Comprensión de la mediana por estudiantes universitarios

  1. Ana Esther Madrid
  2. Silvia M. Valenzuela-Ruiz
  3. Carmen Batanero
  4. José A. Garzón-Guerrero
Revista:
Avances de investigación en educación matemática: AIEM

ISSN: 2254-4313

Ano de publicación: 2022

Número: 22

Páxinas: 1-21

Tipo: Artigo

Outras publicacións en: Avances de investigación en educación matemática: AIEM

Resumo

The median is a central tendency statistics widely used in exploratory data analysis and non-parametric inference, which is why its teaching is included in university statistics courses. To identify se-miotic conflicts in the topic, the results of a study to evaluate the understanding of the median in 148 stu-dents of Physical Activity and Sport Sciences are presented. The open-ended responses to a questionnaire of four tasks related to the definition, calculation and properties of the median are analysed, identifying the students’ conceptual, procedural, and notational semiotic conflicts, some of which have not been de-scribed in previous research

Referencias bibliográficas

  • Batanero, C., Estepa, A., Godino, J. D. & Green, D. R. (1996). Intuitive strategies and preconceptions about association in contingency tables. Journal for Research in Mathematics Education 27(2), 151-169. https://doi.org/10.2307/74959
  • Batanero, C., Valenzuela-Ruiz, S. M. & Begué, N. (2020). Estadísticos de orden y razonamiento proporcional. UNIÓN, 16(60), 233-244.
  • Barr, G. V. (1980). Some student ideas on the median and the mode. Teaching Statistics, 2(2), 38-41. https://doi.org/10.1111/j.1467-9639.1980.tb00381.x
  • Barros, P. (2003). Os futuros professores do 2.º ciclo e a estocástica – Dificuldades sentidas e o ensino do tema. Associação de Professores de Matemática.
  • Boaventura, M. G. & Fernandes, J. (2004). Dificuldades de alunos do 12.º ano nas medidas de tendência central: O contributo dos manuais escolares. En J. A. Fernandes (Ed.), Actas do I Encontro de Probabilidades e Estatística na Escola (pp. 103-126). Universidad de Miño, Portugal.
  • Carvalho, C. (2001). Interacções entre pares: Contributos para a promoção do desenvolvimento lógico e do desempenho estatístico no 7º ano de escolaridade. Tesis doctoral sin publicar. Universidad de Lisboa.
  • Cobo, B. (2003). Significado de las medidas de posición central para los estudiantes de secundaria. Tesis doctoral sin publicar. Universidad de Granada.
  • Cox, V. (2017). Exploratory data analysis. En V. Cox (Ed.), Translating statistics to make decisions (pp. 47-74). Apress. https://doi.org/10.1007/978-1-4842-2256-0_3
  • 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. https://doi.org/10.34624/id.v10i2.11313
  • Gea, M. M., Arteaga, P. & Cañadas, G. (2017). Interpretación de gráficos estadísticos por futuros profesores de Educación Secundaria. Avances de Investigación en Educación Matemática, 12, 19-37. https://doi.org/10.35763/aiem.v1i12.189
  • Gea, M. M., Batanero, C., Fernandes, J. A. & Arteaga, P. (2016). Interpretación de resúmenes estadísticos por futuros profesores de educación secundaria. REDIMAT, 5(2), 135-157. https://doi.org/10.4471/redimat.2016.1902
  • Gibbons, J. D. & Chakraborti, S. (2020). Nonparametric statistical inference. CRC Press.
  • Godino, J. D., Batanero, C. & Font, V. (2007). The onto-semiotic approach to research inmathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127-135.
  • Godino, J. D., Batanero, C. & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 38-43. https://doi.org/10.1007/s11858-006-0004-1
  • Godino, J. D., Burgos, M. & Gea, M. M. (2021). Analysing theories of meaning in mathematics education from the onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 51, 1-28. https://doi.org/10.1080/0020739X.2021.1896042
  • Groth, R. E. & Bergner, J. A. (2006). Preservice elementary teachers' conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8, 37-63. https://doi.org/10.1207/s15327833mtl0801_3
  • 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.
  • Mayén, S., Díaz, C. & Batanero, C. (2009). Conflictos semióticos de estudiantes con el concepto de mediana. Statistics Education Research Journal, 8(2), 74-93. https://doi.org/10.52041/serj.v8i2.396
  • Neuendorf, K. A. (2017). The content analysis guidebook. Sage. https://doi.org/10.4135/9781071802878
  • Watson, J. M. & Moritz, J. B. (1999). The development of concepts of average. Focus on Learning Problems in Mathematics, 21(4), 15-39.
  • Zawojewski, J. S. & Shaughnessy, J. M. (2000). Take time for action: Mean and median: Are they really so easy? Mathematics Teaching in the Middle School, 5(7), 436-440. https://doi.org/10.5951/MTMS.5.7.0436