Students Reasoning About Variation in Risk Context
This chapter explores students’ reasoning about variation when they compare groups and have to interpret spread in terms of risk. In particular, we analyze the responses to two problems administered to 87 ninth-grade students. The first problem consists of losses and winnings in a hypothetical game; the second is about life expectancy of patients after medical treatments. The problems consist of comparing groups of data, and choosing one in which it is more advantageous to bet or to receive medical treatment. In this research we propose three levels of students’ reasoning when they interpret variation. Decision making in the third level of reasoning is influenced by risk. As a conclusion, some characteristics of the problems and the solutions provided by the students are highlighted.
KeywordsMiddle school students Reasoning Risk Statistics education Variation
Grant EDU2016-74848-P (FEDER, AEI). Grant CONACYT No. 254301.
- Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42–63.Google Scholar
- Ben-Zvi, D., & Garfield, J. (2004). Research on reasoning about variability. Statistics Education Research Journal, 3(2), 4–6.Google Scholar
- Biggs, J. B., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.Google Scholar
- Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behaviour. In H. Rowe (Ed.), Intelligence, reconceptualization and measurement (pp. 57–76). Hillsdale, NJ: Laurence Erlbaum Associates.Google Scholar
- Birks, M., & Mills, J. (2011). Grounded theory. Thousand Oaks, CA: Sage.Google Scholar
- Burrill, G., & Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 57–69). New York: Springer.CrossRefGoogle Scholar
- Ciancetta, M. (2007). Statistics students reasoning when comparing distributions of data (Doctoral thesis). Portland State University. Online: http://www.stat.auckland.ac.nz/~iase/publications/dissertations/07.Ciancetta.Dissertation.pdf.
- Gal, I., Rothschild, K., & Wagner, D. A. (1989). Which group is better? The development of statistical reasoning in elementary school children. Paper presented at the meeting of the Society for Research in Child Development, Kansas City, MO.Google Scholar
- Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1), 92–99.Google Scholar
- Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer.Google Scholar
- Moore, D. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.Google Scholar
- Orta, A., & Sánchez, E. (2011). Influential aspects in middle school students' understanding of statistics variation. In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society For Research in Mathematics Education, Rzeszów, Poland.Google Scholar
- SEP. (2011). Programas de Estudio. Educación Básica. Secundaria. Matemáticas. México, D. F.: Secretaría de Educación Pública.Google Scholar
- Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1010). Greenwich, CT: Information Age Publishing, Inc. and National Council of Teachers of Mathematics.Google Scholar
- Shaughnessy, J. M., Ciancetta, M., Best, K., & Canada, D. (2004). Students’ attention to variability when comparing distributions. Paper Presented at the Research Pre-session of the 82nd Annual Meeting of the National Council of Teachers of Mathematics, Philadelphia, PA.Google Scholar
- Tal, J. (2001). Reading between the numbers: Statistical thinking in everyday life. New York: McGraw-Hill.Google Scholar
- Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
- Watson, J.M., & Moritz, J.B. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37(2), 145–168.Google Scholar