Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education pp 121-132 | Cite as

# Complementing Mathematical Thinking and Statistical Thinking in School Mathematics

## Abstract

The introduction of statistics into school curriculum within the mathematics subject poses multifaceted problems to mathematics teachers. This chapter first discusses the relevance of developing mathematical and statistical literacy in schools, and secondly reflects on some current recommendations to teach statistics in the school mathematics and challenges faced in the training of teachers. Then the chapter underlines differences between mathematical and statistical thinking and suggests that, taking account of their specificities, it is possible to generate teaching strategies that allow the harmonious development of both mathematical and statistical thinking in school. Some implications for teacher training are finally included.

## Keywords

Mathematics Teacher Teacher Training School Mathematic Mathematical Thinking Statistical Concept## References

- Batanero, C. (2008, September).
*Training school teachers to teach statistics: an international challenge*. Paper presented in the Premier Colloque Francophone International sur l’Enseignement de la Statistique. Lyon, France: Société Française de Statistique.Google Scholar - 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 - Biehler, R. (2008). From statistical literacy to fundamental ideas in mathematics: How can we bridge the tension in order to support teachers of statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).Google Scholar
- Burrill, G., & Camden, M. (Eds.) (2005).
*Curricular Development in Statistics Education*:*International Association for Statistical Education 2004 Roundtable*. Voorburg, The Netherlands: International Statistical Institute. Online: www.stat.auckland.ac.nz/~iase/publications - Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching.
*The American Mathematical Monthly, 104*, 801–823.CrossRefGoogle Scholar - Dunkels, A. (1990). Examples from the in-service classroom (age group 7–12). In A. Hawkins (Ed.),
*Training teachers to teach statistics: Proceedings of the International Statistical Institute Round Table Conference*(pp. 102–109). Voorburg, The Netherlands: International Statistical Institute.Google Scholar - Estrada, A., & Batanero, C. (2008). Explaining teachers’ attitudes towards statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).Google Scholar
- Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. L. (2005).
*Guidelines for assessment and instruction in statistics education*(*GAISE*)*report*:*A preK*-*12 curriculum framework*. Alexandria, VA: American Statistical Association. Online: www.amstat.org/Education/gaise/ - Gal, I., & Garfield, J. B. (1997).
*The assessment challenge in statistics education*. Amsterdam: IOS Press and International Statistical Institute.Google Scholar - Garfield, J. B., & Ben-Zvi, D. (2004). Research on statistical literacy, reasoning and thinking: Issues, challenges and implications. In D. Ben-Zvi & J. B. Garfield (Eds.),
*The challenge of developing statistical literacy, reasoning and thinking*(pp. 397–409). Dordrecht, The Netherlands: Kluwer.Google Scholar - Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics.
*International Statistical Review, 75*(3), 372–396.CrossRefGoogle Scholar - Garfield, J., & Ben-Zvi, D. (2008).
*Developing students’ statistical reasoning: Connecting research and teaching practice*. Dordrecht, The Netherlands: Springer.Google Scholar - Gattuso, L. (2006). Statistics and mathematics: Is it possible to create fruitful links? In A. Rossman & B. Chance (Eds.),
*Proceedings of the 7th 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 - Gattuso, L. (2008). Mathematics in a statistical context? In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).Google Scholar
- Gini, C. (1966).
*Statistical methods*. Roma, Italy: Università degli Studi di Roma.Google Scholar - Kranendonk, H. (2006). A statistical study of generations. In G. Burrill (Ed.),
*Thinking and reasoning with data and chance, 68th NCTM yearbook (2006)*(pp. 103–116). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Meletiou, M. (2003). On the formalist view of mathematics: Impact on statistics instruction and learning. In A. Mariotti (Ed.),
*Proceedings of the Third European Conference in Mathematics Education*. Bellaria, Italy: European Research in Mathematics Education Society. Online: www.dm.unipi.it/~didattica/CERME3/proceedings - Moore, D. S. (1997). New pedagogy and new content: The case of statistics.
*International Statistical Review, 65*(2), 123–137.CrossRefGoogle Scholar - Moore, D. S., & Cobb, G. (2000). Statistics and mathematics: Tension and cooperation.
*The American Mathematical Monthly, 107*, 615–630.CrossRefGoogle Scholar - National Council of Teachers of Mathematics (1989).
*Curriculum and evaluation standards for school mathematics*. Reston, VA: Author.Google Scholar - Organisation for Economic Co-operation and Development (2006).
*Assessing scientific*,*reading and mathematical literacy*:*A framework for PISA 2006*. Online: www.oecd.org/dataoecd/63/35/37464175.pdf - Ottaviani, M. G. (2008). Statistica e matematica a scuola: due discipline e un solo insegnamento. Confronto culturale e opportunità interdisciplinare (Statistics and mathematics at school: Two disciplines in one subject. Cultural comparisons and interdisciplinary potentialities).
*Induzioni, 36*, 17–38.Google Scholar - Ottaviani, M. G., Peck, R., Pfannkuch, M., & Rossman, A. (2005). Working group report on teacher preparation for statistics education. 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: www.stat.auckland.ac.nz/~iase/publications - Rossman, A., Chance, B., & Medina, E. (2006). Some important comparisons between 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.Google Scholar - Scheaffer, R. L. (2003). Statistics and quantitative literacy. In B. L. Madison & L. A. Steen (Eds.),
*Quantitative literacy*:*Why numeracy matters for schools and colleges*(pp. 145–152). Princeton, NJ: National Council on Education and the Disciplines. Online: www.maa.org/ql/qltoc.html - Scheaffer, R. L. (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.Google Scholar - Schwartz, S. L. (2006). Graphing with four-year-olds: Exploring the possibilities through staff development. In G. Burrill (Ed.),
*Thinking and reasoning with data and chance, 68th NCTM Yearbook (2006)*(pp. 5–17). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Sierpinska, A., & Kilpatrick, J. (Eds.). (1998).
*Mathematics education as a research domain: A search for identity. An ICMI Study*. Dordrecht, The Netherlands: Kluwer.Google Scholar - Steen, L. A. (2003). Data, shapes, symbols: Achieving balance in school mathematics. In B. L. Madison & L. A. Steen (Eds.),
*Quantitative literacy*:*Why numeracy matters for schools and colleges*(pp. 53–74). Princeton, NJ: National Council on Education and the Disciplines. Online: www.maa.org/ql/qltoc.html - Stein, S. (2001).
*Equipped for the future, content standards*. Washington, DC: National Institute for Literacy.Google Scholar - Thisted, R. A., & Velleman, P. F. (1992). Computers and modern statistics. In D. C. Hoaglin & D. S. Moore (Eds.),
*Perspectives on contemporary statistics*(MAA notes 21, pp. 41–53). Washington, DC: Mathematical Association of America.Google Scholar - United Nations Educational, Scientific and Cultural Organisation. (1997).
*UNESCO*’*s sponsorship*. Resolution 29 C/DR126. Online: wmy2000.math.jussieu.fr/unesco.html