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Data seen through different lenses

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Abstract

Statistical reasoning focuses on properties that belong not to individual data values but to the entire aggregate. We analyze students’ statements from three different sources to explore possible building blocks of the idea of data as aggregate and speculate on how young students go about putting these ideas together. We identify four general perspectives that students use in working with data, which in addition to an aggregate perspective include regarding data as pointers, as case values, and as classifiers. Some students seem inclined to view data from only one of these three alternative perspectives, which then influences the types of questions they ask, the data representations they generate or prefer, the interpretations they give to notions such as the average, and the conclusions they draw from the data.

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References

  • Bakker, A. (2004). Reasoning about shape as a pattern in variability. Statistics Education Research Journal, 3(2), 64–83.

    Google Scholar 

  • Bakker, A. (2007). Diagrammatic reasoning and hypostatic abstraction in statistics education. Semiotica, 164(1/4), 9–29.

    Article  Google Scholar 

  • Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 147–168). Dordrecht, The Netherlands: Kluwer Academic Press.

    Chapter  Google Scholar 

  • Ben-Zvi, D. (2004). Reasoning about data analysis. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 121–145). Dordrecht, The Netherlands: Kluwer Academic Press.

    Chapter  Google Scholar 

  • Ben-Zvi, D., & Amir, Y. (2005). How do primary school students begin to reason about distributions? In K. Makar (Ed.), Reasoning about distribution. Proceedings of the Fourth International Research Forum on Statistical Reasoning, Thinking, and Literacy, University of Auckland, New Zealand, 2-7 July, 2005. Brisbane: The University of Queensland. (CD-ROM).

  • Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35–65.

    Article  Google Scholar 

  • Bertin, J. (1983). Semiology of graphics: Diagrams networks maps (W. J. Berg, Trans.). Madison: University of Wisconsin Press. Original work published 1967.

    Google Scholar 

  • Biehler, R. (1994). Probabilistic thinking, statistical reasoning, and the search for causes—Do we need a probabilistic revolution after we have taught data analysis? In J. Garfield (Ed.), Research papers from ICOTS 4 (pp. 20–37). Minneapolis, MN: University of Minnesota.

    Google Scholar 

  • Bowker, G. C., & Star, S. L. (1999). Sorting things out: Classification and its consequences. Cambridge, MA: MIT Press.

  • Bright, G. W., & Friel, S. N. (1998). Helpingstudents interpret data. In S.P. Lajoie (Ed.), Reflections on statistics:Learning, teaching, and assessment in grades K-12 (pp. 63–88). Mahwah, NJ: Lawrence Erlbaum Associates.

  • Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43.

    Article  Google Scholar 

  • Cobb, P., McClain, K., & Gravemeijer, K. (2003). Learning about statistical covariation. Cognition and Instruction, 21(1), 1–78.

    Article  Google Scholar 

  • Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382–393.

    Article  Google Scholar 

  • English, L. D. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81(1), 15–30.

    Article  Google Scholar 

  • Fisher, R. A. (1990). Statistical methods experimental design and scientific inference. Oxford: Oxford University Press. First published in 1925.

    Google Scholar 

  • Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124–158.

    Article  Google Scholar 

  • Gal, I., Rothschild, K., & Wagner, D. A. (1990). Statistical concepts and statistical reasoning in school children: Convergence or divergence? Boston: Paper presented at the annual meeting of the American Educational Research Association, Boston.

    Google Scholar 

  • Gould, S. J. (1996). Full house. New York: Harmony Books.

    Book  Google Scholar 

  • Hammerman, J., & Rubin, A. (2004). Strategies for managing statistical complexity with new software tools. Statistics Education Research Journal, 3(2), 17–41.

    Google Scholar 

  • Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337–364.

    Article  Google Scholar 

  • Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (1999). A framework for assessing students’ statistical thinking. San Francisco: Paper presented at the annual meeting of the Research Presession of the National Council of Teachers of Mathematics, San Francisco.

    Google Scholar 

  • Konold, C., & Higgins, T. (2002). Highlights of related research. In S. J. Russell, D. Schifter, & V. Bastable (Eds.), Developing mathematical ideas: Working with data (pp. 165–201). Parsippany, NJ: Dale Seymour Publications.

    Google Scholar 

  • Konold, C., & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 193–215). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Konold, C., & Khalil, K. (2003). If u can graff these numbers — 2, 15, 6 — your stat literit. Paper presented at the annual meeting of the American Educational Research Association, Chicago.

    Google Scholar 

  • Konold, C., & Lehrer, R. (2008). Technology and mathematics education: An essay in honor of Jim Kaput. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 49–72). New York: Routledge.

  • Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.

    Article  Google Scholar 

  • Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students analyzing data: Research of critical barriers. In J. B. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics: 1996 Proceedings of the 1996 IASE Round Table Conference (pp. 151–167). Voorburg, The Netherlands: International Statistical Institute. Retrieved from http://www.dartmouth.edu/~chance/teaching_aids/IASE/IASE.book.pdf.

  • Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A., Wing, R., et al. (2002). Students’ use of modal clumps to summarize data. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching of Statistics (CD-ROM). Voorburg, The Netherlands: International Statistical Institute.

  • Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41(3), 635–679.

    Article  Google Scholar 

  • Lehrer, R., Schauble, L., Carpenter, S., & Penner, D. (2000). The inter-related development of inscriptions and conceptual understanding. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools and instructional design (pp. 325–360). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Makar, K., & Confrey, J. (2004). Secondary teachers’ reasoning about comparing two groups. In D. Ben-Zv i & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 353–373). Dordrecht, the Netherlands: Kluwer Academic Publisher.

  • Mokros, J., & Russell, S. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20–39.

    Article  Google Scholar 

  • Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants (pp. 95–137). Washington, DC: National Academy Press.

    Google Scholar 

  • Prodromou, T., & Pratt, D. (2006). The role of causality in the co-ordination of two perspectives on distribution within a virtual simulation. Statistics Education Research Journal, 5(2), 69–88.

    Google Scholar 

  • Reading, C., & Canada, D. (2011). Teachers’ knowledge of distribution. 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. 223–234). New York: Springer.

    Chapter  Google Scholar 

  • Reading, C., & Reid, J. (2006). An emerging hierarchy of reasoning about distribution: From a variation perspective. Statistics Education Research Journal, 5(2), 46–68.

    Google Scholar 

  • Roth, W.-M. (2005). Mathematical inscriptions and the reflexive elaboration of understanding: An ethnography of graphing and numeracy in a fish hatchery. Mathematical Thinking and Learning, 7(2), 75–110.

    Article  Google Scholar 

  • Russell, S. J., Schifter, D., & Bastable, V. (2002). Developing mathematical ideas: Working with data casebook. Glenview, IL: Pearson Education, Inc.

    Google Scholar 

  • Shaughnessy, J. M., Watson, J., Moritz, J., & Reading, C. (1999). School mathematics students’ acknowledgment of statistical variation. Paper presented at the 77th annual meeting of the National Council of Teachers of Mathematics, San Francisco.

  • Stigler, S. M. (1999). Statistics on the table: The history of statistical concepts and methods. Cambridge, MA: Harvard University Press.

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.

    Google Scholar 

  • Wainer, H. (2001). Order in the court. Chance, 14(1), 43–46.

    Article  Google Scholar 

  • Watson, J. M. (2009). The influence of variation and expectation on the developing awareness of distribution. Statistics Education Research Journal, 8(1), 32–61.

    Google Scholar 

  • Watson, J. M., & Moritz, J. B. (1999). The beginning of statistical inference: Comparing two sets of data. Educational Studies in Mathematics, 37(2), 145–168.

    Article  Google Scholar 

  • Watson, J. M., & Moritz, J. B. (2000). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2(1), 9–48.

    Google Scholar 

  • Wild, C. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–25.

    Google Scholar 

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Authors and Affiliations

  1. Scientific Reasoning Research Institute, University of Massachusetts Amherst, Amherst, MA, USA

    Clifford Konold & Khalimahtul Khalil

  2. TERC, Cambridge, MA, USA

    Traci Higgins & Susan Jo Russell

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  1. Clifford Konold
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  2. Traci Higgins
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  3. Susan Jo Russell
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  4. Khalimahtul Khalil
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Correspondence to Clifford Konold.

Additional information

This research was supported by the National Science Foundation under Grant Nos. REC-9725228, REC-9814898, ESI-9730683, ESI-9731064, and ESI-9818946. Any opinions, findings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation. Figures 4, 8, 10, and 11 and case excerpts are reprinted from Russell, S. J., Schifter, D., and Bastable, V., Working with Data Casebook from the Developing Mathematical Ideas series. Copyright © 2002 by Education Development Center, Inc. Published by Pearson Education, Inc. Used by permission. All rights reserved.

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Konold, C., Higgins, T., Russell, S.J. et al. Data seen through different lenses. Educ Stud Math 88, 305–325 (2015). https://doi.org/10.1007/s10649-013-9529-8

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