Difficulties in Understanding the Arithmetic Mean: An Experience with Problem-Based Learning and ICT in Hybrid Teaching

Research in statistics education has repeatedly shown that school students master the computational algorithm of the arithmetic mean without appropriating its meanings. This article describes the difficulties that Chilean seventh-grade students display in understanding the arithmetic mean during a teaching sequence based on problem-based learning (PBL) with contextual data and on the use of information and communication technologies (ICT), specifically the Fathom software. The study follows a qualitative descriptive design and was carried out in a single class of twenty students at a municipal school in Santiago de Chile during the COVID-19 pandemic, under hybrid conditions in which one group of students attended in person while another followed the same lessons remotely. Because of the rotating attendance system, effective participation varied between twelve and twenty students across sessions. Data were collected through a pre-test, the written productions generated during three phases of a constructivist learning cycle, and a post-test, and were analysed by means of inductive content analysis, from which six categories emerged. The results show that participants enter and leave the sequence with a stable procedural command of the algorithm and without the interpretations of the mean as a fair share or as a balance point. Most students identify that the mean changes when an outlier is added, but attribute that change to the increase in the number of data rather than to the magnitude of the added value. Given the descriptive scope of the study, the findings do not allow an effect to be attributed to the sequence; they describe that the initial difficulties persist. The study suggests that the mediating role commonly attributed to ICT is not a property of the software but an effect of its didactic integration, and that the rules of PBL must enter the didactic contract in order to operate.

arithmetic mean; problem-based learning; ICT; statistics education

1. Alvarado, J. E. (2017). Propuesta de innovación para la enseñanza de la media aritmética [Master's thesis, Pontificia Universidad Católica de Valparaíso]. [Google Scholar] [Crossref]

2. Alzate, E. J., Montes, J. W., & Escobar, R. M. (2013). Diseño de actividades mediante la metodología ABP para la enseñanza de la matemática. Scientia et Technica, 18(3), 542-547. [Google Scholar] [Crossref]

3. Batanero, C. (2000). Significado y comprensión de las medidas de posición central. UNO. Revista de Didáctica de las Matemáticas, 25, 41-58. [Google Scholar] [Crossref]

4. Behar, R., & Ojeda, M. (2016). El papel de algunas opciones tecnológicas en la educación estadística. Heurística, 18, 21-35. [Google Scholar] [Crossref]

5. Cobo, B. (2003). Significado de las medidas de posición central para los estudiantes de secundaria [Doctoral dissertation, Universidad de Granada]. [Google Scholar] [Crossref]

6. Cobo, B., & Batanero, C. (2004). Significado de la media en los libros de texto de secundaria. Enseñanza de las Ciencias, 22(1), 5-18. [Google Scholar] [Crossref]

7. Espinoza, C., & Sánchez, I. (2014). Aprendizaje basado en problemas para enseñar y aprender estadística y probabilidad. Paradigma, 35(1), 103-128. [Google Scholar] [Crossref]

8. Faustino, A., & Pérez, S. (2013). Utilización de las TIC en la enseñanza de la estadística en la educación superior angolana. Prisma Social, (11), 1-31. [Google Scholar] [Crossref]

9. Gallego, D. E., Quiceno, Y., & Pulgarín, D. (2014). Unidades didácticas: un camino para la transformación de la enseñanza de las ciencias desde un enfoque investigativo. Tecné, Episteme y Didaxis: TED, (special issue), 923-930. [Google Scholar] [Crossref]

10. Garfield, J., & Ben-Zvi, D. (2008). Developing students' statistical reasoning: Connecting research and teaching practice. Springer. [Google Scholar] [Crossref]

11. Gatica Riquelme, C. (2017). Análisis didáctico para promover ideas fundamentales de estadística relacionadas a medidas de tendencia central [Master's thesis, Pontificia Universidad Católica de Valparaíso]. [Google Scholar] [Crossref]

12. Gea, M. M., Batanero, C., López, M. M., & Contreras, J. M. (2015). Los recursos tecnológicos en la estadística bidimensional en los textos españoles de bachillerato. Tecné, Episteme y Didaxis: TED, 38, 113-132. [Google Scholar] [Crossref]

13. Gutiérrez, A., Agudelo, Ó., & Martínez, J. (2019). El uso de las TIC en los procesos de enseñanza del área de probabilidad y estadística en universitarios. In Proceedings of the 17th LACCEI International Multi-Conference for Engineering, Education, and Technology. LACCEI. [Google Scholar] [Crossref]

14. Hernández, R., Fernández, C., & Baptista, P. (2014). Metodología de la investigación (6th ed.). McGraw-Hill. [Google Scholar] [Crossref]

15. Hernández, S., & Cuevas, J. (2013). Programas informáticos de uso libre y su aplicación en la enseñanza de la estadística. Revista Investigación Operacional, 34, 166-174. [Google Scholar] [Crossref]

16. Juárez, J., & Inzunza, S. (2014). Comprensión y razonamiento de profesores de matemáticas de bachillerato sobre conceptos estadísticos básicos. Perfiles Educativos, 36, 14-29. [Google Scholar] [Crossref]

17. Marzábal, A., Rocha, A., & Toledo, B. (2015). Caracterización del desarrollo profesional de profesores de ciencias - parte 2: proceso de apropiación de un modelo didáctico basado en el ciclo de aprendizaje constructivista. Educación Química, 26, 212-223. [Google Scholar] [Crossref]

18. Mayén, S., Batanero, C., & Díaz, C. (2009). Conflictos semióticos de estudiantes mexicanos en un problema de comparación de datos ordinales. Revista Latinoamericana de Investigación en Matemática Educativa, 12(2), 151-178. [Google Scholar] [Crossref]

19. Ortega, J. M., Valencia, V. E., Becerra, M., & Durán, J. (2020). Matemática y vida cotidiana: experiencia escolar de aprendizaje basado en problemas (ABP). Números. Revista de Didáctica de las Matemáticas, 104, 103-117. [Google Scholar] [Crossref]

20. Pollatsek, A., Lima, S., & Well, A. D. (1981). Concept or computation: Students' understanding of the mean. Educational Studies in Mathematics, 12(2), 191-204. [Google Scholar] [Crossref]

21. Strauss, S., & Bichler, E. (1988). The development of children's concepts of the arithmetic average. Journal for Research in Mathematics Education, 19(1), 64-80. [Google Scholar] [Crossref]

22. Watson, J. M., & Moritz, J. B. (2000). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2(1-2), 11-50. [Google Scholar] [Crossref]

23. Zamora, J. A., Aguilar, E., & Guillén, H. (2021). Educación estadística: tendencias para su enseñanza y aprendizaje en educación secundaria y terciaria. Revista Educación, 1-19. [Google Scholar] [Crossref]

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