Educational aspirations as a markovian process: A panel study of college and non‐college plans during high school†

An initial test of the discrete‐time Markov model in the study of educational aspirations throughout high school was carried out. The design of the study permitted testing for sex differences and order effects The results indicate a good fit between the data and the model across several cohorts of students. Order effects were apparent, but sex differences in the transition probabilities were not found. Future change in aspirations appears least likely for students with a history of stable college plans, while it is most likely for those who start with non‐college aspirations and change to college plans.     

The impact of instructor pedagogy on college calculus students’ attitude toward mathematics

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students’ attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students’ attitudes toward mathematics during a ‘mainstream’ calculus course while controlling for student backgrounds. The attitude measure combines students’ self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted ‘good teaching’ practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational ‘technology’ (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students’ attitudes towards mathematics. (3) ‘Ambitious teaching’ (e.g. group work, word problems, ‘flipped’ reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional ‘good teaching’ practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do not appear to have a reliable, positive impact on student attitudes toward mathematics.     

Are beliefs believable? An investigation of college students’ epistemological beliefs and behavior in mathematics

College students’ epistemological belief in their academic performance of mathematics has been documented and is receiving increased attention. However, to what extent and in what ways problem solvers’ beliefs about the nature of mathematical knowledge and thinking impact their performances and behavior is not clear and deserves further investigation. The present study investigated how Taiwanese college students espousing unlike epistemological beliefs in mathematics performed differently within different contexts, and in what contexts these college students’ epistemological beliefs were consistent with their performances and behavior. Results yielded from the survey of students’ performances on standardized tests, semi-open problems, and their behaviors on pattern-finding tasks, suggest mixed consequences. It appears that beliefs played a more reliable role within the well-structured context but lost its credibility in non-standardized tasks.     

Gender difference on spatial visualization by college students’ major types as STEM and non-STEM: a meta-analysis

Gender difference on spatial visualization has been considered an important factor that impacts the gender gap in academic performance in STEM-related disciplines. The purpose of this meta-analysis was to examine the gender difference on spatial visualization between STEM and non-STEM undergraduate majors. Twenty effect sizes representing STEM majors’ spatial ability and 14 effect sizes representing non-STEM majors’ spatial ability were included in the present meta-analysis. Results indicated that the overall effect size equalled 0.613 (95% CI?=?[0.444, 0.782]) in STEM and 0.481 (95% CI?=?[0.359, 0.604]) in non-STEM. These findings showed that the gender differences on spatial visualization were statistically significant in both STEM and non-STEM majors. The gender difference on spatial visualization in STEM was larger than the gender difference on spatial visualization in non-STEM. In addition, male students’ spatial visualization ability was higher than female students’ spatial visualization in both STEM and non-STEM majors.