Characterizing Year 11 Students’ Evaluation

of a Statistical Process

Maxine Pfannkuch

The University of Auckland, New Zealand

m.pfannkuch@auckland.ac.nz

ABSTRACT

Evaluating the statistical process is considered a higher order skill and has received little emphasis in instruction. This study analyses thirty 15-year-old students’ responses to two statistics assessment tasks, which required evaluation of a statistical investigation. The SOLO taxonomy is used as a framework to develop a hierarchy of responses. Focusing on the quality of response allowed insight into and suggestions for how instruction might be improved. The implications for teaching, assessment, and the curriculum are discussed.

Keywords: Statistics education research; Evaluating statistical investigations; Assessment; SOLO taxonomy; Secondary students

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Statistics Education Research Journal, 4(2), 5-26, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), Nov, 2005

References

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

Bloom, B. (1956). Taxonomy of Educational Objectives. New York: David McKay Company.

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

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

Gal, I. (1997). Assessing students’ interpretation of data. In B. Phillips (Ed.), IASE Papers on Statistical Education ICME-8, Spain, 1996, (pp. 49 - 57). Hawthorn, Australia: Swinburne Press.

Gal, I. (2002). Adults’ statistical literacy: meanings, components, responsibilities. International Statistical Review, 70(1), 1-51.

Gal, I., & Garfield, J. (1997). Curricular goals and assessment challenges in statistics education. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 1-13). Amsterdam, The Netherlands: IOS Press.

Gravemeijer, K. (1998). Developmental research as a research method. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (pp. 277-295). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Holmes, P. (1997). Assessing project work by external examiners. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 153-164). Amsterdam, The Netherlands: IOS Press.

Miles, M., & Huberman, M. (1994). Qualitative Data Analysis. Thousand Oaks, CA: Sage Publications.

New Zealand Qualifications Authority (2001). Level 1 achievement standards: Mathematics. [Online: http://www.nzqa.govt.nz/ncea/ach/mathematics/index.shtml]

Pegg, J. (2003). Assessment in mathematics: A developmental approach. In J. Royer (Ed.), Mathematical cognition (pp. 227-259). Greenwich, CT: Information Age Publishing.

Pfannkuch, M. (1996). Statistical interpretation of media reports. In J. Neyland & M. Clark (Eds.), Research in the learning of statistics: Proceedings of the 47^th Annual New Zealand Statistical Association Conference (pp. 67-76). Wellington, New Zealand: Victoria University.

Pfannkuch, M. (2005). Probability and statistical inference: How can teachers enable learners to make the connection? In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 267-294). Dordrecht, The Netherlands: Kluwer Academic Publishers.

Pfannkuch, M., & Horring, J. (in press). Developing statistical thinking in a secondary school: A collaborative curriculum development. In G. Burrill (Ed.), Curricular development in statistics education: Proceedings of the 2004 International Association for Statistical Education Round Table Conference, Lund University, Sweden, 28 June-3 July, 2004.

Pfannkuch, M., & Wild, C. J., (2003). Statistical thinking: How can we develop it? In Bulletin of the International Statistical Institute 54^th Session Proceedings [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.

Pryor, H. (2001). Assessment of the statistical literacy ability of some tertiary students using media reports. Unpublished Masters Thesis, The University of Auckland.

Skovsmose, O., & Borba, M. (2000). Research methodology and critical mathematics education. Publication No. 17 Roskilde, Denmark: Centre for Research in Learning Mathematics, Roskilde University.

Starkings, S. (1997). Assessing student projects. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 139-152). Amsterdam, The Netherlands: IOS Press.

Watson, J. M. (1997). Assessing statistical thinking using the media. In I. Gal & J. Garfield (Eds.), The assessment challenge in statistics education (pp. 107-121). Amsterdam, The Netherlands: IOS Press.

Watson, J. M., Collis, K., & Moritz, J. (1994). Authentic assessment in statistics using the media. Report prepared for the National Center for Research in Mathematical Sciences Education – Models of Authentic Assessment Working Group (University of Wisconsin). Hobart, Australia: University of Tasmania, School of Education.

Watson, J. M., Collis, K., Callingham, R., & Moritz, J. (1995). A model for assessing higher order thinking in statistics. Educational Research and Evaluation, 1, 247-275.

Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223-265.

Wittmann, E. (1998). Mathematics education as a ‘design science’. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (pp. 87-103). Dordrecht, The Netherlands: Kluwer Academic Publishers.

maxine pfannkuch

Department of Statistics

The University of Auckland

Private Bag 92019

Auckland

New Zealand