Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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Development of a Tool to Measure Math Anxiety Factors for High School Students and Validation of Validity

고등학생용 수학불안 요인 측정 도구 개발 및 타당도 검증

  • Received : 2022.05.24
  • Accepted : 2022.06.27
  • Published : 2022.06.30
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Abstract

The purpose of this study was to develop an instrument measuring mathematics anxiety suitable for Korean High school students. In order to achieve this study purpose, the study was conducted according to the procedure of setting components of mathematics anxiety, developing questions, and verifying validity and reliability. First, in order to set the components of mathematic anxiety, previous studies on mathematic anxiety. Through this, six factors of mathematic anxiety were derived. Next, new questions were developed for each of the six constituent factors. The 122 questions were revised and supplemented through two content validity tests, and the final instrument for mathematics anxiety consisted of 49 questions of 6 factors. Finally, to verify the validity and reliability of the measurement instrument for mathematics anxiety, a survey was conducted on 1,848 students from 16 universities in Seoul and the metropolitan area. Next, a validity analysis was conducted with the 1,645 responses, excluding students who answered that there was no mathematics anxiety. As a result of exploratory factor analysis, 15 out of 49 questions were removed. Six factors were named individual characteristics, pressure on achievement, abstraction in mathematics, teaching and learning style, parental attitudes, and cumulative mathematics subjects. As a result of confirmatory factor analysis, the model fit was found to be appropriate, and the convergence validity and discriminant validity were found to be good.

한국 고등학교 학생들에게 적합한 수학불안 요인 측정도구를 개발하기 위하여 요인 탐색, 문항 개발, 타당도 및 신뢰도 검증의 단계로 연구를 실시하였다. 이를 위하여 문헌분석을 통해 기 개발되어 사용되어온 문항을 수정 보완하고, 학생들을 대상으로 한 개방형 조사를 통해 사교육 및 수학 교수 방법에 대한 시대적 배경을 반영한 신규 문항을 추가하였다. 개발된 측정문항에 대한 탐색적 요인분석과 확인적 요인분석을 통해 타당도를 검증하였으며, 연구 결과, 수학교과의 특성에 기인하는 불안 요인이 구체화되었고, 모둠학습이나 발표수업 등과 같은 교수학습 방법 등이 반영되었다.

Keywords

Acknowledgement

이 논문은 2021년 대한민국 교육부와 한국연구재단의 지원을 받아 수행된 연구임(NRF-2021S1A5C2A03089476).

References

  1. Koh, Y. J. (2018). A study on analysis of actual state of mathematics renouncers and treatment at the renouncer's level, Master's thesis at Ulsan University.
  2. Kim, K. S. (2007). (New Amos 7.0) Analysis structural equation modeling, Seoul: Hannarae.
  3. Kim, K. S. (2008). Research methodology of Causal analysis, Seoul: Chungram.
  4. Kim, D. W., Park, J. H., Hwang, J., & Kim, S. H. (2021). Investigation on the Limitations of the 2015 Revised Mathematics Curriculum Implementation, Jounral of Korea Society Educational Studies in Mathematics, 23(3), 387-410.
  5. Kim, R. (2015). A Study on Elementary Teachers' Beliefs about Teaching Mathematics, School Mathematics, 17(4), 593-611.
  6. Kim, R. (2018). Development and Validation of Mathematics Anxiety Scale for Elementary Students, J. Korea Soc. Math. Ed. Ser. C: Education of Primary School Mathematics, 21(4), 431-444.
  7. Kim, R. (2021). Analysis of Changes in Mathematical Anxiety of Elementary School Students: A Longitudinal Study, Communications of Mathematical Education, 35(1), 1-14. https://doi.org/10.7468/JKSMEE.2021.35.1.1
  8. Kim, R. N. & Shin, H. G. (2015). An Analysis of Causes of Elementary Students Mathematics Anxiety, The Journal of Korea elementary education, 26(1), 83-101.
  9. Kim M. S., Im, S. I. & Kim, S. Y. (2011). Development and Validation of the Mathematics Anxiety Scale for High School Students, The Korean Journal of Educational Psychology, 25(4), 717-737.
  10. Kim, Y. S. & Heo, H. J. (1995). A Study on Antecedents of Mathematics Anxiety in High School Students, Journal of Educational Research in Mathematics, 5(2), 111-128.
  11. Kim, J. H., Hong, S. H., & Choo, B. D. (2007). Applications of Structural Equation Modeling in Management Studies: A Critical Review, Korean management review, 36(4), 897-923.
  12. Kim, H. M. & Kang, W. (2006). An Analysis of the Causes of Mathematics Anxiety in the Elementary School Students According to the Grades and Sex, Journal of elementary mathematics education, 10(1), 89-106.
  13. Kim, H. & Choi-Koh, S. (2019). Development and Application of K-UTF Program for Mathematical Anxiety Reduction, Journal of Education & Culture, 25(5), 789-812.
  14. Kim, H K. (2000). Math Anxiety According To Personality, Master's thesis at Ewha Womans University.
  15. Nam, Y. M. & Seo, Y. C. (1998). A study on solving math anxiety factors. Educational theory and practice, 8(1), 195-212.
  16. Noh, K. S. (2019). Statistical analysis of Research: SPSS & AMOS, Hanbit Academy.
  17. Park, K. E. (2020). Relationship between mindfulness and and math anxiety, Korean Society of Mathematical Education Newsletter, 36(3), 23-26.
  18. Bae, B. R. (2011). (Amos 19)Structural Equation Modeling, Seoul: Chungram.
  19. Baek, R. K. (2009). Analysis on the factors of anxiety and evasion of middle school student in learning Mathematics, Master's thesis at National Changwon University.
  20. Sang, K. A., Kwak, Y. S., Choi, J. S., Park, S. W., & Cheon, S. K. (2017). In-depth Analysis of TIMSS 2015 Korean Results, Korea Institute for Curriculum and Evalution.
  21. Seong, T. J. (2005). Reliability and Validity, Seoul: Hakjisa.
  22. Song, H. B. (2001). Development and application of math anxiety measuring tool for middle school students, Master's thesis at Aju University of Education Graduate School.
  23. Oh, H. J. & Lee, J. B. (2000). A study of anxiety factor for the learning of Mathematics, Report of Science Education, 3(1), 47-57.
  24. Ok, B. M., Lee, C. Y., & Koh, S. S. (2021). Reliability and Validity of Mathematics Anxiety Scale for High School Students, Journal of Educational Research in Mathematics, 31(2), 211-230. https://doi.org/10.29275/jerm.2021.31.2.211
  25. Yun, E. J. (2014). Trends and Tasks of Studies on Math Anxiety: Using Cognitive Neuroscience Techniques, Journal of Learner-Centered Curriculum and Instruction, 14, 295-314.
  26. Lee, G. (2016). Changing Trends of Mathematics Anxiety Factor and Word Analysis Associated with Mathematics, Doctoral dissertation at DanKook University, Seoul.
  27. Lee, D. K. (2019). An analysis on factors of mathematics anxiety : focusing on middle and high school students, Master's thesis at Chung-ang University.
  28. Lee, M. L. (2007). An Analysis on factor of mathematics anxiety of middle school and high school students : among The 1st, 2nd and 3rd graders at middle school and The 1st and 2nd graders at high school, Master's thesis at Korea National University of Education.
  29. Lee, S. N. (2010). A Study on the Coping Behavior of Mathematics Anxiety Depending on the Grade, Sex, Mathematics Achievement, and Mathematics Anxiety in Elementary School Students, Korean journal of human ecology, 19(1). 27-38. https://doi.org/10.5934/KJHE.2010.19.1.027
  30. Lee, Y. S. (2000). A Study on the reduction of elementary students' math anxiety, Master's thesis at Incheon National University of Education of Education Graduate School.
  31. Lee, Y. S. (2005). A study on Mathematics anxiety causes among elementary schoolers, Master's thesis at Gyeongin National University of Education Graduate School.
  32. Lee, H. S. (2008). Analysis of Structural equation model and AMOS 7.0, Beopmunsa, Gyeonggi Province.
  33. Lee, H. C., Kim, H. W., Baek S., Ko, H. K., & Yi, H. S. (2017). A Causal Model Analysis of Non-Cognitive Characteristics of Mathematics Learning, Communications of Mathematical Education, 31(2), 187-202. https://doi.org/10.7468/JKSMEE.2017.31.2.187
  34. Jang, S. L. & Cho, S. H. (2013). Development and Validation of the Korean Mathematics Anxiety Rating Scale for College Students. Journal of The Korean Data Analysis Society, 15(4), 1955-1969.
  35. Chang, Y. J. (2004). A Trend Analysis on Mathematics Anxiety :From Elementary to High School Students, Master's thesis at Kunkuk University.
  36. Chong, Y. O., Chang, K. Y., Tak, B., Kang, H. Y., Seo, D. Y., Park, S., Nam, J., Kim, G., Ko H. K., Kim, J. H., Kwon, N. Y. (2016). Comparative Study of Mathematics Curriculum among the United States, Singapore, England, Japan, Australia and Korea, The Journal of Educational Research in Mathematics, 26(3), 371-402.
  37. Jung, J. B. & Whang, W. H. (2013). An Analysis of the Effects of Reducing Mathematics Anxiety using Divided-note-method and Cornell-note-method, The Journal of Curriculum and Instruction Studies, 6(1), 37-65
  38. Choi, K. H. & Han, H. S. (2013). A study on the effects of the reciprocal peer tutoring in high school students' affective characteristics of mathematics, The Mathmatical Education, 52(3), 423-442. https://doi.org/10.7468/mathedu.2013.52.3.423
  39. Choi, B. H. (2014). The Effects of Digital Storytelling on Mathematical Communication Apprehension in 6th graders' Mathematics Instruction, Education of Primary School Mathematics, 17(1), 41-56. https://doi.org/10.7468/JKSMEC.2014.17.1.41
  40. Choi, J. S. (1988). Analysis of relationship betweengeneral anxiety, test anxiety, academic anxiety, math anxiety and math performance, Doctoral dissertation at Kyungpook National University.
  41. Choi, H. C. (2016). Statistical analysis of social science, Gyeonggi Province: Nanam.
  42. Tak, J. K. (2000). Psychological tes, Seoul: Hakjisa.
  43. Heo, H. J. (1996). A study on antecedents of mathematics anxiety in high school students, Doctoral dissertation at Seoul National University, Seoul.
  44. Hong, S. H. (2000). The Criteria for Selecting Appropriate Fit Indices in Structural Equation Modeling and Their Rationales, Korean Journal of Clinical Psychology, 19(1), 161-177.
  45. Hong, A. S. (2012). The Effects of Children's Mathematics Disposition Anxiety and self-efficacy on Mathematics Learning Achievements, The Journal of Child Education, 21(2), 311-323.
  46. Hong, H. J. (2006). A study on the math anxiety factors and solutions in middle school students, Master's thesis at Korea University.
  47. Hwang, S. W. & Lew, K. H. (2018). Relationship Between Mathematics Anxiety and Mathematical Achievement of Middle School Students According to Gender and Grade, Communications of Mathematical Education, 32(2), 175-189. https://doi.org/10.7468/JKSMEE.2018.32.2.175
  48. Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences, Current directions in psychological science, 11(5), 181-185. https://doi.org/10.1111/1467-8721.00196
  49. Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety, Psychonomic bulletin & review, 14(2), 243-248. https://doi.org/10.3758/BF03194059
  50. Ashcraft, M. H., & Ridley, K. S. (2005). Math anxiety and its cognitive consequences: A tutorial review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 315-327). Psychology Press.
  51. Bacon, D. R., Sauer, P. L., & Young, M. (1995). Composite reliability in structural equations modeling, Educational and psychological measurement, 55(3), 394-406. https://doi.org/10.1177/0013164495055003003
  52. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special, Journal of teacher education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  53. Baloglu, M. (2003). Individual differences in statistics anxiety among college students, Personality and Individual Differences, 34(5), 855-865. https://doi.org/10.1016/S0191-8869(02)00076-4
  54. Beilock, S. L., Gunderson, E. A., Ramirez, G., & Levine, S. C. (2010). Female teachers' math anxiety affects girls' math achievement, Proceedings of the National Academy of Sciences, 107(5), 1860-1863.
  55. Ben-Zeev, T., Duncan, S., & Forbes, C. (2005). Stereotypes and math performance. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 235-249). Psychology Press.
  56. Bleeker, M. M., & Jacobs, J. E. (2004). Achievement in math and science: Do mothers' beliefs matter 12 years later?, Journal of Educational Psychology, 96(1), 97. https://doi.org/10.1037/0022-0663.96.1.97
  57. Buckley, S., Reid, K., Goos, M., Lipp, O. V., & Thomson, S. (2016). Understanding and addressing mathematics anxiety using perspectives from education, psychology and neuroscience, Australian Journal of Education, 60(2), 157-170. https://doi.org/10.1177/0004944116653000
  58. Carey, E., Hill, F., Devine, A., & Szucs, D. (2017). The modified abbreviated math anxiety scale: A valid and reliable instrument for use with children, Frontiers in psychology, 8, 11.
  59. Cipora, K., Szczygiel, M., Willmes, K., & Nuerk, H. C. (2015). Math anxiety assessment with the Abbreviated Math Anxiety Scale: Applicability and usefulness: Insights from the Polish adaptation, Frontiers in Psychology, 6, 1833. https://doi.org/10.3389/fpsyg.2015.01833
  60. Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis, Practical assessment, research, and evaluation, 10(1), 7.
  61. Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis, Psychological methods, 1(1), 16. https://doi.org/10.1037/1082-989X.1.1.16
  62. Field, A. (2013). Discovering statistics using IBM SPSS statistics, sage.
  63. Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error, Journal of marketing research, 18(1), 39-50. https://doi.org/10.2307/3151312
  64. Geist, E. (2010). The anti-anxiety curriculum: Combating math anxiety in the classroom, Journal of Instructional Psychology, 37(1), 24-31.
  65. Gilbert, G. E., & Prion, S. (2016). Making sense of methods and measurement: Lawshe's content validity index, Clinical Simulation in Nursing, 12(12), 530-531. https://doi.org/10.1016/j.ecns.2016.08.002
  66. 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. https://doi.org/10.1080/00220973.2012.727888
  67. Hetzel, R. D. (1996). A primer on factor analysis with comments on patterns of practice and reporting. Advances in social science methodology, 4, 175-206.
  68. Ho, H. Z., Senturk, D., Lam, A. G., Zimmer, J. M., Hong, S., Okamoto, Y., & Wang, C. P. (2000). The affective and cognitive dimensions of math anxiety: A cross-national study, Journal for research in Mathematics Education, 31(3), 362-379. https://doi.org/10.2307/749811
  69. Hong, S., Malik, M. L., & Lee, M. K. (2003). Testing configural, metric, scalar, and latent mean invariance across genders in sociotropy and autonomy using a non-Western sample, Educational and psychological measurement, 63(4), 636-654. https://doi.org/10.1177/0013164403251332
  70. Jackson, C. D. & Leffingwell, R. J. (1999). The role of instructors in creating math anxiety in students from kindergarten through college, The Mathematics Teacher, 92(7), 583-586. https://doi.org/10.5951/MT.92.7.0583
  71. Jameson, M. M. (2013). The development and validation of the Children's Anxiety in Math Scale, Journal of psychoeducational assessment, 31(4), 391-395. https://doi.org/10.1177/0734282912470131
  72. Jolliffe, I. (2005). Principal component analysis, Second Edition. Springers.
  73. Kazelskis, R., Reeves, C., Kersh, M. E., Bailey, G., Cole, K., Larmon, M., Hall, L., & Holliday, D. C. (2000). Mathematics anxiety and test anxiety: Separate constructs?, The Journal of Experimental Education, 68(2), 137-146. https://doi.org/10.1080/00220970009598499
  74. Ko, H. K. & Yi, H. S. (2011). Development and validation of a mathematics anxiety scale for students, Asia Pacific Educational Review, 12, 509-521. https://doi.org/10.1007/s12564-011-9150-4
  75. Lazarus, R. B. (1981). Self-similar solutions for converging shocks and collapsing cavities, SIAM Journal on Numerical Analysis, 18(2), 316-371. https://doi.org/10.1137/0718022
  76. 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. https://doi.org/10.1037/0022-0663.82.1.60
  77. Plake, B. S. & Parker, C. S. (1982). The development and validation of a revised version of the Mathematics Anxiety Rating Scale, Educational and psychological measurement, 42(2), 551-557. https://doi.org/10.1177/001316448204200218
  78. 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), Learning and Individual Differences, 34, 51-56. https://doi.org/10.1016/j.lindif.2014.05.012
  79. Reglin, G. L. (1990). The effects of individualized and cooperative computer assisted instruction on mathematics achievement and mathematics anxiety for prospective teachers, Journal of Research on Computing in Education, 22(4), 404-412. https://doi.org/10.1080/08886504.1990.10781930
  80. Rounds, J. B. & Hendel, D. D. (1980). Measurement and dimensionality of mathematics anxiety, Journal of counseling Psychology, 27(2), 138. https://doi.org/10.1037/0022-0167.27.2.138
  81. Suinn, R. M. & Winston, E. H. (2003). The mathematics anxiety rating scale, a brief version: psychometric data, Psychological reports, 92(1), 167-173. https://doi.org/10.2466/PR0.92.1.167-173
  82. Tapia, M. & Marsh, G. E. (2004). The relationship of math anxiety and gender, Academic Exchange Quarterly, 8(2), 130-134.
  83. Tomasetto, C., Alparone, F. R., & Cadinu, M. (2011). Girls' math performance under stereotype threat: The moderating role of mothers' gender stereotypes, Developmental psychology, 47(4), 943. https://doi.org/10.1037/a0024047
  84. Uusimaki, L. & Nason, R. (2004). The origins of pre-service primary education students' anxieties and negative feelings about mathematics, In Performing Educational Research: Theories, Methods and Practices (pp. 225-236), Post Press.
  85. Walsh, J. J. & Ugumba-Agwunobi, G. (2002). Individual differences in statistics anxiety: The roles of perfectionism, procrastination and trait anxiety, Personality and Individual Differences, 33(2), 239-251. https://doi.org/10.1016/S0191-8869(01)00148-9
  86. Young, Christina. B., Wu, S. S., & Menon, V. (2012). The neurodevelopmental basis of math anxiety, Psychological science, 23(5), 492-501. https://doi.org/10.1177/0956797611429134
  87. Yuksel-Sahin, F. (2008). Mathematics anxiety among 4th and 5th grade Turkish elementary school students, International Electronic Journal of Mathematics Education, 3(3), 179-192. https://doi.org/10.29333/iejme/225