Recounts a study documenting the actual learning trajectory of the classroom community and the diversity in eighth-graders' reasoning as they participated in the classroom mathematical practices that constituted this trajectory. Describes the learning of the research team by documenting conjectures about students' statistical learning and the means of supporting it. Proposes a revised learning trajectory to inform design and instruction in other classrooms.
Presents an experimental study on students' strategies and association judgments when faced with comparison of a numerical variable in two different samples. Classifies the strategies from a mathematical standpoint to identify theorems in action and two types of misconceptions about association.
Examines the collaborative efforts of a mathematics educator and statistician to help prospective elementary teachers develop statistical knowledge and experience through merging statistical investigation into existing elementary curricula. Offers insight into preservice teachers' statistical and pedagogical content knowledge based on their application of the process of statistical investigation themselves and with children.
This article explores misconceptions that students hold about sampling techniques on surveys and discusses implications for instruction.
There are two parts to this literature review. The first part includes bibliography directly focusing on variation,: meaning of variation, role of variation in statsitcal reasoing, researchon conceptions of variation, as well as literature discussing the neglect of variation. The second part lists references belonging to four bodies of literature which, although not having the study of intuitions abaout variation as their main object of study, do offer rich insights into people's thinking about variation: literarure on sampling and centers, on intutioons about the stochastic, on the role of technology, and on the effect of the formalist mathematics tradition on statistics education.
People make use of quantitative information on a daily basis. Professional education organizations for mathematics, science, social studies, and geography recommend that students, as early as middle school, have experience collecting, organizing, representing, and interpreting data. However, research on middle school students' statistical thinking is sparse. A cohesive picture of middle school students' statistical thinking is needed to better inform curriculum developers and classroom teachers. The purpose of this study was to develop and validate a framework for characterizing middle school students' thinking across 4 processes: describing data, organizing and reducing data, representing data, and analyzing and interpreting data. The validation process involved interviewing, individually, 12 students across Grades 6 through 8. Results of the study indicate that students progress through 4 levels of thinking within each statistical process. These levels of thinking were consistent with the cognitive levels postulated in a general developmental model by Biggs and Collis (1991).
Describes the PMOSE/IKIRSCH document readability formula for documents. Main document components in which the formula was based; Graphic documents; Entry documents; Density of documents; Usefulness in measuring document complexity.
Focuses on ability of students of fourth grade in structuring error and experimental variation as distribution. Interpretation of centers of distribution by students; Performance of students in various reasoning assignments.
Advancing computer technology is allowing us to downplay instruction in mechanical procedures and shift emphasis towards teaching the "art" of statistics. This paper is based upon interviews with six professional statisticians about statistical thinking and statistical practice. It presents themes emerging from their professional experience, emphasizing dimensions that were surprising to them and were not part of their statistical training. Emerging themes included components of statistical thinking, pointers to good statistical practices and the subtleties of interacting with the thinking of others, particularly coworkers and clients. The main purpose of the research is to uncover basic elements of applied statistical practice and statistical thinking for the use of teachers of statistics.
Investigates students' understanding of the idea of average. Relationship between data and the average of the data; Confusion of the term with mode and median.