An exploration of affective and demographic factors that are related to mathematical thinking and reasoning of university students

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2011
Başaran, Seren
There are four major aims of this study: Firstly, factors regarding university students’ approaches to studying, self-efficacy in mathematics, problem solving strategies, demographic profile, mathematical thinking and reasoning competencies were identified through the adopted survey and the competency test which was designed by the researcher. These scales were administered to 431 undergraduate students of mathematics, elementary and secondary mathematics education in Ankara and in Northern Cyprus and to prospective teachers of classroom teacher and early childhood education of teacher training academy in Northern Cyprus. Secondly, three structural models were proposed to explore the interrelationships among idenitified factors. Thirdly, among three models, the model yielding best fit to data was selected to evaluate the equality of the factor structure across Ankara and Northern Cyprus regions. Lastly, differences regarding pre-identified factors with respect to gender, region and grade level separately and dual, triple interaction effects were investigated through two two-way MANOVA and a three-way ANOVA analyses. Exploratory and confirmatory factor analyses were employed to determine the factors; meaning orientation, mathematics self-efficacy, motivation, disorganized study methods and surface approach for the survey and ‘expressing, extracting and computing mathematically’(fundamental skills) and ‘logical inferencing and evaluating conditional statements in real life situations’(elaborate skills) for the test. The three models commonly revealed that while mathematics self-efficacy has a significant positive effect on both fundamental and elaborate skills, motivation which is a combination of intrinsic, extrinsic and achievement motivational items was found to have a negative direct impact on fundamental skills and has a negative indirect contribution upon elaborate skills. The results generally support the invariance of the tested factor structure across two regions with some evidence of differences. Ankara region sample yielded similar factor structure to that of the entire sample’s results whereas; no significant relationships were observed for Northern Cyprus region sample. Results of gender, grade level and region related differences in the factors of the survey and the test and on the total test indicated that, females are more meaning oriented than males. ‘Fourth and fifth (senior)’ and third year university students use disorganized study methods more often than second year undergraduate students. In addition, senior students are more competent than second and third year undergraduate students in terms of both skills. Freshmen students outscored sophomore students in the elaborate skills. Students from Ankara region are more competent in terms of both skills than students from Northern Cyprus region. This last inference is also valid on the total test score for both regions. Males performed better on the total test than females. Moreover, there exist region and grade level interaction effect upon both skills. Additionally, significant interaction effects of ‘region and gender’, ‘region and grade level’, ‘gender and grade level’ and ‘region and gender and grade level’ were detected upon the total test score.