Análisis de applets de GeoGebra para la enseñanza del límite de una función

  1. Álvaro Barreras Peral
  2. Luis Dubarbie
  3. Oller-Marcen, Antonio M.
Journal:
Bordón: Revista de pedagogía

ISSN: 0210-5934,  2340-6577

Year of publication: 2022

Issue Title: Educación STEM: tecnologías emergentes para el aprendizaje científico

Volume: 74

Issue: 4

Pages: 65-83

Type: Article

DOI: 10.13042/BORDON.2022.93361 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Bordón: Revista de pedagogía

Sustainable development goals

Abstract

INTRODUCTION. The importance of GeoGebra as one of the main tools that offer Mathematics teachers the possibility of working with virtual simulations in their classrooms is indisputable. However, the resources in the official GeoGebra repository do not go through any review process. Therefore, the teacher’s criteria when selecting this type of resource is key for teaching success. Thus, it is necessary to provide teachers with tools to analyze GeoGebra applets for their implementation in the classroom. In particular, this type of resources offers numerous advantages to teach the mathematical concept of the limit of a function. METHOD. In this paper, the didactic suitability of GeoGebra applets for teaching the limit of a function is analyzed. An exploratory and descriptive study has been carried out. The analysis has been carried out using a deductive approach based on five different variables (type of limit, interactivity, conceptual image, representation and action). The analyzed sample, chosen through purposeful sampling, is 150 applets from the official GeoGebra material repository. RESULTS. The results are shown after analyzing the five established variables for each of the studied applets. The influence of interactivity with the rest of the variables is also analyzed, as well as the influence of the number of representations of the limit in the applets. DISCUSSION. In the analysis carried out of the didactic suitability, the importance of the interactivity variable stands out, as it enhances the development of most of the conceptual images of the limit. The use of a greater number of limit representation systems in an applet is also positive, since it favors the development of various actions in said representation systems.

Bibliographic References

  • Beltrán-Pellicer, P., Giacomone, B. y Burgos, M. (2018). Online educational videos according to specific didactics: the case of mathematics / Los vídeos educativos en línea desde las didácticas específicas: el caso de las matemáticas. Culture and Education, 30(4), 633-662. https://doi.org/10.1080/11356405.2018.1524651
  • Blázquez, S. y Ortega, T. (2001). Los sistemas de representación en la enseñanza del límite. Revista Latinoamericana de Investigación en Matemática Educativa, 4(3), 219-236.
  • Burgos, M., Beltrán-Pellicer, P. y Godino, J. D. (2020). La cuestión de la idoneidad de los vídeos educativos de matemáticas: una experiencia de análisis con futuros maestros de educación primaria. Revista Española de Pedagogía, 78(275), 27-49. https://doi.org/10.22550/REP78-1-2020-07
  • Caligaris, M. G., Schivo, M. E. y Romiti, M. R. (2015). Calculus & GeoGebra, an interesting partnership. Procedia-Social and Behavioral Sciences, 174, 1183-1188. https://doi.org/10.1016/j.sbspro.2015.01.735
  • Cid, A. I., Guede, R. y Tolmos, P. (2018). La clase invertida en la formación inicial del profesorado: acercando la realidad del aula de matemáticas. Bordón, Revista de Pedagogía, 70(3), 77-93.
  • Claros, F. J., Sánchez, M. T. y Coriat, M. (2007). Fenómenos que organizan el límite. PNA, 1(3), 125-137.
  • Contreras, Á. y García, M. (2011). Significados pretendidos y personales en un proceso de estudio con el límite funcional. Revista Latinoamericana de Investigación en Matemática Educativa, 14(3), 277-310.
  • Cornu, B. (2002). Limits. En D. Tall (ed.), Advanced mathematical thinking (pp. 153-166). Springer. https://doi.org/10.1007/0-306-47203-1_10
  • Creswell, J. W. (2002). Educational research: planning, conducting, and evaluating quantitative and qualitative research. Pearson.
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1), 103-131. https://doi.org/10.1007/s10649-006-0400-z
  • Flick, U. (2004). Triangulation in qualitative research. En U. Flick, E. Von Kardoff e I. Steinke (eds.), A companion to qualitative research (pp. 178-183). SAGE. https://doi.org/10.4135/9781849209441.n7
  • García, R., Rebollo-Catalán, A. y García, C. (2016). Relación entre las preferencias de formación del profesorado y su competencia digital en las redes sociales. Bordón, Revista de Pedagogía, 68(2), 137-153. https://doi.org/10.13042/Bordon.2016.68209
  • Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. Cuadernos de Investigación y Formación en Educación Matemática, 11, 111-132.
  • Godino, J. D., Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  • Godino, J. D., Batanero, C. y Font, V. (2019). The onto-semiotic approach: implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 38-43. https://www.jstor.org/stable/26742011
  • Godino, J. D., Rivas, H. y Arteaga, P. (2012). Inferencia de indicadores de idoneidad didáctica a partir de orientaciones curriculares. Práxis Educativa, 7(2), 331-354.
  • Hohenwarter, J., Hohenwarter, M. y Lavicza, Z. (2009). Introducing dynamic mathematics software to secondary school teachers: the case of GeoGebra. Journal of Computers in Mathematics and Science Teaching, 28(2), 135-146.
  • Hohenwarter, M. y Lavicza, Z. (2007). Mathematics teacher development with ICT: towards an International GeoGebra Institute. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 49-54.
  • Hutkemri, E. Z. (2014). Impact of using GeoGebra on students’ conceptual and procedural knowledge of limit function. Mediterranean Journal of Social Sciences, 5(23), 873-881. https://doi.org/10.5901/mjss.2014.v5n23p873
  • Leavy, P. (2017). Research design: quantitative, qualitative, mixed methods, arts-based, and communitybased participatory research approaches. The Guilford Press. Onwuegbuzie, A. J. y Leech, N. L. (2007). Validity and qualitative research: an oxymoron? Quality & Quantity, 41(2), 233-249. https://doi.org/10.1007/s11135-006-9000-3
  • Palomino, J., Hurtado, J. y Barrios, E. (2009). Dificultades en los procesos de enseñanza aprendizaje del concepto de límite y su relación con los sistemas de representación. En VI Encuentro Internacional de Matemáticas - EIMAT 2009 (pp. 187-208). Universidad del Atlántico.
  • Pecharromán, C. (2013). Naturaleza de los objetos matemáticos: representación y significado. Enseñanza de las Ciencias, 31(3), 121-134. https://doi.org/10.5565/rev/ec/v31n3.931
  • Przenioslo, M. (2004). Images of the limit of function formed in the course of mathematical studies at the university. Educational Studies in Mathematics, 55, 103-132. https://doi.org/10.1023/B:EDUC.0000017667.70982.05
  • Roussou, M., Oliver, M. y Slater, M. (2006). The virtual playground: an educational virtual reality environment for evaluating interactivity and conceptual learning. Virtual Reality, 10(3-4), 227-240. https://doi.org/10.1007/s10055-006-0035-5
  • Sánchez-Compaña, T. (2012). Límite finito de una función en un punto: fenómenos que organiza [Tesis Doctoral, Universidad de Granada] Repositorio Institucional UG. http://hdl.handle.net/10481/23782
  • Sari, P. (2017). GeoGebra as a means for understanding limit concepts. Southeast Asian Mathematics Education Journal, 7(2), 71-84. https://doi.org/10.46517/seamej.v7i2.55
  • Socas, M. (2007). Dificultades y errores en el aprendizaje de las matemáticas. Análisis desde el enfoque lógico semiótico. En M. Camacho, P. Flores y P. Bolea (eds.), Investigación en educación matemática XI (pp. 19-52). SEIEM.
  • Tall, D. y Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169. https://doi.org/10.1007/BF00305619
  • Turney, C. S. M., Robinson, D., Lee, M. y Soutar, A. (2009). Using technology to direct learning in higher education. The way forward? Active Learning in Higher Education, 10(1), 71-83. https://doi.org/10.1177/1469787408100196
  • Ward, E., Inzunsa, S., Hernández, S. y López, F. (2013). Conceptualización y uso de representaciones sobre el concepto de límite en docentes de bachillerato. En A. Berciano, G. Gutiérrez, A. Estepa y N. Climent (eds.), Investigación en educación matemática XVII (pp. 523-534). SEIEM.
  • Williams, S. R. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22(3), 219-236. https://doi.org/10.2307/749075
Data source: Dialnet