A Mixture Partial Credit Analysis of Math Anxiety

Main Article Content

Ibrahim Burak Olmez Allan S. Cohen https://orcid.org/0000-0002-8776-9378


The purpose of this study was to investigate a new methodology for detection of differences in middle grades students’ math anxiety. A mixture partial credit model analysis was used to detect distinct latent classes based on homogeneities in response patterns. The analysis detected two latent classes. Students in Class 1 had less anxiety about apprehension of math lessons and use of mathematics in daily life, and more self-efficacy for mathematics than students in Class 2. Students in both classes were similar in terms of test and evaluation anxiety. Moreover, students in Class 1 were found to be more successful in mathematics, mostly like mathematics and mathematics teachers, and have better educated mothers than students in Class 2. Manifest variables of gender, attending private or public schools, and education levels of fathers did not differ among the latent classes. Characterizing differences between members of each latent class extends recent advances in measuring math anxiety.

Article Details

How to Cite
Olmez, I., & Cohen, A. (2018). A Mixture Partial Credit Analysis of Math Anxiety. International Journal of Assessment Tools in Education, 5(4), 611-630. Retrieved from http://ijate.net/index.php/ijate/article/view/565


Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.

Alkan, V. (2018). A systematic review research: 'Mathematics anxiety' in Turkey. International Journal of Assessment Tools in Education, 5(3), 567–592.

Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(2), 181–185.

Ashcraft, M. H., Krause, J. A., & Hopko, D. R. (2007). Is math anxiety a mathematical learning disability? In D. B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 329–348). Baltimore: Brookes.

Ashcraft, M. H., & Moore, A. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3), 197–205.

Baghaei, P., & Carstensen, C. H. (2013). Fitting the mixed Rasch model to a reading comprehension test: Identifying reader types. Practical Assessment, Research & Evaluation, 18(5), 1–12.

Baloğlu, M. & Zelhart, P. F. (2007). Psychometric properties of the revised mathematics anxiety rating scale. The Psychological Record, 57, 593–611.

Bekdemir, M. (2010). The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students. Educational Studies in Mathematics, 75, 311–328.

Birgin, O., Baloglu, M., Catlioglu, H., & Gurbuz, R. (2010). An investigation of mathematics anxiety among sixth through eighth grade students in Turkey. Learning and Individual Differences, 20, 654–658.

Bolt, D. M., Cohen, A. S., & Wollack, J. A. (2001). A mixture item response for multiple-choice data. Journal of Educational and Behavioral Statistics, 26, 381–409.

Bolt, D. M., Cohen, A. S., & Wollack, J. A. (2002). Item parameter estimation under conditions of test speededness: Application of a mixture Rasch model with ordinal constraints. Journal of Educational Measurement, 39(4), 331–348.

Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytic extensions. Psychometrika, 52, 345–370.

Cho, S.-J., Bottge, B. A., Cohen, A. S., & Kim, S.-H. (2011). Detecting cognitive change in the math skills of low-achieving adolescents. The Journal of Special Education, 45(2), 67–76.

Cohen, A. S., & Bolt, D. M. (2005). A mixture model analysis of differential item functioning. Journal of Educational Measurement, 42(2), 133–148.

Engelhard, G. (1990). Math anxiety, mother's education, and the mathematics performance of adolescent boys and girls: Evidence from the U.S. and Thailand. Journal of Psychology, 124(3), 289–298.

Erktin, E., Dönmez, G., & Özel, S. (2006). Psychometric characteristics of the mathematics anxiety scale. Education and Science, 31(140), 26–33.

Erol, E. (1989). Prevalence and correlates of math anxiety in Turkish high school students. Unpublished master thesis, Bogazici University.

Gresham, G. (2017). Preservice to inservice: Does mathematics anxiety change with teaching experience. Journal of Teacher Education, 69(1), 90–107.

Harari, R. R., Vukovic, R. K., & Bailey, S. P. (2013). Mathematics anxiety in young children: An exploratory study. The Journal of Experimental Education, 81(4), 538–555.

Harper, N. W., & Daane, C. J. (1998). Causes and reduction of math anxiety in preservice elementary teachers. Action in Teacher Education, 19(4), 29–38.

Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33–46.

Hill, F., Mammarella, I. C., Devine, A., Caviola, S., Passolunghi, M. C., & Szücs, D. (2016). Math anxiety in primary and secondary school students: Gender differences, developmental changes and anxiety specificity. Learning and Individual Differences, 48, 45–53.

Hong, S., & Min, S. (2007). Mixed Rasch modeling of the Self-Rating Depression Scale: Incorporating Latent Class and Rasch Rating Scale models. Educational and Psychological Measurement, 67(2), 280–299.

Hopko, D. R. (2003). Confirmatory factor analysis of the Math Anxiety Rating Scale-Revised. Educational and Psychological Measurement, 63(2), 336–351.

Izsák, A., Jacobson, E., de Araujo, Z., & Orrill, C. H. (2012). Measuring mathematical knowledge for teaching fractions with drawn quantities. Journal for Research in Mathematics Education, 43(4), 391–427.

Izsák, A., Orrill, C. H., Cohen, A. S., & Brown, R. E. (2010). Measuring middle grades teachers’ understanding of rational numbers with the mixture Rasch model. The Elementary School Journal, 110, 279–300.

Kazelskis, R. (1998). Some dimensions of mathematics anxiety: A factor analysis across instruments. Educational and Psychological Measurement, 58, 623–633.

Krinzinger, H., Kaufmann, L., & Willmes, K. (2009). Math anxiety and math ability in early primary school years. Journal of Psychoeducational Assessment, 27(3), 206–225.

Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston, MA: Houghton Mifflin.

Li, F., Cohen, A. S., Kim, S. H., & Cho, S. J. (2009). Model selection methods for dichotomous mixture IRT models. Applied Psychological Measurement, 33(5), 353–373.

Luo, X., Wang, F., & Luo, Z. (2009). Investigation and analysis of mathematics anxiety in middle school students. Journal of Mathematics Education, 2(2), 12–19.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.

Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its influence on young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82(1), 60–70.

Mislevy, R. J., & Verhelst, N. (1990). Modeling item responses when different subjects employ different solution strategies. Psychometrika, 55, 195–215.

Novak, E., & Tassell, J. L. (2017). Studying preservice teacher math anxiety and mathematics performance in geometry, word, and non-word problem solving. Learning and Individual Differences, 54, 20–29.

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: The Danish Institute of Education Research. (Expanded edition (1980) with foreword and afterword by B.D. Wright. Chicago, IL: The University of Chicago Press)

Reckase, M. D. (1979). Unifactor latent trait models applied to multifactor tests: Results and implications. Journal of Educational Statistics, 4, 207–230.

Richardson F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551–554.

Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271–282.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.

Sen, S. (2016). Applying the mixed Rasch model to the Runco ideational behavior scale. Creativity Research Journal, 28(4), 426–434.

SPSS Inc. (2007). SPSS for Windows, Version 16.0. Chicago, SPSS Inc.

Stoehr, K. J. (2017). Mathematics anxiety: One size does not fit all. Journal of Teacher Education, 68(1), 69–84.

Von Davier, M. (2001). WINMIRA [Computer Software]. St. Paul, MN: Assessment Systems Corporation.

Wigfield, A. & Meece, J. L. (1988). Math anxiety in elementary and secondary school students. Journal of Educational Psychology, 80, 210–216.

Young, C. B., Wu, S. S., Menon, V. (2012). The neurodevelopmental basis of math anxiety. Psychological Science, 23(5), 492–501.