Knowledge of Median and Mean Properties by End High School Students
DOI:
https://doi.org/10.5007/1981-1322.2021.e82350Abstract
This article studies the knowledge of Brazilian high school students about the properties of the median and mean that derive from data transformations or declared assertions. To this end, a quantitative, descriptive study was implemented, in which 104 students from the 3rd year of a public high school in the region of São Paulo participated. Data were obtained through the application of an online questionnaire, of which we will study only three of these questions here, exactly those that concern median and mean properties. In the question of open items, we asked about the change in the median and the mean by adding a constant value to all data, and in the two questions of closed items, one questioned whether the median decreases/increases/maintains when adding one or two data under certain conditions and the other questioned whether certain statements were true or false. In terms of results, in general, students revealed many difficulties in open items, while in closed items students performed better. In view of these results, it is concluded that students have a somewhat limited conceptual knowledge of the median and mean, and that more attention should be paid to them in teaching.
References
Ausubel, D., Novak, J. & Hanesian, H. (1980). Psicologia educacional. Rio de Janeiro: Interamericana.
Batanero, C. (2013). Sentido estadístico. Componentes y desarrollo. In J. M. Contreras, G. R. Cañadas, M. M. Gea y P. Arteaga (Eds.), Actas de las Jornadas Virtuales en Didáctica de la Estadística, Probabilidad y Combinatoria (pp. 55-61). Granada, Departamento de Didáctica de la Matemática de la Universidad de Granada.
Boaventura, M. G., & Fernandes, J. A. (2004). Dificuldades de alunos do 12.º ano nas medidas de tendência central: O contributo dos manuais escolares. In J. A. Fernandes, M. V. Sousa, & S. A. Ribeiro (Orgs.), Actas do I Encontro de Probabilidades e Estatística na Escola (pp. 103-126). Braga: Centro de Investigação em Educação da Universidade do Minho.
Brasil (2018). Base Nacional Comum Curricular - Educação é a Base. Brasília: Ministério da Educação.
Cazorla, I. M. (2003). Média aritmética: um conceito prosaico e complexo. In C. Reading (Ed.). Anais do IX Seminário de Estatística Aplicada (pp. 1-14). Rio de Janeiro: Instituto Interamericano de Estatística.
Díaz-Levicoy, D., Batanero, C., Arteaga, P., & Gea, M. M. (2016). Gráficos estadísticos en libros de texto de Educación Primaria: un estudio comparativo entre España y Chile. Bolema, 30(55), 713 – 737.
Estepa, A., & Pino, J. (2013). Elementos de interés en la investigación didáctica y enseñanza de la dispersión estadística. Números, 83(julio), 43-63.
Fernandes, J. A., & Barros, P. M. (2005). Dificuldades de futuros professores do 1º e 2º ciclos em estocástica. Actas do V Congresso Ibero-Americano de Educação Matemática (CIBEM). Porto (Portugal): Faculdade de Ciências da Universidade do Porto.
Fernandes, J. A., & Freitas, A. (2019). Selection and Application of graphical and numerical statistical tools by prospective primary school teachers. Acta Scientiae, 21(6), 82-97.
Fernandes, J. A., Gea, M. M., & Correia, P. F. (2019). Conhecimento de estatística bivariada de futuros professores portugueses dos primeiros anos. Revista Portuguesa de Educação, Braga, 32(2), 40-56.
Fernandes, J. A., Gonçalves, G., & Barros, P. M. (2021). Uso de tabelas de frequências por futuros professores na realização de trabalhos de projeto. Uniciencia, 35(1), 139-151.
Fernandes, J. A., Martinho, M. H., & Gonçalves, G. (2020). Uso de gráficos estatísticos por futuros professores dos primeiros anos na realização de trabalhos de projeto. Jornal Internacional de Estudos em Educação Matemática, 13(4), 394-401.
Fischbein, E. (1987). Intuition in science and mathematics: an educational approach. Dordrecht: Kluwer Academic Publishers.
Freitas, A., Figueiredo, T. S., Silva, N., & Miranda, M. C. (2018). Dificuldades na aprendizagem da mediana e quartis por alunos do 8.º ano de escolaridade: estudo comparativo fórmula versus gráfico. Indagatio Didactica, 10(2), 109-132.
Gall, M. D.; Gall, J. P.; Borg, W. R. (2003). Educational research: An introduction. 7. ed. Boston: A & B Publications, 2003.
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
Jacobbe, T., & Carvalho, C. (2011). Teachers’ understanding of averages. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-Challenges for teaching and teacher education (pp. 199-209). Springer, Dordrecht.
Leon, M. R., & Zawojewski, J. S. (1991). Use of the arithmetic mean: An investigation of four properties. Issues and preliminary results. In D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics (pp. 302-306). Voorburg: International Statistical Institute.
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Revista Eletrônica de Educação Matemática
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors hold the copyright and grant the journal the right for their articles' first publication, being their works simultaneously licensed under the Creative Commons Attribution License (CC BY), which allows the sharing of such works with its authorship acknowledged and its initial publication in this journal.
Authors are allowed to enter into separate additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or as a book chapter, with an acknowledgment of its initial publication in this journal).
