In this meta-analysis I examined 26 studies on the relationship between anxiety toward mathematics and achievement in mathematics among elementary and secondary students. The common population correlation for the relationship is significant (–.27). A series of general linear models indicated that the relationship is consistent across gender groups, grade-level groups, ethnic groups, instruments measuring anxiety, and years of publication. The relationship, however, differs significantly among instruments measuring achievement as well as among types of publication. Researchers using standardized achievement tests tend to report a relationship of significantly smaller magnitude than researchers using mathematics teachers' grades and researcher-made achievement tests. Published studies tend to indicate a significantly smaller magnitude of the relationship than unpublished studies. There are no significant interaction effects among key variables such as gender, grade, and ethnicity.
Jennifer Noll and J. Michael Shaughnessy
Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.