Turkish Adaptation of Utley Geometry Attitude Scale: A Validity and Reliability Study

Abstract

Problem Statement: Among attitude measures, attitude scales are the most common, objective, and effective in gathering attitude data and there is a plenty of scales that measure various factors of attitude towards mathematics. However, there is a need for attitude scales that are content specific such as geometry, algebra, probability and statistics. One reason for this is that students’ attitudes towards mathematics in general and their attitudes towards specific mathematical topics might differ considerably from each other. Besides, to hear a student say they like mathematics but dislike geometry or algebra is not uncommon. Thus, it is thought that it would be significant to have a scale that particularly measures learners’ attitudes towards geometry.
Purpose of the Study: Although, a number of studies have developed scales with the goal of measuring geometry attitudes of middle and secondary school students, there is no such instrument in the accessible literature in Turkey that serve the same purpose for undergraduate students. Therefore, the authors wanted to go further in this direction and attempted to fill this gap by adapting Utley Geometry Attitude Scale to Turkish.

Keywords

• Geometry, attitude scale, undergraduate students, validity and reliability

Kaynakça

1. Aiken, L. R. (1979). Attitudes toward mathematics and science in Iranian middle schools. School Science and Mathematics, 79(3), 229-234.
2. Aiken, L. R. (1985). Attitude towards mathematics. In T. Husen & T. N. Postlethwaite (Eds.), The international encyclopedia of education: Research and studies (Vol. 6, pp.3233-3236). Oxford: Pergamon Press.
3. Aiken, L. R. (1974). Two scale of attitude toward mathematics. Journal for Research in Mathematics Education, 5(2), 67-71.
4. Akay, H., & Boz, N. (2011). Examining the relationships among prospective primary school teachers’ attitude towards mathematics, mathematics self-efficacy beliefs, teacher self-efficacy beliefs. The Journal of Turkish Educational Sciences, 9(2), 309-312.
5. Barlett, M. S. (1954). A note on the multiplying factors for various chi-square approximations. Journal of the Royal Statistical Society, 16 (Series B), 296-298.
6. Bayram, S. (2004). The effect of instruction with concrete models on eighth grade students’ geometry achievement and attitudes toward geometry. Unpublished master’s thesis, Middle East Technical University, Ankara.
7. Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88, 588-606.
8. Bindak, R. (2004). Study of reliability and validity with an application for geometry attitude scale. Unpublished doctoral dissertation, Dicle University, Diyarbakır.

9. Brassell, A., Petry, S., & Brooks, D. M. (1980). Ability grouping, mathematics achievement, and pupil attitudes toward mathematics. Journal for Research in Mathematics Education, 11(1), 22-28.
10. Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford Press.
11. Bulut, S., Ekici, C., İşeri, A. İ., & Helvacı, E. (2002). Education and Science, 27(125), 3-7.
12. Byrne, B. M. (1994). Structural equation modeling with EQS and EQS/Windows: Basic concepts, applications, and programming. California: Sage Publications, Inc.
13. Catell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276.
14. Daskalogianni, K., & Simpson, A. (2000). Towards a definition of attitude: The relationship between the affective and the cognitive in pre-university students. In Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp.217-224). Hiroshima, Japan.
15. De Bellis, V., & Goldin, G. (1999). Aspects of affect: Mathematical intimacy, mathematical integrity. In Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp.249-256). Haifa, Israel.
16. DeVellis, R. F. (2003). Scale development: Theory and applications (2nd ed.). Thousand Oaks, CA: Sage Publications, Inc.
17. Di Martino, P., & Zan, R. (2011). Attitude towards mathematics: A bridge between beliefs and emotions. ZDM The International Journal on Mathematics Education, 43, 471-482.
18. Duatepe, A., & Ubuz, B. (2007). Development of a geometry attitude scale. Academic Exchange Quarterly, 11(2), 205-209.
19. Ercikan, K., McCreith, T., & Lapointe, V. (2005). Factors associated with mathematics achievement and participation in advanced mathematics courses: An examination of gender differences from an international perspective. School Science and Mathematics, 105(1), 5-14.
20. Eryiğit, P. (2010). The effect of utilizing the three dimensional dynamic geometry software in geometry teaching on 12th grade students, their academic standings, and their attitude towards geometry. Unpublished master’s thesis, Dokuz Eylül University, İzmir.
21. Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman mathematics attitudes scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. Journal for Research in Mathematics Education, 7(5), 324-326.
22. George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and reference (4th ed.). Boston: Allyn & Bacon.
23. Haladyna, T., Shaughnessy, J., & Shaughnessy, M. J. (1983). A causal analysis of attitude toward mathematics. Journal for Research in Mathematics Education, 14(1), 19-29.
24. Hambleton, R. K. (2005). Issues, designs, and technical guidelines for adapting tests into multiple languages and cultures. In R. K. Hambleton, P. F. Merenda, & C. D. Spielberger (Eds.), Adapting educational and psychological tests for cross-cultural assessment (pp.3-38). Mahwah, NJ: Lawrence Erlbaum.
25. Hannula, M., Evans, J., Philippou, G., & Zan, R. (2004). Research Forum 01. Affect in mathematics education – exploring theoretical frameworks. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference (Vol. 1, pp.125-154). Bergen, Norway.
26. Hart, L. (1989). Describing the affective domain: Saying what we mean. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving (pp.37-45). New York: Springer.
27. Hooper, D., Coughlan, J., & Mullen, M. (2008). Structural equation modeling: Guidelines for determining model fit. The Electronic Journal of Business Research Methods, 6(1), 53-60.
28. Hoyle, R. H. (1995). Structural equation modeling: Concepts, issues, and applications. Thousand Oaks, CA: Sage Publications, Inc.
29. Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55.
30. Jöreskog, K. G., & Sörbom, D. (2007). LISREL 8.8: User’s reference guide. Chicago: Scientific Software.
31. Jöreskog, K., & Sörbom, D. (1993). LISREL 8: User’s reference guide. Chicago: Scientific Software International.
32. Kaiser, H. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31-36.
33. Kelloway, K. E. (1998). Using LISREL for structural equation modeling: A researcher’s guide. London: Sage.
34. Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York: Guilford Press.
35. Lim, S. Y., & Chapman, E. (2013). Development of a short form of the attitudes towards mathematics inventory. Educational Studies in Mathematics, 82, 145-164.
36. Ma, X. (1997). Reciprocal relationships between attitude toward mathematics and achievement in mathematics. The Journal of Educational Research, 90(4), 221-229.
37. Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics Education, 28(1), 26-47.
38. Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391-410.
39. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. G. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.575-596). New York: McMillan.
40. Mogari, D. (2004). Attitudinal scale measures in Euclidean geometry: What do they measure? South African Journal of Education, 24(1), 1-4.
41. Mulaik, S. A., James, L. R., Van Altine, J., Bennett, N., Lind, S., & Stilwell, C.D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 105, 430-445.
42. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.
43. Nisbet, S. (1991). A new instrument to measure pre-service primary teachers’ attitudes to teaching mathematics. Mathematics Education Research Journal, 3(2), 34-56.
44. Nunnally, J. C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill.
45. Nunnally, J., & Bernstein, I. (1994). Psychometric theory (3rd ed.). New York: McGraw-Hill.
46. Pallant, J. (2007). SPSS survival manual: A step by step guide to data analysis using SPSS for windows (3rd ed.). Buckingham: Open University Press.
47. Quinn, B., & Jadav, A. D. (1987). Causal relationship between attitude and achievement for elementary grade mathematics and reading. The Journal of Educational Research, 80(6), 366-372.
48. Raykov, T., & Marcoulides, G. A. (2000). A first course in structural equation modeling. Mahwah, NJ: Lawrence Erlbaum Associates.
49. Raykov, T., & Marcoulides, G. A. (2008). An introduction to applied multivariate analysis. New York: Taylor & Francis.
50. Reyes, L. H. (1984). Affective variables and mathematics education. The Elementary School Journal, 84(5), 558-581.
51. Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19, 551-554.
52. Samuelsson, J., & Granstrom, K. (2007). Important prerequisite for students’ mathematical achievement. Journal of Theory and Practice in Education, 3(2), 150–170.
53. Schumacker, R. E., & Lomax, R. G. (2004). A beginner’s guide to structural equation modeling (2nd ed.). NJ: Lawrence Erlbaum Associates, Inc.
54. Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston: Pearson Education.
55. Tapia, M., & Marsh, G. E. (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly, 8(2), 16-21.
56. Thorndike, R. M. (1978). Correlational procedures for research. New York: Gardner Press.
57. Thurstone, L. L. (1947). Multiple-factor analysis. Chicago: University of Chicago Press.
58. Utley, J. (2007). Construction and validity of geometry attitude scales. School Science and Mathematics, 107(3), 89-93.
59. Watkins, M. W. (2000). Monte Carlo PCA for Parallel Analysis (Computer Software). State College, PA: Ed & Psych Associate.
60. White, J. N. (2001). Socioeconomic, demographic, attitudinal and involvement factors associated with math achievement in elementary school. Unpublished doctoral dissertation, East Tennessee State University, USA.
61. Yücel, Z., & Koç, M. (2011). The relationship between the prediction level of elementary school students’ math achievement by their math attitudes and gender. Elementary Education Online, 10(1), 133-143.
62. Zan, R., & Di Martino, P. (2007). Attitude toward mathematics: Overcoming the positive/negative dichotomy. The Montana Mathematics Enthusiast, Monograph 3, pp. 157-168.
63. Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63, 113-121.
64. Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432-442.