JOŠ JEDAN PSIHOMETRIJSKI DOKAZ O KORISNOSTI SKRAĆENE SKALE MATEMATIČKE ANKSIOZNOSTI: IRT ANALIZA
DOI:
https://doi.org/10.19090/pp.2018.3.301-323Ključne reči:
AMAS, srednja škola, Teorija ajtemskog odgovora, matematička anksioznostApstrakt
Cilj ovog istraživanja usmeren je na ispitivanje psihometrijskih svojstava Skraćene skale matematičke anksioznosti (AMAS) kod učenika srednjih škola. AMAS operacionalizuje matematičku an- skioznost, po modelu konteksta, kao dvodimenzionalni fenomen, koji se sastoji od anksioznosti tokom učenja (MAL) i anksioznosti tokom evaluacije znanja (MAE). MAL predstavlja tendenciju is- poljavanja matematičke anksioznosti prilikom učenja matematike, dok MAE predstavlja tendenciju njenog ispoljavanja u svim situ- acijama koje uključuju formalnu evaluaciju znanja iz matematike. Uzorak je činilo 514 učenika srednjih škola (45.3% mladića), uzra- sta od 15 do 19 godina. Konfirmatorna faktorska analiza ukazuje na to da je AMAS jednodimenzionalna skala sa dve facete, kao i na to da bifaktorsko rešenje poseduje najbolje pokazatelje pode- snosti modela. Psihometrijska svojstva AMAS skale ispitana su korišćenjem Teorije ajtemskog odgovora (Item Response Theory
– IRT). IRT analiza ukazuje na adekvatne psihometrijske karak- teristike ajtema i skale u celini. AMAS skala je takođe ostvarila očekivane relacije sa matematičkim postignućem, motivacijom za učenje matematike, uzrastom i polom ispitanika.
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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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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
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
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Sadiković, S., Milovanović, I., & Oljača, M. (2018). JOŠ JEDAN PSIHOMETRIJSKI DOKAZ O KORISNOSTI SKRAĆENE SKALE MATEMATIČKE ANKSIOZNOSTI: IRT ANALIZA. Primenjena Psihologija, 11(3), 301–323. https://doi.org/10.19090/pp.2018.3.301-323
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