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In exploratory factor analysis, although the researchers decide which items belong to which factors by considering statistical results, the decisions taken sometimes can be subjective in case of having items with similar factor loadings and complex factor structures. The aim of this study was to examine the validity of classifying items into dimensions with exploratory graph analysis (EGA), which has been used in determining the number of dimensions in recent years and machine learning methods. A Monte Carlo simulation was performed with a total number of 96 simulation conditions including average factor loadings, sample size, number of items per dimension, number of dimensions, and distribution of data. Percent correct and Kappa concordance values were used in the evaluation of the methods. When the findings obtained for different conditions were evaluated together, it was seen that the machine learning methods gave results comparable to those of EGA. Machine learning methods showed high performance in terms of percent correct values, especially in small and medium-sized samples. In all conditions where the average factor loading was .70, BayesNet, Naive Bayes, RandomForest, and RseslibKnn methods showed accurate classification performances above 80% like EGA method. BayesNet, Simple Logistic and RBFNetwork methods also demonstrated acceptable or high performance under many conditions. In general, Kappa concordance values also supported these results. The results revealed that machine learning methods can be used for similar conditions to examine whether the distribution of items across factors is done accurately or not.

Mathematical modeling has come into prominenceduring the last few decades in many countries’ mathematics teaching curricula.It combines real life situations with mathematical context. Although evaluatingstudents’ mathematical modeling performances with a unique Likert typeinstrument is questionable, having an instrument about their self-efficacybeliefs in mathematical modeling may help to comment about their ideas relatedto their competencies in mathematical modeling. The purpose of this study is todevelop a reliable and valid measurement scale to determine mathematicalmodeling self-efficacy of mathematics teacher candidates. For this purpose, thedraft and final form of the scale were applied to a total of 562 pre-serviceelementary mathematics teachers from various public universities in Turkey. Thefindings of study revealed that the scale is unidimensional according to theresults of exploratory factor analysis. The unidimensionality of the scale wasvalidated by confirmatory factor analysis. The reliability of mathematicalmodeling self-efficacy scale was very high (.97). Finally, it was found thatthis scale is an appropriate measurement tool to evaluate students’self-efficacy beliefs on their mathematical modeling competencies. Somesuggestions related to the scale and for further studies were given at the end., 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.