Abstract
This chapter considers several perspectives on approaches to teaching statistics and summarises some of the literature related to these perspectives, in particular looking at the relationship between probability and statistics. Adapting criteria from the literature, each perspective is examined to identify statistical ideas that seem to be fundamental for understanding and being able to use statistics in the workplace, in personal lives, and as citizens. The chapter next considers the possible tensions between mathematics and statistics in the way each discipline approaches these fundamental ideas and finishes with implications for training teachers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Batanero, C., Burrill, G., Reading, C., & Rossman, A. (Eds.). (2008). Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey, Mexico: International Commission on Mathematical Instruction and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications
Batanero, C., Godino, J., & Estepa, A. (1998). Building the meaning of statistical association through data analysis activities. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (pp. 221–236). Stellenbosch, South Africa: University of Stellenbosch.
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 the Fourth International Conference on Teaching Statistics (ICOTS 4) (pp. 20–37). Minneapolis, MN: University of Minnesota.
Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education. The 14th ICMI Study. Berlin: Springer.
Borovcnik, M. (2006). Probabilistic and statistical thinking. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 484–506). Sant Feliu de Guitxols, Spain: European Research in Mathematics Education. Online: ermeweb.free.fr/CERME4/
Cobb, G. (1992). Teaching statistics. In A. S. Lynn (Ed.), Heading the call for change suggestions for curriculum action (pp. 3–43). Washington, DC: Mathematical Association of America.
Coutinho, C. (2008). Teaching statistics in elementary and high school and teacher training. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).
Cuoco, A., Goldenberg, P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375–402.
Fischbein, E. (1990). Training teachers for teaching statistics. In A. Hawkins (Ed.), Training Teachers to Teach Statistics. Proceedings of the International Statistical Institute Roundtable Conference (pp. 48–57). Voorburg, The Netherlands: International Statistical Institute.
Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association. Online: amstat.org/education/gaise/
Freudenthal, H. (1961). Models in applied probability. In B. H. Kazemier & D. Vuysje (Eds.), The concept and the role of the model in mathematics and natural and social sciences (pp. 78–88). Dordrecht: Reidel.
Freudenthal, H. (1974). The crux of course design in probability. Educational Studies in Mathematics, 5, 261–277.
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.
Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70, 1–51.
Gattuso, L. (2008). Mathematics in a statistical context? In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).
Hacking, I. (1965). Logic of statistical inference. Cambridge, UK: Cambridge University Press.
Heitele, D. (1975). An epistemological view on fundamental stochastic ideas. Educational Studies in Mathematics, 6(2), 187–205.
Heymann, H. (2003). Why teach mathematics: A focus on general education. Dordrecht: Kluwer Academic Publishers.
Kultusministerkonferenz (2004). Bildungsstandards im fach mathematik für den mittleren schulabschluss (Educational standards for secondary school mathematics (grade 10)). München, Germany: Wolters Kluwer.
Moore, D. (1997a). New pedagogy and new content: The case of statistics. International Statistical Review, 65, 123–165.
Moore, D. (1997b). Probability and statistics in the core curriculum. In J. Dossey (Ed.), Confronting the core curriculum (pp. 93–98). Washington, DC: Mathematical Association of America.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
New Zealand Ministry of Education. (2006). The New Zealand Curriculum: Mathematics and statistics. Online: nzcurriculum.tki.org.nz/
North, D., & Schieber, J. (2008). Introducing statistics at school level in South Africa: The crucial role played by the National Statistics Office in training in-service teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).
Pfannkuch, M. (2006). Informal inferential reasoning. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Bahia, Brazil: International Statistical Institute and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications
Rossman, A., & Chance, B. (2004). A data-oriented, active learning, post-calculus introduction to statistical concepts, methods, and theory. In G. Burrill & M. Camden (Eds.), Curricular Development in Statistics Education: International Association for Statistical Education 2004 Roundtable. Voorburg, The Netherlands: International Statistical Institute. Online: stat.auckland.ac.nz/~iase/publications
Rossman, A., Chance, B., & Medina, E. (2006). Some key comparisons: statistics and mathematics, and why teachers should care. In G. Burrill (Ed.), Thinking and reasoning with data and chance, 68th NCTM Yearbook (2006) (pp. 323–334). Reston, VA: National Council of Teachers of Mathematics.
Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualization software. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Bahia, Brazil: International Statistical Institute and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications
Scheaffer, R. (1990). The ASA-NCTM quantitative literacy project: An overview. In D. Vere-Jones (Ed.), Proceedings of the Third International Congress on Teaching Statistics. Dunedin, New Zealand: International Statistical Institute. Online: www.stat.auckland.ac.nz/~iase/publications
Scheaffer, R. (2006). Statistics and mathematics: On making a happy marriage. In G. Burrill (Ed.), Thinking and reasoning with data and chance, 68th NCTM Yearbook (2006) (pp. 309–321). Reston, VA: National Council of Teachers of Mathematics.
Schield, M. (1999). Statistical literacy: Thinking critically about statistics. Of Significance, 1(1), 15–20.
Schupp, H. (1982). Zum Verhältnis statistischer und wahrscheinlichkeitstheoretischer Komponenten im Stochastikunterricht der Sekundarstufe I (On the relationship between statistical and probabilistic components in lower secondary stochastics teaching). Journal für Mathematik-Didaktik, 3(3/4), 207–226.
Snee, R. D. (1990). Statistical thinking and its contribution to total quality. American Statistician, 44, 116–121.
Tukey, J. W. (1972). Data analysis, computation and mathematics. Quarterly of Applied Mathematics, 30, 51–65.
Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105–110.
Watson, J. M. (1997). Assessing statistical literacy using the media. In I. Gal & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 107–121). Amsterdam: IOS Press and International Statistical Institute.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67, 223–265.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Burrill, G., Biehler, R. (2011). Fundamental Statistical Ideas in the School Curriculum and in Training Teachers. In: Batanero, C., Burrill, G., Reading, C. (eds) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education. New ICMI Study Series, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1131-0_10
Download citation
DOI: https://doi.org/10.1007/978-94-007-1131-0_10
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-1130-3
Online ISBN: 978-94-007-1131-0
eBook Packages: Humanities, Social Sciences and LawEducation (R0)