Typology of questions on variability in school textbooks and their relationship to statistical literacy and thinking
DOI:
https://doi.org/10.15359/ru.37-1.4Keywords:
Variability, textbooks, questions, statistical literacy, statistical thinking, cognitive levelAbstract
[Objective] The purpose of this study is to analyze whether the questions related to the concept of variability that are presented in secondary school textbooks in Chile, contribute to the development of statistics literacy and thinking among students in the school system. [Methodology] To achieve this objective, a qualitative approach was used based on a content analysis of the secondary education textbooks published in the years 2016, 2018, 2020 and 2021. Units of analysis were selected using non-probabilistic subjective sampling. [Results] Among the most relevant findings, it was determined that a large part of the questions in the textbooks consulted made use of the interrogative pronouns “what” and “which.” In these cases, the questions were associated with simple tasks aimed essentially at the calculation of descriptive summaries of variability without the use of technological tools. On the other hand, questions related to more complex tasks such as reading, analyzing and making decisions, were poorly represented in the textbooks analyzed. The concept of variability in the textbooks consulted is fundamentally related to the notion of dispersion, an approach that has been questioned by English-speaking researchers. [Conclusions] In brief, based on the results obtained it is recommended that teachers in the school system guide, reformulate and design questions related to the concept of variability based in more complex activities such as analysis, argumentation and evaluation to better assist students in developing statistical literacy and thinking.
References
Anderson, L., Krathwohl, D. (2001). A taxonomy for learning, teaching and assessing: a revision of Bloom’s taxonomy of educational objectives. New York: Longman.
Batanero, C. (2000). Significado y comprensión de las medidas de posición central. Uno. Revista de Didáctica de las Matemáticas, Barcelona, 25, 41-58.
Batanero, C. (2005). Significados de la probabilidad en educación secundaria. Relime, 8(3), 247-263.
Batanero, C., Díaz, C., Contreras, J. M. y Roa, R. (2013). El sentido estadístico y su desarrollo. Números, 83, 7-18.
Ben-Zvi, D & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: goals, definitions, and challenges. In: GARFIELD, Joan; BEN-ZVI, Dani (Eds.). The challenge of developing statistical literacy, reasoning and thinking. Dordrecht: Kluwer, 3-16. https://doi.org/10.1007/1-4020-2278-6
Ben-Zvi, D. y Garfield, J. (2004). Research on Reasoning about Variability: A Forward. Statistical Education Research Journal, 3(2), 4-6. https://doi.org/10.52041/serj.v3i2.536
Ben-Zvi, D., & Makar, K. (Eds.). (2016). The Teaching and Learning of Statistics. https://doi.org/10.1007/978-3-319-23470-0.
Burgos, M., Castillo, M.J., Beltrán-Pellicer, P. Giacomone, B. y Godino, J.D. (2020). Análisis didáctico de una lección sobre la proporcionalidad en un libro de texto de primaria con herramientas del enfoque ontosemiótico. Bolema: Boletim de Educação Matemática, 34(66), 40- 68. https://doi.org/10.1590/1980-4415v34n66a03
Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10(3),1-14. https://doi.org/10.1080/10691898.2002.11910677
Cobb, G., & Moore, D. (1997). Mathematics, Statistics, and Teaching. American Mathematical Monthly, 104(9), 801–823. https://doi.org/10.1080/00029890.1997.11990723
Cobo, B. (2003). Significados de las medidas de posición central para los estudiantes de secundaria (Tesis doctoral). Universidad de Granada, España.
Estepa, A. y Ortega, J. (2005). Estudio del significado de las medidas de dispersión estadísticas. Trabajo presentado en el IX Congreso de Metodología de las Ciencias Sociales y de la Salud, Granada. España.
Estrella, S. (2017). Enseñar estadística para alfabetizar estadísticamente y desarrollar el razonamiento estadístico. En Salcedo, A. (Ed.), Alternativas Pedagógicas para la Educación Matemática del Siglo XXI (173-194). Caracas: Centro de Investigaciones Educativas, Escuela de Educación. Universidad Central de Venezuela.
Estrella, S., Vergara, A., & González, O. (2021). El desarrollo del sentido del dato: haciendo inferencias desde la variabilidad de los tsunamis en primaria. Statistics Education Research Journal, 20(2), 1-14. https://doi.org/10.52041/serj.v20i2.413.
Ferreira C., A., Salcedo L., P., & del Valle L., M. (2018). Estudio de disponibilidad léxica en el ámbito de las matemáticas. Estudios Filológicos, (54), 69-84. https://doi.org/10.4067/S0071-17132014000200004
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., Scheaffer, R. (2005). Guideslines for Assessment and Instruction in Statistics Education (GAISE) Report: A pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association.
GAISE (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A curriculum framework for PreK-12 statistics education. ASA
GAISE (2016). College Report ASA Revision Committee, “Guidelines for Assessment and Instruction in Statistics Education College Report 2016,” https://www.amstat.org/education/guidelines-for-assessment-and-instruction-in-statistics-education-(gaise)-reports
Gal, I. (2004). Statistical Literacy. In D. Ben-Zvi & J. Garfi eld (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 47–78). Dordrecht, The Netherlands: Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-2278-6_3
Garfield, J. (1994). Beyond Testing and Grading: Using Assessment To Improve Student Learning. Journal of Statistics Education, 2(1), 1-10. https://doi.org/10.1080/10691898.1994.11910462
Garfield J. B., Ben-Zvi D., Chance, B., Medina, E., Roseth, C., Zieffler, A. (2008). Learning to reason about variability. En J. B. Garfield y D. Ben-Zvi (Eds.), Developing Students’ Statistical Reasoning (pp. 201-214). Dordrecht: Springer. https://doi.org/10.1007/978-1-4020-8383-9_10
Garfield, J. y Ben-Zvi, D. (2008). Developing students’ statistical reasoning: connecting research and teaching practice. Dordrecht: Springer.
Inzunza Cazares, Santiago. (2016). Análisis de datos bivariados en un ambiente basado en applets y software dinámico. Educación matemática, 28(3), 61-90. Epub 08 de abril de 2022.https://doi.org/10.24844/em2803.03
Isoda, M., Chitmun, S., & González, O. (2018). Japanese and Thai senior high school mathematics teachers’ knowledge of variability. Statistics Education Research Journal, 17(2), 196–215.https://doi.org/10.52041/serj.v17i2.166
Kaplan, J., Fisher, D. G., & Rogness, N. T. (2010). Lexical Ambiguity in Statistics: How Students Use and Define the Words: Association, Average, Confidence, Random and Spread. Journal of Statistics Education, 18(2). https://doi.org/10.1080/10691898.2010.11889491
León Gómez, N. A. (2020). Alcances de la enseñanza de la estadística a través de la investigación en la educación media en Venezuela. Revista Paradigma (Edición Cuadragésimo Aniversario:1980-2020), Vol. XLI, 657-684. https://doi.org/10.37618/PARADIGMA.1011-2251.2020.p657-684.id808
Makar, K. y Confrey, J. (2005). Variation talk: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27-54. https://doi.org/10.52041/serj.v4i1.524
Mayring, P. (2000). Qualitative content analysis. Forum Qualitative Social Research, 1(2), 20. https://doi.org/10.17169/fqs-1.2.1089.
McMillan, J. & Schumacher, S. (2011). Investigación educativa. Pearson-Adisson Wesley.
MINEDUC (2019). Bases curriculares tercero y cuarto medio. Ministerio de Educación. Gobierno de Chile.
Moore, D. (1990). Uncertainty. En L. A. Steen (Ed.), On the shoulders of giant: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.
OCDE. (2019). OECD Future of Education and Skills 2030: OECD Learning Compass 2030. OECD.
Pérez Ariza, Karel, & Hernández Sánchez, José Emilio. (2017). La elaboración de preguntas en la enseñanza de la comprensión de problemas matemáticos. Revista latinoamericana de investigación en matemática educativa, 20(2), 223-248. https://doi.org/10.12802/relime.17.2024
Rodríguez-Alveal, F., Díaz-Levicoy, D., & Aguerrea, M. (2022). Alfabetización y pensamiento probabilístico en docentes de matemática, en formación inicial y en activo. Uniciencia, 36(1), 1-16. https://doi.org/10.15359/ru.36-1.22.
Ruíz-Reyes, K., Begué, N., Batanero, C. y Contreras, J. (2017). Un estudio comparado de los contenidos de muestreo en la Educación Secundaria Obligatoria en Chile. Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 19(3), 67-83. https://doi.org/10.23925/1983-3156.2017v19i3p67-83
Salazar Solórzano, L. (2016). Induciendo a la formulación de preguntas como producto de conexiones intramatemáticas. Revista del Congrés Internacional de Docència Universitària i Innovació (CIDUI), (3).
Sánchez, E., da Silva, C. B., & Coutinho, C. (2011). Teachers’ Understanding of Variation. New ICMI Study Series, 211–221. https://doi.org/10.1007/978-94-007-1131-0_22
Suarez Ávila, N. Y., Galindo Mendoza, S. M., & Jiménez Espinosa, A. (2010). La comunicación: eje en la clase de matemáticas. Praxis & Saber, 1(2), 173–202. https://doi.org/10.19053/22160159.1104
Thibaut Páez, C., Medrano Polizzi, D., & Jiménez Saldaña, A. (2018). Evaluación en aula de textos escolares: ¿una estrategia posible? Estudios Pedagógicos, 38(2), 243-257. https://doi.org/10.4067/S0718-07052012000200015
Thompson, D. and Rubenstein, R. (2000). Learning mathematics vocabulary: Potential pitfalls and instructional strategies. Mathematics Teacher, 93(7). pp. 568 – 574. https://doi.org/10.5951/MT.93.7.0568
Torok, R., & Watson, J. (2000). Development of the concept of statistical variation: An exploratory study. Mathematics Education Research Journal, 12(2), 147–169. https://doi.org/10.1007/BF03217081
Utts, Jessica A. (2014). Seeing Through Statistics. Pacific Grove, CA: Duxbury, 4th edition.
Watson, J., Kelly, B., Callingham, R. & Shaughnessy, M. (2003). The measurement of school students´ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1-29. https://doi.org/10.1080/0020739021000018791
Wild, C. J & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
Zapata-Cardona, L., Rocha-Salamanca, P. (2016). Ben-Zvi, D., & Makar, K. (Eds.). (2016). The Teaching and Learning of Statistics. https://doi.org/10.1007/978-3-319-23470-0.
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