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Part of the book series: Springer International Handbooks of Education ((SIHE))

Abstract

This chapter presents an overview of the Practice of Statistics focusing mainly on research at the school level. After introducing several frameworks for the practice, research is summarized in relation to posing and refining statistical questions for investigation, to planning for and collecting appropriate data, to analyzing data through visual representations, to analyzing data by summarizing them with specific measures, and to making decisions acknowledging uncertainty. The importance of combining these stages through complete investigations is then stressed both in terms of student learning and of the needs of teachers for implementation. The need for occasional backtracking is also acknowledged, and more research in relation to complete investigations is seen as a priority. Having considered the Practice of Statistics as an active engagement by learners, the chapter reviews presentations of the Big Ideas underlying the practice, with a call for research linking classroom investigations with the fundamental understanding of the Big Ideas. The chapter ends with a consideration of the place of statistical literacy in relation to the Practice of Statistics and the question of the responsibility of the school curriculum to provide understanding and proficiency in both.

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References

  • Ainley, J. (2000). Transparency in graphs and graphing tasks: An iterative design process. The Journal of Mathematical Behavior, 19(3), 365–384.

    Article  Google Scholar 

  • Allmond, S., & Makar, K. (2010). Developing primary students’ ability to pose questions in statistical investigations. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society (Proceedings of the 8th International Conference on the Teaching of Statistics, Ljubljana, Slovenia, July 11–16). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Arnold, P. (2008). What about the P in the PPDAC cycle? An initial look at posing questions for statistical investigation. Proceedings of the 11th International Congress of Mathematics Education, Monterrey, Mexico, 6–13 July 2008.

    Google Scholar 

  • Australian Bureau of Statistics. (2011). CensusAtSchool Australia: Your random data sample. Retrieved from www.cas.abs.gov.au/cgi-local/cassampler.pl

    Google Scholar 

  • Australian Curriculum, Assessment and Reporting Authority. (2013). General capabilities in the Australian Curriculum, January, 2013. Sydney: Author.

    Google Scholar 

  • Australian Curriculum, Assessment and Reporting Authority. (2015). The Australian curriculum: Mathematics, Version 8.0, August 21, 2015. Sydney: Author.

    Google Scholar 

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

    Google Scholar 

  • Bakker, A., Biehler, R., & Konold, C. (2005). Should young students learn about box plots? In G. Burrill & M. Camden (Eds.), Curricular development in statistics education: International Association for Education (IASE) Roundtable (pp. 163–173). Voorburg, The Netherlands: International Statistics Institute.

    Google Scholar 

  • Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1 & 2), 5–26.

    Article  Google Scholar 

  • Bakker, A., Derry, J., & Konold, C. (2006, July). Using technology to support diagrammatic reasoning about center and variation. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education (Proceedings of the 7th International Conference on the Teaching of Statistics, Salvador, Bahia, Brazil, July 2–7). Voorburg, The Netherlands: International Association for Statistical Education and the International Statistical Institute.

    Google Scholar 

  • Batanero, C., Burrill, G., & Reading, C. (Eds.). (2011). Teaching statistics in school mathematics—Challenges for teaching and teacher education: A joint ICMI/IASE study. Dordrecht, The Netherlands: Springer.

    Google Scholar 

  • Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.

    Article  Google Scholar 

  • Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning and thinking. Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Bidgood, P. (2014). Towards statistical literacy—Relating assessment to the real world. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 643–690). New York: Springer.

    Google Scholar 

  • Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.

    Google Scholar 

  • Boland, P. J. (2002). Promoting statistics thinking amongst secondary school students in the national context. In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Botting, B., & Stone, D. (2002). Experience of dealing with the media on congenital anomaly research. In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Bright, G. W., & Friel, S. N. (1998). Graphical representations: Helping students 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.

    Google Scholar 

  • Budgett, S., Pfannkuch, M., Regan, M., & Wild, C. J. (2013). Dynamic visualizations and the randomization test. Technology Innovations in Statistics Education, 7(2), Article 5.

    Google Scholar 

  • Burgess, T. A. (2011). Teacher knowledge of and for statistical investigations. 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. 259–270). Dordrecht, The Netherlands: Springer.

    Chapter  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). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Cai, J. (1998). Exploring students’ conceptual understanding of the averaging algorithm. School Science and Mathematics, 98(2), 93–98.

    Article  Google Scholar 

  • Chance, B., delMas, R., & Garfield, J. (2004). Reasoning about sampling distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 295–323). Dordrecht, The Netherlands: Kluwer.

    Chapter  Google Scholar 

  • Chick, H. L., Pfannkuch, M., & Watson, J. M. (2005). Transnumerative thinking: Finding and telling stories with data. Curriculum Matters, 1, 87–108.

    Google Scholar 

  • Chick, H. L., & Watson, J. M. (2001). Data representation and interpretation by primary school students working in groups. Mathematics Education Research Journal, 13(2), 91–111.

    Article  Google Scholar 

  • Chin, S., & Kayalvizhi, G. (2002). Posing questions for open investigations: What questions do pupils ask? Research in Science & Technology Education, 20(2), 269–287.

    Article  Google Scholar 

  • Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 375–395). Dordrecht, The Netherlands: Kluwer.

    Chapter  Google Scholar 

  • Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association for Best Practices and the Council of Chief State School Officers.

    Google Scholar 

  • Crites, T., & St. Laurent, R. (2015). Putting essential understanding of statistics into practice in grades 9–12. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Doerr, H. M., & Pratt, D. (2008). The learning of mathematics and mathematical modeling. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Volume 1 Research syntheses (pp. 259–286). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24–47.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • English, L. D. (2015). STEM: Challenges and opportunities for mathematics education. In K. Beswick, T. Muir, & J. Wells (Eds.), Climbing mountains, building bridges (Proceedings of 39th conference of the International Group for the Psychology of Mathematics Education, Hobart, Tasmania, 13–18 July, Vol. 1, pp. 3–18). Hobart, Australia: PME Program Committee.

    Google Scholar 

  • English, L. D., & Watson, J. M. (2015). Statistical literacy in the elementary school: Opportunities for problem posing. In F. Singer, N. Ellerton, & J. Cai (Eds.), Problem posing: From research to effective practice (pp. 241–256). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Esfandiari, M., Sorenson, K., Zes, D., & Nichols, K. (2014). Enhancing statistical literacy and thinking through analysis of scientific journal articles. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Fielding-Wells, J. (2010). Linking problems, conclusions and evidence: Primary students’ early experiences of planning statistical investigations. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society (Proceedings of the 8th International Conference on the Teaching of Statistics, Ljubljana, Slovenia, July 11–16). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Fielding-Wells, J., & Makar, K. (2012). Developing primary students’ argumentation skills in inquiry-based mathematics classrooms. In K. T. Jan van Aalst, M. J. Jacobson, & P. Reimann (Eds.), The Future of learning: Proceedings of the 10th International Conference of the Learning Sciences [ICLS 2012]—Volume 2 Short Papers, Symposia, and Abstracts (pp. 149–153). Sydney, Australia: International Society of the Learning Sciences.

    Google Scholar 

  • Fielding-Wells, J., & Makar, K. (2015). Inferring to a model: Using inquiry-based argumentation to challenge young children’s expectations of equally likely outcomes. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. 1–27). Minneapolis, MN: Catalyst Press.

    Google Scholar 

  • Finzer, W. (2012). Fathom dynamic data software [computer software, Version 2.13]. Emeryville, CA: Key Curriculum Press and KCP Technologies.

    Google Scholar 

  • Finzer, W., & Parvate, V. (2008). Who will teach them about data? Paper presented at the International Conference on Mathematics Education, Monterrey, Mexico.

    Google Scholar 

  • Fitzallen, N. (2012). Interpreting graphs: Students developing an understanding of covariation. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 290–297). Singapore: MERGA.

    Google Scholar 

  • Fitzallen, N. (2013). Characterising students’ strategies with TinkerPlots. Technology Innovations in Statistics Education, 7(1), Article 2.

    Google Scholar 

  • Fitzallen, N., Watson, J., & English, E. (2015). Assessing a statistical inquiry. In K. Beswick, T. Muir, & J. Wells, (Eds.), Climbing mountains, building bridges (Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education, July 13–18, Vol. 2, pp. 305–312). Hobart, Australia: PME Program Committee.

    Google Scholar 

  • Forster, M., & Wild, C. J. (2010). Writing about findings: Integrating teaching and assessment. In P. Bidgood, N. Hunt, & F. Jolliffe (Eds.), Assessment methods in statistical education: An international perspective (pp. 87–102). Chichester, UK: Wiley.

    Chapter  Google Scholar 

  • Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A preK-12 curriculum framework. Alexandria, VA: American Statistical Association.

    Google Scholar 

  • Friel, S., 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. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1–51.

    Article  Google Scholar 

  • Gal, I. (2005). Towards “Probability Literacy” for all citizens: Building blocks and instructional dilemmas. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39–63). New York: Springer.

    Chapter  Google Scholar 

  • Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer.

    Google Scholar 

  • Gigerenzer, G., & Edwards, A. (2003). Simple tools for understanding risks: From innumeracy to insight. BMJ: British Medical Journal, 327(7417), 741–744.

    Article  Google Scholar 

  • Gil, E., & Ben-Zvi, D. (2010). Emergence of reasoning about sampling among young students in the context of informal inferential reasoning. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society (Proceedings of the 8th International Conference on the Teaching of Statistics, Ljubljana, Slovenia, July 11–16). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Goodchild, S. (1988). School pupils’ understanding of average. Teaching Statistics, 10(3), 77–81.

    Article  Google Scholar 

  • Hammerman, J. (2009). Exploring large scientific data sets as an entrée to statistical ideas in secondary schools. Paper presented at the IASE Satellite conference: Next steps in statistics education, Durban, South Africa.

    Google Scholar 

  • Holmes, P. (1980). Teaching statistics 11–16. Slough, UK: Schools Council Publications and W. Foulsham.

    Google Scholar 

  • Hovermill, J., Beaudrie, B., & Boschmans, B. (2014). Statistical literacy requirements for teachers. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Jacobs, V. R. (1999). How do students think about statistical sampling before instruction? Mathematics in the Middle School, 5(4), 240–263.

    Google Scholar 

  • Konold, C. (2007). Designing a data analysis tool for learners. In M. C. Lovett & P. Shah (Eds.), Thinking with data (pp. 267–291). New York: Lawrence Erlbaum.

    Google Scholar 

  • Konold, C., Finzer, W., Kreetong, K., & Gaston, R. (2014, April). Modeling as a core component of structuring data. Paper presented at the annual meeting of the Research Conference of the National Council of Teachers of Mathematics, New Orleans.

    Google Scholar 

  • Konold, C., & Harradine, A. (2014). Contexts for highlighting signal and noise. In T. Wassong, D. Frischemeier, P. R. Fischer, R. Hochmuth, & P. Bender (Eds.), Using tools for learning mathematics and statistics (pp. 237–250). Heidelberg: Springer Spektrum.

    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., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.

    Article  Google Scholar 

  • Konold, C., & Miller, C. D. (2015). TinkerPlots: Dynamic data exploration [Computer software, Version 2.3]. Adelaide, SA: Learn Troop.

    Google Scholar 

  • Lane, D. M., & Peres, S. C. (2006). Interactive simulations in the teaching of statistics: Promise and pitfalls. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education (Proceedings of the 7th International Conference on the Teaching of Statistics, Salvador, Bahai, Brazil, July 2–7). Voorburg, The Netherlands: International Association for Statistical Education and the International Statistical Institute.

    Google Scholar 

  • Lavigne, N. C., & Lajoie, S. P. (2007). Statistical reasoning of middle school children engaging in survey inquiry. Contemporary Educational Psychology, 32(4), 630–666.

    Article  Google Scholar 

  • Leavy, A. M., Friel, S. N., & Mamer, J. D. (2009). It’s a fird! Can you compute a median of categorical data? Mathematics Teaching in the Middle School, 14(6), 344–351.

    Google Scholar 

  • Lehrer, R., Kim, M., & Jones, R. S. (2011). Developing conceptions of statistics by designing measures of distribution. ZDM Mathematics Education, 43(5), 723–736.

    Article  Google Scholar 

  • Lehrer, R., Kim, M.-J., & Schauble, L. (2007). Supporting the development of conceptions of statistics by engaging students in measuring and modeling variability. International Journal of Computers for Mathematical Learning, 12(3), 195–222.

    Article  Google Scholar 

  • MacFeely, S., & MacCuirc, E. (2014). More ways to heaven than one: Improving statistical literacy in Ireland. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, AZ, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Madden, S. R. (2011). Statistically, technologically, and contextually provocative tasks: Supporting teachers’ informal inferential reasoning. Mathematical Thinking and Learning, 13(1–2), 109–131.

    Article  Google Scholar 

  • Madden, S. R. (2013). Supporting teachers’ instrumental genesis with dynamic mathematical software. In D. Polly (Ed.), Common core mathematics standards and implementing digital technologies (pp. 295–318). Hershey, PA: IGI Global.

    Chapter  Google Scholar 

  • Makar, K. (2010). Teaching primary teachers to teach statistical inquiry: The uniqueness of initial experiences. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society (Proceedings of the 8th International Conference on the Teaching of Statistics, Ljubljana, Slovenia, July 11–16). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Makar, K. (2014). Young children’s explorations of average through informal inferential reasoning. Educational Studies in Mathematics, 86(1), 61–78.

    Article  Google Scholar 

  • Makar, K. (2016). Developing young children’s emergent inferential practices in statistics. Mathematical Thinking and Learning, 18(1), 1–24.

    Article  Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom. ZDM Mathematics Education, 47(7), 1107–1120.

    Article  Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13, 152–173.

    Google Scholar 

  • Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 1–4.

    Article  Google Scholar 

  • Makar, K., & Fielding-Wells, J. (2011). Teaching teachers to teach statistical investigations. 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. 347–358). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.

    Google Scholar 

  • Manor, H., & Ben-Zvi, D. (2015). Students’ articulations of uncertainty in informally exploring sampling distributions. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. 57–94). Minneapolis, MN: Catalyst Press.

    Google Scholar 

  • Meletiou-Mavrotheris, M., & Paparistodemou, E. (2015). Developing students’ reasoning about samples and sampling in the context of informal inferences. Educational Studies in Mathematics, 88(3), 385–404.

    Article  Google Scholar 

  • Mills, J. D. (2002). Using computer simulation methods to teach statistics: A review of the literature. Journal of Statistics Education, 10(1), Article 4.

    Google Scholar 

  • Ministry of Education. (2007). The New Zealand curriculum. Wellington, NZ: Author. Retrieved from http://nzcurriculum.tki.org.nz/The-New-Zealand-Curriculum

    Google Scholar 

  • Ministry of Education. (2009). The New Zealand curriculum: Mathematics standards for years 1–8. Wellington, NZ: Author. Retrieved from http://nzcurriculum.tki.org.nz/The-New-Zealand-Curriculum/Learning-areas/Mathematics-and-statistics

    Google Scholar 

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

    Article  Google Scholar 

  • Monk, S. (2003). Representation in school mathematics: Learning to graph and graphing to learn. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 250–262). Reston, VA: The National Council of Teachers of Mathematics.

    Google Scholar 

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

    Google Scholar 

  • Moore, D. S., & McCabe, G. P. (1989). Introduction to the practice of statistics. New York: W. H. Freeman.

    Google Scholar 

  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2014). Introduction to the practice of statistics (8th ed.). New York: W. H. Freeman.

    Google Scholar 

  • Moreno, J. L. (2002). Toward a statistically literacy citizenry: What statistics everyone should know. In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Murray, S., & Gal, I. (2002). Preparing for diversity in statistics literacy: Institutional and educational implications. In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • North, D., Zewotir, T., & Gal, I. (2014). Developing statistical literacy amongst in-service teachers through a collaborative project. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, AZ, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Osana, H. P., Leath, E. P., & Thompson, S. E. (2004). Improving evidential argumentation through statistical sampling: evaluating the effects of a classroom intervention for at-risk 7th-graders. The Journal of Mathematical Behavior, 23(3), 351–370.

    Article  Google Scholar 

  • Pea, R. (1985). Beyond amplification: Using the computer to reorganize mental functioning. Educational Psychologist, 20(4), 167–182.

    Article  Google Scholar 

  • Peck, R., Gould, R., & Miller, S. (2013). Developing essential understanding of statistics for teaching mathematics in grades 9–12. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Pfannkuch, M. (2005). Thinking tools and variation. Statistics Education Research Journal, 4(1), 83–91.

    Google Scholar 

  • Pfannkuch, M., Arnold, P., & Wild, C. (2015). What I see is not quite the way it is: Students’ emergent reasoning about sampling variability? Educational Studies in Mathematics, 88(3), 343–360.

    Article  Google Scholar 

  • Phillips, A. M. (2002). DNA “fingerprints” and their statistical analysis in human populations. In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Pollatsek, A., Lima, S., & Well, A. D. (1981). Concept or computation: Students’ understanding of the mean. Educational Studies in Mathematics, 12(2), 191–204.

    Article  Google Scholar 

  • Pratt, D., Johnston-Wilder, P., Ainley, J., & Mason, J. (2008). Local and global thinking in statistical influence. Statistics Education Research Journal, 7(2), 107–129.

    Google Scholar 

  • Rao, C. R. (1975). Teaching of statistics at the secondary level: An interdisciplinary approach. International Journal of Mathematical Education in Science and Technology, 6, 151–162.

    Google Scholar 

  • Reaburn, R. (2014). Introductory statistics course tertiary students’ understanding of p-values. Statistics Education Research Journal, 13(1), 53–65.

    Google Scholar 

  • Rubin, A., Bruce, B., & Tenney, Y. (1990). Learning about sampling: Trouble at the core of statistics. In D. Vere-Jones (Ed.), School and general issues (Proceedings of the 3rd International Conference on the Teaching of Statistics, Dunedin, New Zealand, August 19–24). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Russell, S. J., & Mokros, J. (1990). What’s typical? Children’s and teachers’ ideas about average. In D. Vere-Jones (Ed.), School and general issues (Proceedings of the 3rd International Conference on the Teaching of Statistics, Dunedin, New Zealand, August 19–24). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Saldanha, L., & McAllister, M. (2014). Using re-sampling and sampling variability in an applied context as a basis for making statistical inferences with confidence. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Santos, R., & Ponte, J. P. (2014). Learning and teaching statistical investigations: A case study of a prospective teacher. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Schield, M. (2002). Three kinds of statistical literacy: What should we teach? In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Shaughnessy, J. M. (1997). Missed opportunities in research on the teaching and learning of data and chance. In F. Biddulph & K. Carr (Eds.), People in mathematics education (Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 6–22), Waikato, New Zealand: MERGA.

    Google Scholar 

  • Shaughnessy, J. M. (2006). Research on students’ understanding of some big concepts in statistics. In G. Burrill & P. Elliott (Eds.), Thinking and reasoning with data and chance (pp. 77–98). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Shaughnessy, J. M., & Pfannkuch, M. (2002). How faithful is old faithful? Statistical thinking: A story of variation and prediction. Mathematics Teacher, 95(4), 252–259.

    Google Scholar 

  • Sproesser, U., Kuntze, S., & Engel, J. (2014). A multilevel perspective on factors influencing students’ statistical literacy. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Strauss, S., & Bichler, E. (1988). The development of children’s concepts of the arithmetic average. Journal for Research in Mathematics Education, 19(1), 64–80.

    Google Scholar 

  • Till, C. (2014). Risk literacy: First steps in primary school. In K. Makar, B. deSousa, & R. Gould (Eds.), Sustainability in statistics education (Proceedings of the 9th International Conference on the Teaching of Statistics, Flagstaff, Arizona, July 13–18). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Toulmin, S., Rieke, R. D., & Janik, A. (1984). An introduction to reasoning. New York: McMillan.

    Google Scholar 

  • Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 197–230). New York: Springer Science and Business Media.

    Chapter  Google Scholar 

  • Utts, J. (2002). What educated citizens should know about statistics and probability. In B. Phillips (Ed.), Developing a statistically literate society (Proceedings of the 6th International Conference on the Teaching of Statistics, Cape Town, South Africa, July 7–12). Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Watson, J. M. (2005). Variation and expectation as foundations for the chance and data curriculum. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Theory, research and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, Melbourne, pp. 35–42). Sydney: MERGA.

    Google Scholar 

  • Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum.

    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. (2016). Linking science and statistics: Curriculum expectations in three countries. International Journal of Science and Mathematics Education, 15(6), 1057–1073.

    Article  Google Scholar 

  • Watson, J. M., & Callingham, R. A. (2003). Statistical literacy: A complex hierarchical construct. Statistics Education Research Journal, 2(2), 3–46.

    Google Scholar 

  • Watson, J., Chick, H., & Callingham, R. (2014). Average: The juxtaposition of procedure and context. Mathematics Education Research Journal, 26(3), 477–502.

    Article  Google Scholar 

  • Watson, J., & Donne, J. (2009). TinkerPlots as a resource tool to explore student understanding. Technology Innovations in Statistics Education, 3(1), Article 1.

    Google Scholar 

  • Watson, J., & English, L. (2015). Introducing the practice of statistics: Are we environmentally friendly? Mathematics Education Research Journal, 27(4), 585–613.

    Article  Google Scholar 

  • Watson, J., & Fitzallen, N. (2016). Statistical software and mathematics education: Affordances for learning. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 563–594). New York: Taylor and Francis.

    Google Scholar 

  • Watson, J. M., Fitzallen, N., & Carter, P. (2013). Top drawer teachers: Statistics. Adelaide, Australia: Australian Association of Mathematics Teachers and Education Services Australia. Retrieved from http://topdrawer.aamt.edu.au/Statistics

    Google Scholar 

  • Watson, J. M., Fitzallen, N. E., Wilson, K. G., & Creed, J. F. (2008). The representational value of hats. Mathematics Teaching in the Middle School, 14(1), 4–10.

    Google Scholar 

  • Watson, J., & Kelly, B. A. (2005). Cognition and instruction: Reasoning about bias in sampling. Mathematics Education Research Journal, 17(1), 25–57.

    Article  Google Scholar 

  • Watson, J. M., & Moritz, J. B. (1999). The development of the concept of average. Focus on Learning Problems in Mathematics, 21(4), 15–39.

    Google Scholar 

  • Watson, J. M., & Moritz, J. B. (2000a). Development of understanding of sampling for statistical literacy. The Journal of Mathematical Behavior, 19(1), 109–136.

    Article  Google Scholar 

  • Watson, J. M., & Moritz, J. B. (2000b). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2(1 & 2), 11–50.

    Article  Google Scholar 

  • Whitaker, D., Foti, S., & Jacobbe, T. (2015). The levels of conceptual understanding in statistics (LOCUS) project: Results of the pilot study. Numeracy: Advancing Education in Quantitative Literacy, 8(2), Article 3.

    Article  Google Scholar 

  • Wild, C. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26.

    Google Scholar 

  • Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.

    Article  Google Scholar 

  • Zakaria, E., & Salleh, F. (2012). Teachers’ creativity in posing statistical problems from discrete data. Creative Education, 3(8), 1380–1383.

    Article  Google Scholar 

  • Zieffler, A., Garfield, J., Alt, S., Dupuis, D., Holleque, K., & Chang, B. (2008). What does research suggest about the teaching and learning of introductory statistics at the college level? A review of the literature. Journal of Statistics Education, 16(2), Article 8.

    Article  Google Scholar 

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Watson, J., Fitzallen, N., Fielding-Wells, J., Madden, S. (2018). The Practice of Statistics. In: Ben-Zvi, D., Makar, K., Garfield, J. (eds) International Handbook of Research in Statistics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-319-66195-7_4

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