The development of a self-efficacy scale for mathematical modeling competencies

Yıl 2017, Cilt: 4 Sayı: 1, 19 - 36, 12.12.2016

İlhan Koyuncu Cem Oktay Guzeller Didem Akyuz

https://doi.org/10.21449/ijate.256552

Cited By: 9

Öz

Mathematical modeling has come into prominence
during the last few decades in many countries’ mathematics teaching curricula.
It combines real life situations with mathematical context. Although evaluating
students’ mathematical modeling performances with a unique Likert type
instrument is questionable, having an instrument about their self-efficacy
beliefs in mathematical modeling may help to comment about their ideas related
to their competencies in mathematical modeling. The purpose of this study is to
develop a reliable and valid measurement scale to determine mathematical
modeling self-efficacy of mathematics teacher candidates. For this purpose, the
draft and final form of the scale were applied to a total of 562 pre-service
elementary mathematics teachers from various public universities in Turkey. The
findings of study revealed that the scale is unidimensional according to the
results of exploratory factor analysis. The unidimensionality of the scale was
validated by confirmatory factor analysis. The reliability of mathematical
modeling self-efficacy scale was very high (.97). Finally, it was found that
this scale is an appropriate measurement tool to evaluate students’
self-efficacy beliefs on their mathematical modeling competencies. Some
suggestions related to the scale and for further studies were given at the end.

Anahtar Kelimeler

Factor analysis, mathematical modeling, modeling competencies, pre-service teachers, self-efficacy

The development of a self-efficacy scale for mathematical modeling competencies

Öz

Mathematical modeling has come into prominence during the last few decades in many countries’ mathematics teaching curricula. It combines real life situations with mathematical context. Although evaluating students’ mathematical modeling performances with a unique Likert type instrument is questionable, having an instrument about their self-efficacy beliefs in mathematical modeling may help to comment about their ideas related to their competencies in mathematical modeling. The purpose of this study is to develop a reliable and valid measurement scale to determine mathematical modeling self-efficacy of mathematics teacher candidates. For this purpose, the draft and final form of the scale were applied to a total of 562 pre-service elementary mathematics teachers from various public universities in Turkey. The findings of study revealed that the scale is unidimensional according to the results of exploratory factor analysis. The unidimensionality of the scale was validated by confirmatory factor analysis. The reliability of mathematical modeling self-efficacy scale was very high (.97). Finally, it was found that this scale is an appropriate measurement tool to evaluate students’ self-efficacy beliefs on their mathematical modeling competencies. Some suggestions related to the scale and for further studies were given at the end.

Anahtar Kelimeler

Factor analysis, mathematical modeling, modeling competencies, pre-service teachers, self-efficacy

Kaynakça

• Anderson, J.C., & Gerbing, D.W. (1984). The effect of sampling error on convergence, improper solutions and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49(2), 155–173.
• Bacon, D.R., Sauer, P.L. & Young M. (1995). Composite reliability in structural equations modeling. Educational and Psychological Measurement, 55(3), 394-406.
• Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W.H. Freeman.
• Blum, W. (1993). Mathematical modeling in mathematics education and instruction. Germany: Ellis Horwood Limited.
• Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges (pp. 73-96). New York, NY: Springer.
• Blum, W., & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen anwendungsfähigkeiten von englischen und deutschen Lernenden [Comparative empirical studies at mathematical application skills of English and German learners]. Unpublished manuscript, German Research Foundation, Bonn, Germany.
• Brown, R. (2002). Mathematical modeling in the international baccalaureate, teacher beliefs and technology usage. Teaching Mathematics and Its Applications, 21(2), 67-74.
• Büyüköztürk, Ş. (2013). Sosyal bilimler için veri analizi el kitabi [The data analysis manual for social sciences]. Ankara: Pegem Akademi.
• Campbell, D.T., & Fiske D.W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological Bulletin, 56(2), 81-105.
• Cole, D.A. (1987). Utility of confirmatory factor analysis in test validation research. Journal of Consulting and Clinical Psychology, 55, 1019–1031.