A structural equation model analyzing the

relationship OF students’ attitudes toward

statistics, prior reasoning abilities and course

performance

 

Dirk T. Tempelaar

Maastricht University, The Netherlands

D.Tempelaar@ke.unimaas.nl

 

Sybrand Schim van der Loeff

Maastricht University, The Netherlands

S.Loeff@ke.unimaas.nl

 

Wim H. Gijselaers

Maastricht University, The Netherlands

W.Gijselaers@erd.unimaas.nl

 

ABSTRACT

 

Recent research in statistical reasoning has focused on the developmental process in students when learning statistical reasoning skills. This study investigates statistical reasoning from the perspective of individual differences. As manifestation of heterogeneity, students’ prior attitudes toward statistics, measured by the extended Survey of Attitudes Toward Statistics (SATS), are used (Schau, Stevens, Dauphinee & DeVecchio, 1995). Students’ statistical reasoning abilities are identified by the Statistical Reasoning Assessment (SRA) instrument (Garfield 1996, 1998a, 2003). The aim of the study is to investigate the relationship between attitudes and reasoning abilities by estimating a full structural equation model. Instructional implications of the model for the teaching of statistical reasoning are discussed.

 

Keywords: Statistics education research; Statistical reasoning; Achievement motivations; SATS; SRA; Structural equation modelling

 

 

__________________________

Statistics Education Research Journal, 6(2), 78-102, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), November, 2007

 

 

 

REFERENCES

 

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

Ben-Zvi, D., & Garfield, J. B. (Eds.). (2004b). Research on reasoning about variability [Special issue]. Statistics Education Research Journal, 3(2).

Ben-Zvi, D., & Garfield, J. B. (2004c). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi & J. B. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 3-15). Dordrecht, The Netherlands: Kluwer Academic Publishing.

Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.

Bruer, J. T. (1993). Schools for thought: A science of learning in the classroom. Cambridge, MA: The MIT Press.

Byrne, B. M. (1998). Structural equation modeling with LISREL, PRELIS, and SIMPLIS: Basic concepts, applications, and programming. Mahwah, NJ: Lawrence Erlbaum.

Cashin, S. E., & Elmore, P. B. (2005). The Survey of Attitudes Toward Statistics scale: A construct validity study. Educational and Psychological Measurement, 65(3), 509-524.

Chance, B. L. (2002). Components of statistical thinking and implications for instruction and assessment. Journal of Statistics Education, 10(3).

[Online: http://www.amstat.org/publications/jse/v10n3/chance.html]

Chance, B. L. & Garfield, J. B. (2002). New approaches to gathering data on student learning for research in statistics education. Statistics Education Research Journal, 1(2), 38-41.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ1(2).pdf]

Dauphinee, T. L., Schau, C., & Stevens, J. J. (1997). Survey of Attitudes Toward Statistics: Factor structure and factorial invariance for women and men. Structural Equation Modeling, 4(2), 129-141.

delMas, R. (2002). Statistical literacy, reasoning, and learning. Journal of Statistics Education, 10(3).

[Online: http://www.amstat.org/publications/jse/v10n3/delmas_intro.html and  http://www.amstat.org/publications/jse/v10n3/delmas_discussion.html]

delMas, R. (2004a).A comparison of mathematical and statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 79-95). Dordrecht, The Netherlands: Kluwer Academic Publishing.

delMas, R. (2004b). Overview of ARTIST website and Assessment Builder. Proceedings of the ARTIST Roundtable Conference, Lawrence University.

[Online: http://www.rossmanchance.com/artist/Proctoc.html]

Eccles, J. S. (2005). Subjective task value and the Eccles et al. model of achievement-related choices. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of competence and motivation (pp. 105-121). New York: The Guilford Press.

Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109-132.

Gal, I. (2004). Statistical literacy, meanings, components, responsibilities. In D. Ben-Zvi & J. B. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 47-78). Dordrecht, The Netherlands: Kluwer Academic Publishing.

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

Gal, I., & Ginsburg, L. (1994). The role of beliefs and attitudes in learning statistics: Towards an assessment framework. Journal of Statistics Education, 2(2).

[Online: http://www.amstat.org/publications/jse/v2n2/gal.html]

Garfield, J. B. (1996). Assessing student learning in the context of evaluating a chance course. Communications in Statistics; Part A: Theory and Methods, 25, 2863-2873.

Garfield, J. B. (1998a, April). Challenges in assessing statistical reasoning. Paper presented at the American Educational Research Association Annual Meeting, San Diego, CA.

Garfield, J. B. (2003). Assessing statistical reasoning. Statistics Education Research Journal, 2(1), 22-38.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ2(1).pdf]

Garfield, J. B., & Ahlgren, A. (1988). Difficulties in learning basic concepts in statistics: Implications for research. Journal for Research in Mathematics Education, 19, 44-63.

Garfield, J. B., & Ben-Zvi, D. (2004a). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi & J. B. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 3-15). Dordrecht, The Netherlands: Kluwer Academic Publishing.

Garfield, J. B., & Ben-Zvi, D. (2004b). 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 Academic Publishing.

Garfield, J. B., & Ben-Zvi, D. (Eds.) (2005). Reasoning about variation [Special section]. Statistics Education Research Journal, 4(1).

Garfield, J., & Chance, B. (2000). Assessment in statistics education: Issues and challenges. Mathematics Thinking and Learning, 2(1&2), 99-125.

Garfield, J. B., Hogg, B., Schau, C, & Whittinghill, D. (2002). First courses in statistical science: The status of educational reform efforts. Journal of Statistics Education, 10(2).

[Online: www.amstat.org/publications/jse/v10n2/garfield.html]

Harris, M. B., & Schau, C. (1999). Successful strategies for teaching statistics. In S.N. Davis, M. Crawford, & J. Sebrechts (Eds.), Coming into her own: Educational success in girls and women (pp. 193-210). San Francisco: Jossey-Bass.

Hau, K. T., & Marsh, H. W. (2004). The use of item parcels in structural equation modelling: Non-normal data and small sample sizes. British Journal of Mathematical Statistical Psychology, 57, 327-351.

Hilton, S. C., Schau, C., & Olsen, J. A. (2004). Survey of Attitudes Toward Statistics: Factor structure invariance by gender and by administration time. Structural Equation Modeling, 11(1), 92-109.

Jolliffe, F. (1998). What is research in statistical education? In L. Pereira-Mendoza, L. Seu Kea, T. Wee Kee, & W. K. Wong (Eds.), Proceedings of the Fifth International Conference on Teaching Statistics (pp. 801-806). Voorburg, The Netherlands: International Statistical Institute.

Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. Cambridge, MA: Cambridge University Press.

Kline, R. B. (2005). Principles and practice of structural equation modelling (2nd ed.). New York: Guilford Press.

Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59-98.

Liu, H. J. (1998). A cross-cultural study of sex-differences in statistical reasoning for college students in Taiwan and the United States. Unpublished doctoral dissertation, University of Minnesota, Minneapolis.

Marsh, H. W., Hau, K. T., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33, 181–220.

McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, a project of the National Council of Teachers of Mathematics (pp. 575-596). New York: Macmillan.

Pfannkuch, M., & Wild, C. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi & J. B. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 17-46). Dordrecht, The Netherlands: Kluwer Academic Publishing.

Rumsey, D. J. (2002). Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education, 10(3).

[Online: http://www.amstat.org/publications/jse/v10n3/rumsey2.html]

Schau, C. (2003, August). Students’ attitudes: The “other” important outcome in statistics education. Paper presented at the Joint Statistical Meetings, San Francisco.

Schau, C., Dauphinee, T. L., Del Vecchio, A., & Stevens, J. (1999). Survey of attitudes toward statistics (SATS).

[Online: http://www.unm.edu/~cschau/downloadsats.pdf]

Schau, C., Stevens, J., Dauphinee, T. L., & Del Vecchio, A. (1995). The development and validation of the Survey of Attitudes Toward Statistics. Educational and Psychological Measurement, 55(5), 868-875.

Schumacker, R. E., & Lomax, R. G. (2004). A beginner’s guide to structural equation modeling. Mahwah, NJ: Lawrence Erlbaum.

Short, T. H. (Ed.) (2002). Statistical literacy, reasoning, and thinking [Special section]. Journal of Statistics Education, 10(3).

     [Online: http://www.amstat.org/publications/jse/v10n3/abstracts.html]

Sorge, C., & Schau, C. (2002, April). Impact of engineering students’ attitudes on achievement in statistics. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.

Sundre, D. L. (2003, April), Assessment of Quantitative reasoning to enhance educational quality. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago.

[Online: http://www.gen.umn.edu/artist/articles/AERA_2003_QRQ.pdf]

Tempelaar, D. (2004). Statistical reasoning assessment: An Analysis of the SRA instrument. Proceedings of the ARTIST Roundtable Conference, Lawrence University. [Online: http://www.rossmanchance.com/artist/Proctoc.html]

Tempelaar, D. T., Gijselaers, W. H., & Schim van der Loeff, S. (2006). Puzzles in statistical reasoning. Journal of Statistics Education, 14(1).

[Online: http://www.amstat.org/publications/jse/v14n1/tempelaar.html]

Tempelaar, D. T., Gijselaers, W.H., Schim van der Loeff, S., & Nijhuis, J. (2007). A structural equation model analyzing the relationship of student achievement motivations and personality factors in a range of academic subject-matter areas. Contemporary Educational Psychology, 32(1), 105-131.

Tempelaar, D., Schim van der Loeff, S., Gijselaers, W., & De Crombrugghe, D. (2007). Preferred learning approaches and statistical reasoning. Unpublished manuscript.

Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25(1), 68-81.

Wigfield, A., & Eccles, J. S. (2002). The development of competence beliefs, expectancies for success, and achievement values from childhood through adolescence. In A. Wigfield & J. S. Eccles (Eds.), Development of achievement motivation (pp. 92-122). San Diego: Academic Press.

 

Dirk T. tempelaar

Department of Quantitative Economics,

Faculty of Economics and Business Administration

University of Maastricht

PO Box 616, 6200 MD Maastricht

the Netherlands