. (2001). Visualization and affect in non- routine problem solving. Mathematical Thinking and Learning, 3 (4), 289-313. https://doi.org/10.1207/S15327833MTL0304_03

Presmeg, N.C. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present and future (pp. 205-235). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087901127_009

Rabardel, P. (1995). Les hommes et les technologies. Une approche cognitive des instruments contemporains. Université Paris 8.

Rivera, F. D. (2011). Toward a visually-oriented school mathematics curriculum: research, theory, practice and issues. New York: Springer. https://doi.org/10.1007/978-94-007-0014-7

Thomas, M. O. J., & Hong, Y. Y. (2005a). Teacher factors in integration of graphic calculators into mathematics learning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 257-264). University of Melbourne.

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Published

2012-11-19

How to Cite

Gómez-Chacón, I. M. (2012). Affective pathways and interactive visualization in the context of technological and professional mathematical knowledge. NOMAD Nordic Studies in Mathematics Education, 17(3-4), 57–74. https://doi.org/10.7146/nomad.v17i3-4.148474

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Articles