Professional Work
A Model for Development of Statistical Literacy
Having collected survey data from over 4000 students on a wide range of items
related to chance and data, including variation and applications in media
contexts, it was important to put it all together and propose a model of
development of understanding. The wide range of contexts within which items were
set permitted an interpretation of a variable associated with the goal of
statistical literacy and achieving a level of critical questioning by the time
students leave school. Contributing to this were the mathematical and
statistical skills required of tasks, the understanding of concepts alone and in
context, and then the ability to question claims made in various social
contexts. Work in this area has employed partial credit Rasch analysis to
produce a variable map that simultaneously plots student ability and item
difficulty on the same graph. A student on the same value as an item has a 50%
chance of achieving success on that item. With multiple coding levels applied to
items reflecting hierarchical structure, the objective was to be able to explain
the overall distribution of items in terms of a global structure. Initial work
suggested a developmental sequence similar to that in the Table, where it is
seen that engagement with context is a salient feature. Using items with
contexts ranging from very “classroom-mathematical” like tossing a die, to
“classroom-social” like planning a school survey, to “unfamiliar-social” like
critiquing a media article, brought out how there is a hierarchy of contexts
present in items as well as other hierarchical aspects.
Table. Six hypothesized levels of development of Statistical Literacy
Level 1 |
Idiosyncratic-personal engagement with context using basic graph/table reading skills. |
Level 2 |
Colloquial-informal engagement with context using basic chance, graph, and numeracy skills. |
Level 3 |
Selective engagement with context involving qualitative interpretation of statistical ideas. |
Level 4 |
Appropriate non-critical engagement with context using basic statistical skills. |
Level 5 |
Critical-questioning engagement with context using appropriate statistical terminology. |
Level 6 |
Critical-questioning engagement with context using sophisticated mathematical-statistical understanding. |
Recent work in this area has focused on developing two shortened survey forms
for use in classrooms, and using 10-year longitudinal data to confirm the
developmental aspects of the model.
References
1. Watson, J.M. (2002). Doing research in statistics education: More than just
data. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on
Teaching Statistics: Developing a statistically literate society, Cape
Town, South Africa. Voorburg, The Netherlands: International Statistical
Institute. Reprinted in B. Phillips (Ed.), ~ICOTS6 Papers for School Teachers
(pp. 13-20). Voorburg, The Netherlands: International Statistical Institute.
2. Watson, J.M. (2005). Is statistical literacy relevant for middle school
students? Vinculum, 42(1), 3-10. [Invited Keynote at the annual conference of
the Mathematical Association of Victoria, December, 2004]
3. Watson, J.M. (2003). Statistical literacy at the school level: What should
students know and do? In Bulletin of the International Statistical Institute
54thSession Proceedings Berlin (Volume LX, Book2, Invited Papers, Topic 49, pp.
68-71). Berlin: ISI.
4. Watson, J.M., & Kelly, B.A. (2003). The vocabulary of statistical literacy.
In Educational Research, Risks, & Dilemmas: Proceedings of the joint conferences
of the New Zealand Association for Research in Education and the Australian
Association for Research in Education [CD-ROM]. Auckland, New Zealand,
December, 2003. (Refereed paper) Available at: http://www.aare.edu.au/03pap/alpha.htm
5. Callingham, R.A., & Watson, J.M. (2002, December). Implications of
differential item function in statistical literacy: Is gender still an issue?
Refereed paper presented at the Measurement Special Interest Group of the
Australian Association for Research in Education conference, Brisbane. Available
at: http://www.aare.edu.au/02pap/index.htm
6. Watson,J.M., & Callingham, R.A. (2003). Statistical literacy: A complex
hierarchical construct. Statistics Education Research Journal, 2(2),3-46.
7. Callingham, R.A., & Watson, J.M. (2005). Measuring statistical literacy.
Journal of Applied Measurement, 6(1), 19-47.
8. Watson, J.M. (2005). Lessons from research: Students’ understanding of
statistical literacy. In M. Coupland, J. Anderson, & T. Spencer (Eds.), Making
mathematics vital (Proceedings of the 20th biennial conference of the Australian
Association of Mathematics Teachers, Sydney, pp. 253-260). Adelaide, SA: AAMT,
Inc.
9. Watson, J.M., & Callingham, R.A. (2005). Statistical literacy: From
idiosyncratic to critical thinking. In G. Burrill & M. Camden (Eds.), Curricular
Development in Statistics Education. International Association for Statistical
Education (IASE) Roundtable, Lund, Sweden, 2004 (pp. 116-162). Voorburg, The
Netherlands: International Statistical Institute.
10. Watson, J.M., Kelly, B.A., & Izard, J.F. (2005). Statistical literacy over a
decade. 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. 775-782). Sydney: MERGA.
11. Watson, J.M. (2006). Statistical literacy at school: Growth and goals.
Mahwah, NJ: Lawrence Erlbaum.
12. Watson, J.M. (2006). Issues for statistical literacy in the middle school.
In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International
Conference on Teaching Statistics: Working cooperatively in statistics
education, Salvador, Brazil. [CDRom]. Voorburg, The Netherlands: International
Association for Statistical Education and the International Statistical
Institute.
13. Watson, J.M., Kelly, B.A., & Izard, J.F. (2006). A longitudinal study of
student understanding of chance and data. Mathematics Education Research
Journal, 18(2), 40-55.
Contact me...
Faculty of Education
University of Tasmania
Private Bag 66 Hobart Tasmania Australia 7001
Phone: 61-3-6226-2570; Fax: 61-3-6226-2569
Jane.Watson@utas.edu.au