Analysis of statistical variability activities in secondary education textbooks: a study from an international proposal standpoint

Keywords: variability, school activities, statistics, textbooks, secondary education, mathematics education

Abstract

The purpose of this paper is to analyze variability activities in secondary education textbooks, which are provided free of charge by the Chilean Ministry of Education, in accordance with the Guidelines for Assessment and Instruction in Statistics Education endorsed by the American Statistical Association and the Common Core State Standards in Mathematics. A qualitative methodology is followed, using content analysis as a method. Sampling was intentional and included eight textbooks of secondary education (freshman, sophomore, junior, and senior), which are in accordance with the current math curriculum in Chile. Results show that, in general, these textbooks do not use real data and do not mention the types of variability, whether natural, induced, or sample variability, to summarize information. In addition, contents are frequently approached in a procedural manner, which restricts teaching to using formulas and, in specific cases, to clarifying certain notations. There is no pedagogical use of computational tools like Excel or GeoGebra. The study evidenced textbook flaws to teach variability, including a lack of clear definitions and their role in statistics. Therefore, teachers should complement what has been indicated in the textbook with new readings and scientific articles on these topics, such as the introduction of appropriate methodologies to teaching statistics and probability, teaching through projects, and case studies with problematic situations in which this concept plays a fundamental role in the decision making.

References

Bargagliotti, A. E. (2012). How well do the NSF funded elementary mathematics curricula align with the GAISE report recommendations? Journal of Statistics Education, 20(3), 1-26. doi: https://doi.org/10.1080/10691898.2012.11889646
Batanero, C., Díaz, C., Contreras, J. M. y Arteaga P. (2011). Enseñanza de la estadística a través de proyectos. En C. Batanero y C. Díaz (Eds.), Estadística con proyectos (pp. 9-46). Universidad de Granada.
Begué, N., Batanero, C. y Gea, M. (2018). Comprensión del valor esperado y variabilidad de la proporción muestral por estudiantes de educación secundaria obligatoria. Enseñanza de las Ciencias, 36(2), 63-79. doi: https://doi.org/10.5565/rev/ensciencias.2256
Ben-Zvi, D. y Garfield, J. (2004). Research on Reasoning about Variability: A Forward. Statistical Education Research Journal, 3(2), 4-6. www.stat.auckland.ac.nz/serj
CCSSI (2010). Common Core State Standars for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Oficers.
Chan, S.W. e Ismail, Z. (2013). Assessing misconceptions in reasoning about variability among high school students. Procedia. Social and Behavioral Sciences, 93, 1478-1483. doi: https://doi.org/10.1016/j.sbspro.2013.10.067
Cobb, G. y Moore, D. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104(9), 801-823. doi: https://doi.org/10.1080/00029890.1997.11990723
Cooper, L. y Shore, F. (2010). The effects of data and graph type on concepts and visualizations of variability. Journal of Statistics Education, 18(2), 1-16. doi: https://doi.org/10.1080/10691898.2010.11889487
Díaz-Levicoy, D., Giacomone, B. y Arteaga, P. (2017). Caracterización de los gráficos estadísticos en libros de texto argentinos del segundo ciclo de Educación Primaria. Profesorado. Revista de Currículum y Formación del Profesorado, 21(3), 299-326.
Díaz-Levicoy, D., Vásquez, C. y Molina-Portillo, E. (2018). Estudio exploratorio sobre tablas estadísticas en libros de texto de tercer año de Educación Primaria. TANGRAM. Revista de Educação Matemática, 1(2), 18-39. doi: https://doi.org/10.30612/tangram.v1i2.7574
Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M. y Scheaffer, R. (2005). A curriculum framework for K-12 statistics education. GAISE report. Alexandria, VA: American Statistical Association.
Franklin, C., Kader, G., Newborn, D., Moreno, J., Peck, R., Perry, M. y Scheaffer, R. (2007). Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: a Pre-k–12 Curriculum Framework. Alexandria, VA: American Statistical Association.
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. doi: https://doi.org/10.1007/978-1-4020-8383-9_10
Gea, M. M., Batanero, C., Arteaga, P., Cañadas, G. R. y Contreras, J. M. (2014). Análisis del lenguaje sobre la correlación y regresión en libros de texto de bachillerato. SUMA. Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 76, 37-45
Hernández, R., Fernández, C. y Baptista, P. (2014). Metodología de la investigación. México: McGraw Hill.
Inzunsa, S. (2014). Geogebra: Una herramienta cognitiva para la enseñanza de la probabilidad. En J. Asenjo, O. Macías y J. C. Toscano (Eds.), Memorias del Congreso Iberoamericano de Ciencia, Tecnología, Innovación y Educación (pp. 1-11). Buenos Aires: OEI.
Krippendorff, K. (1997). Metodología de análisis de contenido. Teoría y práctica. Paidós.
Lee, C. y Meletiou-Mavrotheris, M. (2003). Some difficulties of learning histograms in introductory statistics. En American Statistical Association (Eds.), Proceedings of 2003 Joint Statistical Meeting: Section on Statistical Education (pp. 2326-2336). American Statistical Association.
MINEDUC. (2008). Política de textos escolares. Ministerio de Educación.
MINEDUC. (2012). Estándares orientadores para egresados de Pedagogía en Educación Media. Unidad de Currículum y Evaluación.
MINEDUC. (2015a). Bases Curriculares. 7º básico a 2º medio. Unidad de Currículum y Evaluación.
MINEDUC. (2015b). Matemática. Programa de estudio. Tercero medio. Unidad de Currículum y Evaluación.
Pea, R. (1987). Cognitive technologies for Mathematics Education. En A. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 89-122). Lawrence Erlbaum Associates.
Sandoval, P., Rodríguez-Alveal, F. y Maldonado-Fuentes, A. C. (2011). Competencias TIC en la formación inicial docente: Estudio descriptivo para la toma de decisiones en el currículum. Reflexão e Ação, 19(1), 271-295.
Sandoval, P., Rodríguez-Alveal, F. y Maldonado-Fuentes, A. C. (2017). Evaluación de la alfabetización digital y pedagógica en TIC, a partir de las opiniones de estudiantes en formación inicial docente. Educação e Pesquisa, 43(1), 127-143. doi: https://dx.doi.org/10.1590/s1517-9702201701154907
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. doi: https://doi.org/10.1080/0020739021000018791
Wild, C. J. & Pfannkuch, M. (1999). Statistical Thinking in Empirical Enquiry. International Statistical Review, 67(3), 223-265. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
Published
2021-01-31
How to Cite
Rodríguez-Alveal, F., Díaz-Levicoy, D., & Vásquez, C. (2021). Analysis of statistical variability activities in secondary education textbooks: a study from an international proposal standpoint. Uniciencia, 35(1), 108-123. https://doi.org/10.15359/ru.35-1.7
Section
Original scientific papers (evaluated by academic peers)

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