**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

S.Loeff@ke.unimaas.nl

Wim H. Gijselaers

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*.

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).

Bollen, K. A. (1989). *Structural equations with latent variables*.

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*.

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).

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).

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

Gal, *The** challenge of
developing statistical literacy, reasoning, and thinking* (pp. 47-78).

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

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

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).

*Statistics Education Research
Journal*, *4*(1).

*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).

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. *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*.

Kline, R. B. (2005). *Principles and practice of structural equation modelling*
(2^{nd} ed.).

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).

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.*

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,

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).

Dirk T. tempelaar

Department of Quantitative Economics,

Faculty of Economics and Business
Administration

University
of Maastricht

PO
Box 616, 6200 MD Maastricht

the Netherlands