Study about the difficulties that higher-level students have when solving Calculus problems and the use of the technological learning scenario as a support in the classroom work

Elena F. Ruiz-Ledesma

Abstract


Introduction: The work carried out through the use of a techno-pedagogical scenario is described, which is made up of the content of the subject of Applied Calculus in the Higher Level, the use of teaching and learning strategies (pedagogical work) and the use of technology. Specifically, we worked with an expert system called SIMAATCA, in which there are several multimedia resources to which students have access. It is intended to determine if with the employment of the techno-pedagogical scenario the students manage to improve their performance in one of the units of the curriculum (Unit 1. Applications of the Derivative) of the subject of Applied Calculus.

Method: The research study was developed with two groups of 33 students each one, who were starting their second semester in the degree, one group was considered as the control one (GC) and the other was an experimental group (GE). In both groups the same Unit of the curriculum was approached, what differentiates the two groups is the teaching strategy used. In the control group was worked in a traditional way, using exclusively the blackboard and the textbook; while in the experimental group was worked with the techno-pedagogical scenario. The student's academic performance was measured by comparing the results obtained between the pretest and the posttest, both questionnaires applied to the two groups (control and experimental).

Results: The results obtained in the diagnostic questionnaire (pre-test) both by the control group (CG) and the experimental group (EG) was very low since the students presented difficulties in the approaches of most of the problems. After having worked with both groups using different strategies, the post-test was applied. This time there was an improvement in the results obtained by both groups, but the EG excelled in the number of correct answers and the way to face each problem, compared to the CG.


Keywords


calculus applications; teaching process; learning process; multimedia resources; problem solving

References


Area, M. & Adell, J. (2009). E-Learning: Enseñar y aprender en espacios virtuales. En Tecnología Educativa. La formación del profesorado en la era de Internet, editado por De Pablos J. (391-424).

Artigue, Michelle. (2011). Tecnología y enseñanza de las matemáticas: desarrollo y aportes de la aproximación instrumental. Cuadernos de Investigación y Formación en Educación Matemática, 8 (1): 13 – 33.

Boneu, Josep M. (2007). Plataformas abiertas de e-learning para el soporte de contenidos educativos abiertos. RUSC Universities and Knowledge Society Journal, 4(1): 36-47.

Cuesta, A; Escalante, J.; Ruiz J. (2016). Velocidad. Significados manifestados por estudiantes universitarios a partir de representaciones gráficas. Avances de Investigación en Educación Matemática, (9): 105 – 125.

Drijvers, P., Kieran, C., Mariotti, M.-A., Ainley, J., Andresen, M., Chan, Y., Meagher, M. (2009). Integrating Technology into Mathematics Education: Theoretical Perspectives. En Mathematics Education and Technology-Rethinking the Terrain: The 17th ICMI Study, editado por C. Hoyles (89-132). Boston, MA: Springer US. doi:https://doi.org/10.1007/978-1-4419-0146-0_7

Duval, Raymond (1988). Registros de Representación Semiótica y funcionamiento cognitivo del pensamiento. Investigaciones en Matemática Educativa II: 173-201.

Flores, A. (2013). Ayudando a futuros profesores a mejorar la comprensión conceptual del cálculo. En La enseñanza del cálculo Diferencial e Integral compendio de investigaciones y reflexiones para profesores, formadores e investigadores en matemática educativa, editado por Cuevas, Armando, Pluvinage, Francoise & Flores, Attelier (43 – 83). México: Pearson.

García-Peñalvo, F. J. (2005). Estado actual de los sistemas E-Learning. Teoría de la Educación. Educación y Cultura en la Sociedad de la Información, 6(2): 1.

Harris, J. and Hofer, M. (2009). Instructional planning activity types as vehicles for curriculum-based TPACK development, En Research highlights in technology and teacher education, Chesapeake, Society for Information Technology in Teacher Education (SITE)., Editado por Cleborne D. Disponible en: http://activitytypes.wmwikis.net/file/view/HarrisHoferTPACKDevelopment.pdf Acceso en: 8/10/2018.

Hernández-Sampieri, R., Fernández-Collado, C. & Baptista-Lucio, P. (2014). Metodología de la Investigación. 6ª. Ed. México: McGraw-Hill.

Hitt, Fernando. (2013). Un análisis sobre la enseñanza del concepto de derivada en el nivel pre-universitario del rol del libro de texto y del uso de sus conexiones con la tecnología. En La enseñanza del cálculo Diferencial e Integral, editado por Cuevas Armando & Pluvinage, Fancoise. Pearson. México.

Hitt, Fernando. (2014). Nuevas Tendencias en la Enseñanza del Cálculo: La Derivada en Ambientes TICE. AMIUTEM, 2(2): 1-19, Disponible en: http://revista.amiutem.edu.mx/ojs/index.php/relecamiutem/article/view/20 Acceso en: 21/11/2018.

Hitt, F., González-Martín, A. Et Morasse C. (2008). Visualization and students’ functional representations in the construction of mathematical concepts. An example: The concept of co-variation as a prelude to the concept of function. In 11th International Congress on Mathematics Education (ICME11), Topic Study Group 20 (TSG 20), Visualization in the Teaching and Learning of Mathematics, Monterrey, N. L., Mexico. http://tsg.icme11.org/tsg/show/21

INEGI (2018). Encuesta Nacional sobre Disponibilidad y Uso de Tecnologías de la Información en los Hogares 2018. Disponible en: http://www.beta.inegi.org.mx/proyectos/enchogares/regulares/dutih/2018/default.htm. Acceso en: 12/10/2018

IPN. ESCOM. Plan de estudios de Cálculo Aplicado. 2009. Recuperado de: http://www.escom.ipn.mx/docs/ofertaEducativa/uapdf/calculoAplicado.pdf

Kaput, J.J. (2008). What is algebra? What is Algebraic Reasoning? In J.J. Kaput, D. Carraher & M.L.Blanton (Eds.), Algebra in the Early Grades (pp. 5-17). New York: Routledge.

Kieran, C. (2007). Learning and Teaching Algebra at the Middle School Through College Levels. En Lester, F. K. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning (pp. 707-762). Reston, Virginia: NCTM e IAP.

Koehler, M. and Mishra, P. (2006). Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record, 108(6): 1017-1054. Disponible en inglés en: http://punya.educ.msu.edu/publications/journal_articles/mishra-koehlertcr2006.pdf Acceso en: 15/11/2018.

Moschkovich, J. N. y Brenner, M. (2000). Integrating a Naturalistic Paradigm Into Research on Mathematics and Science Cognition and Learning. En R. Lesh y A. Kelly (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 457-486). Mahwah, NJ: Lawrence Erlbaum Associates.

Sánchez, G., García, M., & Llinares, S. (2008). La Comprensión de la Derivada como Objeto de Investigación en Didáctica de la Matemática. Revista Latinoamericana de Investigación en Matemática Educativa, 11(2): 267 – 296.

Stewart, J. (2012). Cálculo de una variable. Trascendentes tempranas. Trad. de Rodríguez Pedroza, M. C. (2012). México: Cengage Learning Editores.

Oliveros, J. R. (1999). El estudio de la Tasa de Cambio Instantánea en el entendimiento de la Derivada Situado en el salón de Clase. 1999. Tesis Doctorado en Ciencias especialidad de matemática educativa. Cinvestav, México.

Larson, R & Edwars, B. H. (2010). Cálculo 1 en una variable. 9ª. Ed. México: McGraw –Hill

Rosenberg, M. J. (2001). E-Learning. Strategies for delivering knowledge in the Digital Age. New Cork, McGraw-Hill.

Saboya, M. (2010). Élaboration et analyse d'une intervention didactique co-construite entre chercheur et enseignant, visant le développement d'un contrôle sur l'activité mathématique chez les élèves du secondaire. Tesis de doctorado no publicada. Université du Québec à Montréal.

Shulman, L. S. (2005).Those who understand: Knowledge growth in teaching. Educational Researcher, v. 15, n. 2, 4-14. 1986. Trad. y edición española (“El saber y entender de la profesión docente”) en Estudios Públicos (Centro de Estudios Públicos, Chile), (99):195-224

Swan, K., Kratcoski, A., And Van't Hooft, M. (2007). Highly Mobile Devices, Pedagogical Possibilities, and How Teaching Needs to Be. Educational Technology, 47(10): Disponible en: http://www.rcet.org/research/publications/ET_May-June_2007_swan.pdf Acceso en: 14/10/2018

UNESCO. (2013). Directrices para las políticas de aprendizaje móvil. UNESCO: Francia.

Zimmermann, W. & Cunningham, S. (Eds.) (1991). Visualization in Teaching and Mathematics (pp. 25-37). MAA Series, No. 19. USA.




DOI: https://doi.org/10.21640/ns.v11i23.1840

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