ANOTHER PSYCHOMETRIC PROOF OF THE ABBREVIATED MATH ANXIETY SCALE USEFULNESS: IRT ANALYSIS
DOI:
https://doi.org/10.19090/pp.2018.3.301-323Keywords:
AMAS, high school, Item Response Theory, math anxietyAbstract
The aim of this research is the psychometric evaluation of the Abbreviation Math Anxiety Scale (AMAS) on a sample of high school students. AMAS operationalizes math anxiety as a two- dimensional construct, basing its main components on the context model: math learning anxiety (MAL) and math evaluation anxiety (MAE). MAL represents the tendency of manifesting mathematical anxiety during the process of learning mathematics, while MAE represents math anxiety present in all situations that imply formal evaluation of math knowledge. The sample consisted of 514 high school students (45.3% male), aged 15 to 19. Confirmatory factor analysis pointed that AMAS is a one–dimensional scale with two facets, with the bifactorial solution showing the best fit parameters. Psychometric attributes of AMAS were tested by using Item Response Theory. Items and the questionnaire showed appropriate psychometric properties. The AMAS scale has expected patterns of relatedness with mathematical achievement, motivation for learning math, age and gender.
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References
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Ashcraft, M. H., & Moore, A. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3), 197–205. doi:10.1177/0734282908330580
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Chinn, S. (2009). Mathematics anxiety in secondary students in England. Dyslexia,
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Ching–Yun, Y. (2002). Evaluating Cut off Criteria of Model Fit Indices for Latent Var- iable Models with Binary and Continuous Outcomes. (Doctoral thesis, Univer- sity of California, Los Angeles, USA). Retrieved from: http://ww.statmodel2. com/download/Yudissertation.pdf.
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De Mars, C. (2010). Item response theory. New York: Oxford University Press. Devine, A., Fawcett, K., Szűcs, D., & Dowker, A. (2012). Gender differences in mathe-
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Else–Quest, N. M., Hyde, J. S., & Linn, M. C. (2010). Cross–national patterns of gender differences in mathematics: a meta–analysis. Psychological Bulletin, 136(1), 103–127. doi:10.1037/a0018053
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: a 5–year longitudinal study. Developmental Psychology, 47(6), 1539–1552. doi:10.1037/a0025510
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Githua, B. N., & Mwangi, J. G. (2003). Students’ mathematics self–concept and mo- tivation to learn mathematics: relationship and gender differences among Kenya’s secondary school students in Nairobiand Rift Valley provinces. Inter- national Journal of Educational Development, 23(5), 487–499. doi:10.1016/ s0738–0593(03)00025–7
Glaister, K. (2007). The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations. Nurse Educa- tion Today, 27(4), 341–347. doi:10.1016/j.nedt.2006.05.015
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33–46. doi:10.2307/749455
Hirschfeld, G., & von Brachel, R. (2014). Multiple–Group confirmatory factor anal- ysis in R–A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19(7), 1–12.
Hopko, D. R. (2003). Confirmatory factor analysis of the math anxiety rating scale–revised. Educational and Psychological Measurement, 63(2), 336–351. doi:10.1177/0013164402251041
Hopko, D. R., Mahadevan, R., Bare, R. L., & Hunt, M. K. (2003). The abbreviated math anxiety scale (AMAS) construction, validity, and reliability. Assessment, 10(2), 178–182. doi:10.1177/1073191103010002008
Kline, R. B. (2010). Principles and practice of structural equation modeling. New York, NY: Guilford.
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. doi:10.1177/0734282908330583
Ma, X. (1999). A meta–analysis of the relationship between anxiety toward math- ematics and achievement in mathematics. Journal for Research in Mathemat- ics Education, 520–540. doi:10.2307/749772
Ma, X., & Xu, J. (2004). The causal ordering of mathematics anxiety and mathemat- ics Achievement: a longitudinal panel analysis. Journal of Adolescence, 27(2), 165–179. doi:10.1016/j.adolescence.2003.11.003
Maloney, E. A., Waechter, S., Risko, E. F., & Fugelsang, J. A. (2012). Reducing the sex difference in math anxiety: The role of spatial processing ability. Learning and Individual Differences, 22(3), 380–384. doi:10.1016/j.lindif.2012.01.001
Milovanović, I. (2016). Implicitne teorije inteligencije i motivacija za učenje matematike kod učenika srednjih škola [Implicit theories of intelligence and motivation for learning mathematics in high school students]. Nastava i vaspitanje, 65(3), 509-524. doi:10.5937/nasvas1603509M
Milovanović, I. (2018). Matematička anksioznost i postignuće na ranom osnovnoškolskom uzrastu: uloga uključenosti roditelja u podučavanje [Math anxiety and achievement at early elementary stage: The role of parental involvement in teaching]. Godišnjak Filozofskog fakulteta u Novom Sadu, XLI- II(1), 271‒287. doi:10.19090/gff.2018.1.271-287
Milovanović, I., & Kodžopeljić, J. (2018). Faktorska struktura i konvergentna validnost upitnika matematičke anksioznosti za učenike srednjih škola [Fac- tor structure and convergent validity of the Math Anxiety Questionnaire for high school students]. Nastava i vaspitanje, 67(1), 113-128. doi:10.5937/nas- vas1801113M
Morizot, J., Ainsworth, A. T., & Reise, S. P. (2007). Toward modern psychometrics. In R. W. Robins, C. R. Fraley, & R. F. Krueger (Eds.), Handbook of Research Methods in Personality Psychology (pp. 407 – 423). New York: Guilford Press. Núñez–Peña, M. I., Guilera, G., & Suárez–Pellicioni, M. (2014). The single– item math anxiety scale: An alternative way of measuring mathemati-
cal anxiety. Journal of Psychoeducational Assessment, 32(4), 306–317. doi:10.1177/0734282913508528
Núñez–Peña, M. I., Suárez–Pellicioni, M., Guilera, G., & Mercadé–Carranza, C. (2013). A Spanish version of the short Mathematics Anxiety Rating Scale (sMARS). Learning and Individual Differences, 24, 204–210. doi:10.1016/j. lindif.2012.12.009
Prevatt, F., Welles, T. L., Li, H., & Proctor, B. (2010). The contribution of memory and anxiety to the math performance of college students with learning disa- bilities. Learning Disabilities Research & Practice, 25(1), 39–47. doi:10.1111/ j.1540–5826.2009.00299.x
Primi, C., Busdraghi, C., Tomasetto, C., Morsanyi, K., & Chiesi, F. (2014). Measuring math anxiety in Italian college and high school students: validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS). Learn- ing and Individual Differences, 34, 51–56. doi:10.1016/j.lindif.2014.05.012
R CoreTeam (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna; Austria. Retrieved from: htt- ps://www.R–project.org/.
Radišić, J., Videnović, M., & Baucal, A. (2018). Distinguishing successful students in mathematics: A comparison across European countries. Psihologija, 51(1), 69–89. doi:10.2298/psi170522019r
Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187–202. doi:10.1080/15248372.201 2.664593
Revelle, W. (2015). psych: Procedures for Personality and Psychological Research.
Northwestern University, Evanston, Illinois: USA.
Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551–554. doi:10.1037/h0033456
Rizopoulos, D. (2006). ltm: An R package for latent variable modeling and item response theory analyses. Journal of Statistical Software, 17(5), 1-25. doi:10.18637/jss.v017.i05
Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36. doi:10.18637/jss.v048.i02
Samejima, F. (1969). Estimation of Latent Ability Using a Response Pattern of Grad- ed Scores (Psychometric Monograph No. 17). Richmond, VA: Psychometric So- ciety.
Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics, 6th ed. Bos- ton: Pearson.
Vahedi, S., & Farrokhi, F. (2011). A confirmatory factor analysis of the structure of abbreviated math anxiety scale. Iranian Journal of Psychiatry, 6(2), 47–53.
Van de Vijver, F., & Tanzer, N. K. (2004). Bias and equivalence in cross–cultural as- sessment: An overview. Revue Européenne de Psychologie Appliquée/European Review of Applied Psychology, 54, 119–135. doi:10.1016/j.erap.2003.12.004.
Watkins, M. W. (2013). Omega [Computer software]. Phoenix, AZ: Ed & Psych As- sociates. URL: http://edpsychassociates.com/Watkins3.html
Westland, J. C. (2010). Lower bounds on sample size in structural equation modeling. Electronic Commerce Research and Applications, 9(6), 476–487. doi:10.1016/j.elerap.2010.07.003
Wigfield, A., & Meece, J. L. (1988). Math anxiety in elementary and second- ary school students. Journal of Educational Psychology, 80(2), 210–216. doi:10.1037//0022–0663.80.2.210
Wu, S., Amin, H., Barth, M., Malcarne, V., & Menon, V. (2012). Math anxiety in sec- ond and third graders and its relation to mathematics achievement. Frontiers in Psychology, 3, 162–173. doi:10.3389/fpsyg.2012.00162
Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ω H: Their relations with each other and two alternative con- ceptualizations of reliability. Psychometrika, 70(1), 123–133. doi:10.1007/ s11336–003–0974–7
Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive con- sequences. Current Directions in Psychological Science, 11(5), 181–185. doi:10.1111/1467-8721.00196
Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. doi:10.1037//0096–3445.130.2.224
Ashcraft, M. H., & Moore, A. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3), 197–205. doi:10.1177/0734282908330580
Baucal, A., & Pavlović–Babić, D. (2010). Nauči me da mislim, nauči me da učim: PISA 2009 u Srbiji [Learn me to think, learn me to learn: PISA 2009 in Ser- bia]: Prvi rezultati [First results]. Beograd: Institut za psihologiju, Filozofski fakultet Univerzitet u Beogradu [Belgrade: Institute for Psychology, Faculty od Philosophy, University of Belgrade].
Caviola, S., Primi, C., Chiesi, F., & Mammarella, I. C. (2017). Psychometric proper- ties of the Abbreviated Math Anxiety Scale (AMAS) in Italian primary school children. Learning and Individual Differences, 55, 174–182. doi:10.1016/j.lin- dif.2017.03.006
Chinn, S. (2009). Mathematics anxiety in secondary students in England. Dyslexia,
15(1), 61–68. doi:10.1002/dys.381
Ching–Yun, Y. (2002). Evaluating Cut off Criteria of Model Fit Indices for Latent Var- iable Models with Binary and Continuous Outcomes. (Doctoral thesis, Univer- sity of California, Los Angeles, USA). Retrieved from: http://ww.statmodel2. com/download/Yudissertation.pdf.
Chiu, L. H., & Henry, L. L. (1990). Development and validation of the Mathemat- ics Anxiety Scale for Children. Measurement and Evaluation in Counseling and Development, 23(3), 121–127.
De Mars, C. (2010). Item response theory. New York: Oxford University Press. Devine, A., Fawcett, K., Szűcs, D., & Dowker, A. (2012). Gender differences in mathe-
matics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and Brain Functions, 8(1), 33. doi:10.1186/1744– 9081–8–33
Dogan, H. (2012). Emotion, confidence, perception and expectation case of math- ematics. International Journal of Science and Mathematics Education, 10(1), 49–69. doi:10.1007/s10763–011–9277–0
Eden, C., Heine, A., & Jacobs, A. M. (2013). Mathematics anxiety and its develop- ment in the course of formal schooling—a review. Psychology, 4(6), 27–35. doi:10.4236/psych.2013.46a2005
Evans, J. D. (1996). Straightforward statistics for the behavioral sciences. Pacific Grove, CA: Brooks/Cole Publishing.
Else–Quest, N. M., Hyde, J. S., & Linn, M. C. (2010). Cross–national patterns of gender differences in mathematics: a meta–analysis. Psychological Bulletin, 136(1), 103–127. doi:10.1037/a0018053
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: a 5–year longitudinal study. Developmental Psychology, 47(6), 1539–1552. doi:10.1037/a0025510
Gierl, M. J., & Bisanz, J. (1995). Anxieties and attitudes related to mathematics in grades 3 and 6. The Journal of Experimental Education, 63(2), 139–158. doi:1 0.1080/00220973.1995.9943818
Githua, B. N., & Mwangi, J. G. (2003). Students’ mathematics self–concept and mo- tivation to learn mathematics: relationship and gender differences among Kenya’s secondary school students in Nairobiand Rift Valley provinces. Inter- national Journal of Educational Development, 23(5), 487–499. doi:10.1016/ s0738–0593(03)00025–7
Glaister, K. (2007). The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations. Nurse Educa- tion Today, 27(4), 341–347. doi:10.1016/j.nedt.2006.05.015
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33–46. doi:10.2307/749455
Hirschfeld, G., & von Brachel, R. (2014). Multiple–Group confirmatory factor anal- ysis in R–A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19(7), 1–12.
Hopko, D. R. (2003). Confirmatory factor analysis of the math anxiety rating scale–revised. Educational and Psychological Measurement, 63(2), 336–351. doi:10.1177/0013164402251041
Hopko, D. R., Mahadevan, R., Bare, R. L., & Hunt, M. K. (2003). The abbreviated math anxiety scale (AMAS) construction, validity, and reliability. Assessment, 10(2), 178–182. doi:10.1177/1073191103010002008
Kline, R. B. (2010). Principles and practice of structural equation modeling. New York, NY: Guilford.
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. doi:10.1177/0734282908330583
Ma, X. (1999). A meta–analysis of the relationship between anxiety toward math- ematics and achievement in mathematics. Journal for Research in Mathemat- ics Education, 520–540. doi:10.2307/749772
Ma, X., & Xu, J. (2004). The causal ordering of mathematics anxiety and mathemat- ics Achievement: a longitudinal panel analysis. Journal of Adolescence, 27(2), 165–179. doi:10.1016/j.adolescence.2003.11.003
Maloney, E. A., Waechter, S., Risko, E. F., & Fugelsang, J. A. (2012). Reducing the sex difference in math anxiety: The role of spatial processing ability. Learning and Individual Differences, 22(3), 380–384. doi:10.1016/j.lindif.2012.01.001
Milovanović, I. (2016). Implicitne teorije inteligencije i motivacija za učenje matematike kod učenika srednjih škola [Implicit theories of intelligence and motivation for learning mathematics in high school students]. Nastava i vaspitanje, 65(3), 509-524. doi:10.5937/nasvas1603509M
Milovanović, I. (2018). Matematička anksioznost i postignuće na ranom osnovnoškolskom uzrastu: uloga uključenosti roditelja u podučavanje [Math anxiety and achievement at early elementary stage: The role of parental involvement in teaching]. Godišnjak Filozofskog fakulteta u Novom Sadu, XLI- II(1), 271‒287. doi:10.19090/gff.2018.1.271-287
Milovanović, I., & Kodžopeljić, J. (2018). Faktorska struktura i konvergentna validnost upitnika matematičke anksioznosti za učenike srednjih škola [Fac- tor structure and convergent validity of the Math Anxiety Questionnaire for high school students]. Nastava i vaspitanje, 67(1), 113-128. doi:10.5937/nas- vas1801113M
Morizot, J., Ainsworth, A. T., & Reise, S. P. (2007). Toward modern psychometrics. In R. W. Robins, C. R. Fraley, & R. F. Krueger (Eds.), Handbook of Research Methods in Personality Psychology (pp. 407 – 423). New York: Guilford Press. Núñez–Peña, M. I., Guilera, G., & Suárez–Pellicioni, M. (2014). The single– item math anxiety scale: An alternative way of measuring mathemati-
cal anxiety. Journal of Psychoeducational Assessment, 32(4), 306–317. doi:10.1177/0734282913508528
Núñez–Peña, M. I., Suárez–Pellicioni, M., Guilera, G., & Mercadé–Carranza, C. (2013). A Spanish version of the short Mathematics Anxiety Rating Scale (sMARS). Learning and Individual Differences, 24, 204–210. doi:10.1016/j. lindif.2012.12.009
Prevatt, F., Welles, T. L., Li, H., & Proctor, B. (2010). The contribution of memory and anxiety to the math performance of college students with learning disa- bilities. Learning Disabilities Research & Practice, 25(1), 39–47. doi:10.1111/ j.1540–5826.2009.00299.x
Primi, C., Busdraghi, C., Tomasetto, C., Morsanyi, K., & Chiesi, F. (2014). Measuring math anxiety in Italian college and high school students: validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS). Learn- ing and Individual Differences, 34, 51–56. doi:10.1016/j.lindif.2014.05.012
R CoreTeam (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna; Austria. Retrieved from: htt- ps://www.R–project.org/.
Radišić, J., Videnović, M., & Baucal, A. (2018). Distinguishing successful students in mathematics: A comparison across European countries. Psihologija, 51(1), 69–89. doi:10.2298/psi170522019r
Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 14(2), 187–202. doi:10.1080/15248372.201 2.664593
Revelle, W. (2015). psych: Procedures for Personality and Psychological Research.
Northwestern University, Evanston, Illinois: USA.
Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551–554. doi:10.1037/h0033456
Rizopoulos, D. (2006). ltm: An R package for latent variable modeling and item response theory analyses. Journal of Statistical Software, 17(5), 1-25. doi:10.18637/jss.v017.i05
Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36. doi:10.18637/jss.v048.i02
Samejima, F. (1969). Estimation of Latent Ability Using a Response Pattern of Grad- ed Scores (Psychometric Monograph No. 17). Richmond, VA: Psychometric So- ciety.
Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics, 6th ed. Bos- ton: Pearson.
Vahedi, S., & Farrokhi, F. (2011). A confirmatory factor analysis of the structure of abbreviated math anxiety scale. Iranian Journal of Psychiatry, 6(2), 47–53.
Van de Vijver, F., & Tanzer, N. K. (2004). Bias and equivalence in cross–cultural as- sessment: An overview. Revue Européenne de Psychologie Appliquée/European Review of Applied Psychology, 54, 119–135. doi:10.1016/j.erap.2003.12.004.
Watkins, M. W. (2013). Omega [Computer software]. Phoenix, AZ: Ed & Psych As- sociates. URL: http://edpsychassociates.com/Watkins3.html
Westland, J. C. (2010). Lower bounds on sample size in structural equation modeling. Electronic Commerce Research and Applications, 9(6), 476–487. doi:10.1016/j.elerap.2010.07.003
Wigfield, A., & Meece, J. L. (1988). Math anxiety in elementary and second- ary school students. Journal of Educational Psychology, 80(2), 210–216. doi:10.1037//0022–0663.80.2.210
Wu, S., Amin, H., Barth, M., Malcarne, V., & Menon, V. (2012). Math anxiety in sec- ond and third graders and its relation to mathematics achievement. Frontiers in Psychology, 3, 162–173. doi:10.3389/fpsyg.2012.00162
Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ω H: Their relations with each other and two alternative con- ceptualizations of reliability. Psychometrika, 70(1), 123–133. doi:10.1007/ s11336–003–0974–7
