COGNITIVE AND NON-COGNITIVE FACTORS RELATED TO STUDENTS’ STATISTICS ACHIEVEMENT
FRANCESCA CHIESI
University of Florence, Italy
f.chiesi@tin.it
CATERINA PRIMI
University of Florence, Italy
cprimi@texnet.it
ABSTRACT
The aim of this study was to investigate students’ achievement in introductory statistics courses taking into account the relationships between cognitive and non-cognitive factors. It was hypothesised that achievement was related to background in mathematics (a cognitive variable), as well as to attitudes toward statistics and anxiety (non-cognitive variables). Students were presented with measures assessing their attitudes, mathematical competence, and anxiety toward courses and examinations at the beginning and at the end of their statistics course. Achievement was assessed by tasks assigned during the course, as well as by students’ final grades and the number of exam failures. The results reveal the relationships between cognitive and non-cognitive factors, their changes during the course, and how both interact in predicting achievement.
Keywords: Statistics
education research; Statistics
attitudes; Statistics anxiety; Mathematical competence; Structural equation
modelling
__________________________
Statistics Education Research
Journal, 9(1), 6-26, http://www.stat.auckland.ac.nz/serj
Ó International
Association for Statistical Education (IASE/ISI), May, 2010
REFERENCES
Arbuckle, J. L. (2003). Amos 5.0 [Computer software]. Chicago:
Smallwaters.
Auzmendi, E.
(1991, April). Factors related to attitude toward statistics: A study with a
Spanish sample. Paper
presented at the annual
meeting of the American Educational Research Association, Chicago, IL.
Baloglu,
M. (2002). Psychometric properties of the statistics anxiety scale. Psychological Reports, 90(11), 315-125.
Bandalos, D.
L., Finney, S. J., & Geske, J. A. (2003). A model of statistics performance
based on achievement
goal theory. Journal of Educational Psychology, 95(3), 604-616.
Bell,
J. A. (1998). International students have statistics anxiety too! Education, 118(4), 634-636.
Bentler,
P. M. (1990). Comparative fit indexes in structural models. Psychological
Bulletin, 107(2),
238–246.
Bentler,
P. M. (1995). EQS: Structural equations program manual.
Encino, CA: Multivariate Software, Inc.
Bentler,
P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in
the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606.
Bollen, K. A. (1986). Sample size and Bentler and Bonett’s nonnormed fit index. Psychometrika, 51(3), 375–377.
Bollen,
K. A. (1989a). Structural equations with
latent variables. New York: Wiley.
Bollen,
K. A. (1989b). A new incremental fit index for general structural equation
models. Sociological Methods and Research, 17(3), 303–316.
Browne,
M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K.
A. Bollen, & J. S. Long (Eds.) Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.
Budé, L., Van De Wiel, M. W. J., Imbos, T., Candel, M. J. J. M., Broers, N.
J., & Berger, M. P. F. (2007). Students’ achievements in a statistics
course in relation to motivational aspects and study behaviour. Statistics Education Research Journal, 6(1), 5-21.
[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ6(1)_Bude.pdf]
Carmona,
M. J. (2004a, July). Mathematical
background and attitudes toward statistics in a sample of undergraduate
students. Paper presented at the 10th International Congress on
Mathematics Education, Copenhagen, Denmark.
[Online: http://www.stat.auckland.ac.nz/~iase/publications/11/Carmona.doc]
Carmona, M.
J. (2004b). Una revisión de las evidencias de fiabilidad y validez de los
cuestionarios de actitudes y ansiedad hacia la estadística [A review of the evidence of reliability and
validity of questionnaires of attitudes and anxiety towards statistics]. Statistics
Education Research Journal, 3(1), 5-28.
Carmona J., Primi, C., & Chiesi, F. (2008, July). Testing for measurement invariance of the
Survey of Attitudes Toward Statistics: A comparison of Italian and Spanish
students. III European Congress of Methodology, Oviedo, Spain.
Cashin,
S. E., & Elmore, P. B. (2005). The Survey of Attitudes Toward Statistics
scale: A construct validity study. Educational and Psychological
Measurement, 65(3), 1-16.
Chiesi, F,. & Primi, C. (2009). Assessing statistics attitudes among college students: Psychometric properties of the Italian version of the Survey of Attitudes Toward Statistics (SATS). Learning and Individual Differences, 19(2), 309-313.
Chiesi, F., Primi, C., & Ciancaleoni, M. (2008). Le proprietà psicometriche della Statistics Anxiety
Rating Scale [The psychometric properties of STARS]. Psicologia
dell’Educazione, 3(2), 48-58.
Chiorri C., Chiesi F., Piattino S., Primi C., &
Vannucci M. (2009). Ansia nei confronti della statistica e stile cognitivo:
Un'indagine sugli studenti di psicologia [Anxiety about statistics and
cognitive style: A survey of psychology students]. Proceedings of the III Congress “Verso una nuova qualità
dell'insegnamento e apprendimento della Psicologia.” [Online: http://convdidattica.psy.unipd.it/]
Ciancaleoni, M., Galli, S., Chiesi, F., & Primi, C. (2008, July). Assessing
the predictive validity of the mathematical ability scale constructed applying
the Rasch model. Paper
presented at III European Congress of Methodology, Spagna, Oviedo.
Cruise,
J. R., Cash, R. W., & Bolton, L. D. (1985). Development and validation of
an instrument to measure statistical anxiety. In American Statistical
Association Proceedings of the Section on Statistical Education (pp.
92-97). Alexandria, VA: American Statistical Association.
D’Andrea,
L., & Waters, C. (2002). Teaching statistics using short stories: Reducing
anxiety and changing attitudes. In B. Phillips
(Ed.), Proceedings of the Sixth
International Conference on Teaching Statistics: Developing a statistically
literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The
Netherlands: International Statistical Institute.
[Online: http://www.stat.auckland.ac.nz/~iase/publications/1/8a2_dand.pdf ]
Dauphinee,
T. L., Schau, C., & Stevens, J. J. (1997). Survey of Attitudes Toward
Statistics: Factor structure and factorial invariance for female and males. Structural Equation Modeling, 4(2),
129-141.
Eccles,
J., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., et
al. (1983). Expectations, values, and academic behaviors. In J. T. Spence
(Ed.), Achievement and Achievement Motivation (pp. 75-146). W. H.
Freeman: San Francisco.
Elmore,
P. B., & Lewis, E. L. (1991, April). Statistics
and computer attitudes and achievement of students enrolled in Applied
Statistics: Effect of a computer laboratory. Paper presented at the Annual
Meeting of the American Educational Research Association, Chicago, IL.
Feldt, L. B., Woodruff, D. J., Salih, F. A., &
Srichai, M. (1986). Statistical tests and
confidence intervals for Cronbach’s coefficient alpha (Iowa Testing
Programs Occasional Papers No. 33). (ERIC Document Reproduction Service No.
ED291755)
Finney,
S. J., & Schraw, G. (2003). Self-efficacy beliefs in college statistics
courses. Contemporary Educational Psychology, 28(2), 161-186.
Fitzgerald,
S. M., Jurs, S., & Hudson, L. M. (1996). A model predicting statistics
achievement among graduate students. College Student Journal, 30,
361-366.
Franklin, C. A., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K–12 curriculum framework. Alexandria, VA: American Statistical Association.
[Online: http://www.amstat.org/Education/gaise/GAISECollege.htm]
Gal, I.,
Ginsburg, L., & Schau, C. (1997). Monitoring attitudes and beliefs in statistics education. In I. Gal
& J. B. Garfield (Eds.), The assessment challenge in statistics
education (pp. 37-51). Amsterdam: IOS Press.
Galli, S., Chiesi, F., & Primi, C. (2008). The
construction of a scale to measure mathematical ability in psychology students:
An application of the Rasch Model. TPM (Testing Psicometria Metodologia), 15(1), 1-16.
Garfield,
J. (2003). Assessing statistical reasoning. Statistics Education Research
Journal, 2(1), 22-38.
[Online:
http://www.stat.auckland.ac.nz/~iase/serj/SERJ2(1).pdf]
Gravetter,
F. J., & Wallnau, L. B. (1996). Statistics for the behavioural sciences:
A first course for students of psychology and education. St. Paul, MN:
West.
Harlow,
L. L., Burkholder, G. J., & Morrow, J. A. (2002). Evaluating attitudes,
skill, and performance in a learning-enhanced quantitative methods course: A
structural modelling approach. Structural Equation Modeling, 9(3), 413-430.
Hilton,
S. C., Schau, C., & Olsen, J. A. (2004). Survey Attitudes Toward
Statistics: Factor structure invariance by gender and by administration time.
Structural Equation Modeling, 11(1),
92-109.
Keeley, J., Zayac, R. M.,
& Correia, C. (2008). Curvilinear relationships between statistics anxiety
and performance among undergraduate students: Evidence for optimal anxiety. Statistics Education Research Journal, 7(1), 4-15.
[Online:
http://www.stat.auckland.ac.nz/~iase/serj/SERJ7(1)]
Kline,
R. B. (1998). Principles and practice of
Structural Equation Modeling. New York: Guilford Press.
Lalonde,
R. N., & Gardner, R. C. (1993). Statistics as a second language? A model
for predicting performance in psychology students. Canadian Journal of
Behavioural Science, 25(1),
108-125.
Marcoulides,
G. A., & Hershberger, S. L. (1997). Multivariate
statistical methods. A first course. Mahwah, NJ: Lawrence Erlbaum
Associates.
Marsh,
H. W., & Hocevar, D. (1985). Application of confirmatory factor analysis to
the study of self-concept: First- and higher-order factor models and their
invariance across groups. Psychological
Bulletin, 97(3), 562-582.
McCall,
C. H., Belli, G., & Madjidi, F. (1991). The complexities of teaching
graduate students in educational administration introductory statistical
concepts. PICTeachSt, 3, 495-497.
Muthén,
B., & Kaplan, D. (1985). A comparison of some methodologies for the factor
analysis of non-normal Likert variables. British
Journal of Mathematical and Statistical Psychology, 38(1), 171-189.
Nasser,
F. (2004). Structural model of the effects of cognitive and affective factors
on the achievement of Arabic-speaking pre-service teachers in introductory
statistics. Journal of Statistics Education, 12(1).
[Online: www.amstat.org/publications/
jse/v12n1/nasser.html]
Onwuegbuzie,
A. J. (1998). Statistics anxiety: A function of learning style? Research in
School, 5(1), 43-52.
Onwuegbuzie,
A. J. (2000). Statistics anxiety and the role of self-perceptions. Journal
of Educational Research, 93(5),
323-335.
Onwuegbuzie,
A. J. (2003). Modeling statistics achievement among graduate students. Educational
and Psychological Measurement, 63(6),
1020-1038.
Onwuegbuzie,
A. J., & Seaman, M. (1995). The effect of time constraints and statistics
test anxiety on test performance in a statistics course. Journal of
Experimental Education, 63(2),
115-124.
Onwuegbuzie,
A. J., & Wilson, V. A. (2000, November). Statistics anxiety: Nature,
etiology, antecedents, effects, and treatments: A comprensive review of the
literature. Paper presented at the Annual
Meeting of the Mid-South Educational Research Association, Lexington,
KY.
Onwuegbuzie,
J. A., Bailey, P., & Daley, C. E. (2002). The role of foreign language
anxiety and students’ expectations in foreign language learning. Research in
the Schools, 9(1), 33-50.
Perney,
J., & Ravid, R. (1990, April). The relationship between attitudes toward
statistics, math self-concepts, test anxiety and graduate students’ achievement
in an introductory statistics course.
Paper presented at the Annual Meeting of the American Educational
Research Association, Boston.
Primi, C., & Chiesi, F. (2007). Come promuovere il rendimento all’esame di Psicometria: un modello per identificare i predittori sui quali intervenire [How to promote the efficiency of psychometrics under consideration: A model to identify the influential predictors]. Proceedings of the II° Convegno“Verso una nuova qualità dell'insegnamento e apprendimento della Psicologia” (pp. 624-637).
[Online: http://convdidattica.psy.unipd.it/]
Roberts, D. M., & Bilderback, E. W. (1980). Reliability and validity of statistics attitudes survey. Educational and Psychological Measurement, 40(1), 235-238.
Schau,
C. (2003, August). Students’ attitudes: The “other” important outcome in
statistics education. Paper presented at the Joint Statistical Meetings,
San Francisco, CA.
Schau, C., Stevens, J. 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.
Schumaker,
R. E., & Lomax, R. G. (1996). A
beginner’s guide to structural equation modeling. Mahwah, NJ: Lawrence
Erlbaum.
Schutz, P.
A., Drogosz, L. M., White, V. E., & Distefano, C. (1998). Prior knowledge, attitude, and
strategy use in an introduction to statistics course. Learning and
Individual Differences, 10(4),
291-308.
Sorge, C.,
& Schau, C. (2002, April). Impact of engineering students’ attitudes on achievement in statistics:
A structural model.
Paper presented at the Annual Meeting of the American Educational Research
Association, New Orleans.
Steiger,
J. H., & Lind, J. C. (1980, May). Statistically-based tests for the
number of common factors. Paper presented at the Annual Spring Meeting of
the Psychometric Society, Iowa City.
Tempelaar, D. T., van Der Loeff, S. S., & Gijselaers, W. H. (2007). A structural equation model analyzing the relationship of students’ attitudes toward statistics, prior reasoning abilities and course performance. Statistics Education Journal, 6(2), 78- 102.
[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ6(2)_Tempelaar.pdf]
Tremblay,
P.F., Gardner, R. C., & Heipel, G. (2000). A model of the relationships
among measures of affect, aptitude, and performance in introductory statistics.
Canadian Journal of Behavioral Science, 32(1), 40-48.
Tucker,
L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood
factor analysis. Psychometrika, 38(1), 1–10.
Wheaton,
B., Muthén, B., Alwin, D. F., & Summers, G. F. (1977). Assessing
reliability and stability in panel models. In D. R. Heise (Ed.), Sociological
methodology (pp. 84–136).
San Francisco, CA: Jossey-Bass.
Wise,
S. L. (1985). The development and validation of a scale measuring attitudes
toward statistics. Educational and Psychological Measurement, 45(2), 401-405.
Wisenbaker,
J. M., Scott, J. S., & Nasser, F. (2000, July/August). Structural equation models relating attitudes about and achievement in
introductory statistics courses: A comparison of results from the U.S. and
Israel. Paper presented at the 9th International Congress on
Mathematics Education, Tokyo, Japan.
Zeidner,
M. (1991). Statistics and mathematics anxiety in social science students: Some
interesting parallels. British Journal of Educational Psychology, 61(3), 319-328.
FRANCESCA CHIESI
Department of Psychology, University of Florence
via di San Salvi 12, Complesso di San Salvi, Padiglione 26
50135 Florence ITALY