Application of statistics to the study of cognitive processes in mathematics education : a case study of theoretical thinking as a factor of students' success in linear algebra

Factors influencing students' success in mathematics in general and linear algebra in particular are examined, drawing on the literature of mathematics and science education. Based on the findings from a sample of 14 high achieving university undergraduate students, certain features of theoretical thinking are identified as necessary factors of the students' success in two linear algebra courses. The nature of the resulting data presented a peculiar problem. An extensive study of the possibility of applying different forms of statistical analysis to these data is conducted from different perspectives on statistical methodology namely, descriptive/exploratory statistics and statistical modeling. A number of indices for measuring theoretical behavior tendencies are defined and a new method of analysis is develope