Reasoning levels about sampling notions in university students: an exploratory study with Mexican students

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Eleazar Silvestre Castro
Universidad de Sonora, México
https://orcid.org/0000-0002-9472-483X
Maricela Armenta Castro
Universidad de Sonora, México
https://orcid.org/0000-0002-4992-5763

Abstract

The objective of this study is to characterize the reasoning levels of a sample of university students about notions related to the concept of sampling. For this, we analyze and classify students’ responses to four problems that require them: a definition of the concept of sample, the evaluation of statistical conclusions based on the procedural aspects of sampling, and an understanding of representativeness and sample variability in a probabilistic context. The answers to each problem are ranked using the SOLO Taxonomy. Our results suggest that students adequately characterize the concept of sample, but also that they have considerable difficulties in: correctly applying the part-whole notion that characterizes a sample, identifying the sample size in a given survey, recognizing sampling methods that carry bias and, appropriately link the notions of representativeness and sample variability with a frequentist approach to probability. Results are compared with reference studies and points of attention for the teaching of the topic are discussed.

Item information
Published: Dec 6, 2022
Issue: Vol. 1 No. 1 (2022): Revista de Educación Estadística
Section: Investigación
DOI: https://doi.org/10.29035/redes.1.1.9
Keywords: Sampling, sampling representativeness and sampling variability, reasoning levels, SOLO taxonomy, tertiary statistics

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References

Ainley, J. Gould, R. y Pratt, D. (2015). Learning to reason from samples: Commentary from the perspectives of task design and the emergence of “big data”. Educational Studies in Mathematics, 88(3), 405-412. https://doi.org/10.1007/s10649-015-9592-4


Begué, N., Batanero, C., Gea, M.M. y Beltrán, P. (2020). Comprensión de la representatividad y variabilidad muestral por estudiantes de educación secundaria. Yupana, 12, 8-22. https://doi.org/10.14409/yu.v0i12.9624





Begué, N., Batanero, C., Ruiz, K. y Gea, M. M. (2019). Understanding sampling: A summary of the research. Boletín de estadística e investigación operativa–BEIO, 35(1), 49-78.


Biggs, J. B. y Collis, K. F. (1991). Multimodal learning and the quality of intelligence behavior. En H. A. Rowe (Ed.), Intelligence: reconceptualization and measurement (pp. 57-76).Erlbaum.


Burrill, G. y Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. En C. Batanero, G. Burrill y C. Reading (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education. A Joint ICMI/IASE study. (pp. 57-69). Springer.


Carver, R.H., Everson, M., Gabrosek, J., Horton, N.J., Lock, R.H., Mocko, M., Rossman, A., Roswell, G., Velleman, P.F., Witmer, J.A. y Wood, B. (2016). Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report 2016.


delMas, R., Garfield, J. y Zieffler, A. (2009). The tyranny of context. Trabajo presentado en el International Collaboration for Research on Statistical Reasoning, Thinking, and Literacy, Brisbane, Australia.


Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70, 1-51. https://doi.org/10.2307/1403713


Gómez-Blancarte, A. L., Rocha, R. y Chávez, R. D. (2021). A survey of the teaching of statistical literacy, reasoning and thinking: teachers’ classroom practice in mexican high school education. Statistics Education Journal, 20(2). https://doi.org/10.52041/serj.v20i2.397


Harradine, A., Batanero, C. y Rossman, A. (2011). Students and teachers’ knowledge of sampling and inference. En Batanero, C., Burrill, G. y Reading, C. (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education. A Joint ICMI/IASE study (pp. 235-246). Springer. https://doi.org/10.1007/978-94-007-1131-0_24


Heitele, D. (1975). An epistemological view on fundamental stochastic ideas. Educational Studies in Mathematics, 6(2), 187-205.


Inzunza, S. (2020). Fundamental statistical ideas in primary, secondary and high school mexican curriculum: reflections from the international perspective. En A.I. Sacristán, J.C. Cortés-Zavala Y P.M. Ruiz-Arias (Eds.), Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1308-1311). Cinvestav, AMIUTEM, PME-NA. https://doi.org/10.51272/pmena.42.2020


Inzunza, S. e Islas, E. (2019). Análisis de una trayectoria de aprendizaje para desarrollar razonamiento sobre muestras, variabilidad y distribuciones muestrales. Revista Educación Matemática, 31(3), 203-230. https://doi.org/10.24844/em3103.08


Kahneman, D. y Tversky, A. (1982). Judgments of and by representativeness. En D. Kahneman, P. Slovic y A. Tversky (Eds.), Judgement under uncertainty: Heuristics and biases (pp. 117-128). Cambridge University Press.


Lee, H., Angotti, R. y Tarr, J. (2010). Making comparisons between observed data and expected outcomes: Students’ informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68-96. https://doi.org/10.52041/serj.v9i1.388 


Moore, D. y Cobb, G. (2000). Statistics and mathematics: Tension and cooperation. The American Mathematical Monthly, 107(7), 615-630. https://doi.org/10.1080/00029890.2000.12005247


Nilsson, P., Eckert, A. y Pratt, D. (2018). Challenges and Opportunities in Experimentation-Based Instruction in Probability. En C. Batanero y E. J. Chernoff (Eds.), Teaching and Learning Stochastics, ICME-13 Monographs. (pp.51-71). Springer International Publishing. https://doi.org/10.1007/978-3-319-72871-1_4


Reading, C. y Reid, J. (2010). Reasoning about variation: rethinking theoretical frameworks to inform practice. En C. Reading (Ed.), Data and context in statistics education: towards an evidence-based society. Proceedings of the eighth international conference on teaching statistics, ICOTS 8. International Statistical Institute.


Rossman, A. (2008). Reasoning about informal statistical inference: One statistician’s view. Statistics Education Research Journal, 7(2), 5-19.


Ruiz, K. y Contreras, J.M. (2021). Understanding sampling by chilean secondary school students. Statistics Education Journal, 20(2), 1-12. https://doi.org/10.52041/serj.v20i2.383


Saldanha, L. y Thompson, P. (2002). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51(3), 257-270. https://doi.org/10.1023/A:1023692604014


Sánchez, E. y Landín, P. (2014). Levels of Probabilistic Reasoning of High School Students About Binomial Problems. En E.J. Chernoff, B. Sriraman (Eds.), Probabilistic Thinking, Advances in Mathematics Education, (pp.581-597). Springer. https://doi.org/10.1007/978-94-007-7155-0_31


Secretaría de Educación Pública. (2017). Planes de Estudio de Referencia del Marco Curricular Común de la Educación Media Superior. Recuperado de https://www.gob.mx/cms/uploads/attachment/file/241519/planes-estudio-sems.pdf


Silvestre, E., Sánchez, E. e Inzunza, S. (2022). El razonamiento de estudiantes de bachillerato sobre el muestreo repetido y la distribución muestral empírica. Revista Educación Matemática, 34(1), 100-130. https://doi.org/10.24844/EM3401.04


Watson, J. (2004). Developing reasoning about samples. En D. Ben-Zvi y J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 277-294). Kluwer.


Watson, J. y Moritz, J. (2000). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behavior, 19, 109-136.


Watson, J. y Kelly, B. (2005). Cognition and instruction: Reasoning about bias in sampling. Mathematics Education Research Journal, 17(1), 24-57. https://doi.org/10.1007/BF03217408


Wroughton, J. R., McGowan, H. M., Weiss, L. V. y Cope, T. M. (2013). Exploring the role of context in students’ understanding of sampling. Statistics Education Research Journal, 12(2), 32-58. https://doi.org/10.52041/serj.v12i2.303



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