Aspects of Students' Reasoning About Variation in Empirical Sampling Distributions.
- Resource Type
- Article
- Authors
- Noll, Jennifer; Shaughnessy, J. Michael
- Source
- Journal for Research in Mathematics Education. Nov2012, Vol. 43 Issue 5, p509-556. 48p.
- Subject
- *REASONING
*STUDENT response systems
*EMPIRICAL research
*CLASSROOMS
*PARTICIPANT-researcher relationships
*CLASSES (Groups of students)
*SURVEYS
*ACQUISITION of data
- Language
- ISSN
- 0021-8251
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. [ABSTRACT FROM AUTHOR]