The idea of variation is a foundation of statistical reasoning, and many curriculum documents, including the "Australian Curriculum", include variation in the learning required for the primary years. In this paper, we consider the design of activities that can exemplify the idea of variation for young students and investigate how…

As an extension to an activity introducing Year 5 students to the practice of statistics, the software "TinkerPlots" made it possible to collect repeated random samples from a finite population to informally explore students' capacity to begin reasoning with a distribution of sample statistics. This article provides background for the…

This study considers the evolving influence of variation and expectation on the development of school students' appreciation of distribution as displayed in their construction of graphical representations of data sets. Three interview protocols are employed, presenting different contexts within which 109 students, ranging in age from 6 to 15…

This study documented efforts to facilitate ideas of beginning inference in novice grade 7 students. A design experiment allowed modified teaching opportunities in light of observation of components of a framework adapted from that developed by Pfannkuch for teaching informal inference with box plots. Box plots were replaced by hat plots, a…

A magazine article is shown to contain material that could lead to discussions of several topics in mathematics. The article and the related mathematics are discussed in detail. (MP)

This study uses the context of the weather to explore the development of students' intuitive ideas of variation from pre-Grade 1 to Grade 9. Three aspects of understanding these intuitions associated with variation are explored in individual videotaped interviews with 73 students: explanations, suggestions of data, and graphing. The development of…

The use of microcomputers to aid geometry instruction is emphasized through discussion of a program written in BASIC which provides for experimenting with polynomial curves. The program listing is included. (MP)

Investigates students' abilities to draw inferences. Introduces cognitive conflict in the form of video clips of reasoning expressed by students. Documents change with regard to the levels of observed response for the protocol and the use of displayed variation in the graphs. Analyzes change associated with the presentation of cognitive conflict.…

The issue of division by zero is discussed. Activities that cover the topics of measurement division, partition division, relationship to fractions, confusion with dividing into zero, dividing zero by zero, and relation to more formal numbers are presented. (KR)

Three hundred and twenty-four middle school students considered a group of three graphs in a newspaper article about boating deaths. The graphs contained discrepancies and the students were asked to "comment on unusual features." This form of questioning produced a distribution of responses surprising to the authors and perhaps…

Describes an activity which allows students with a range of abilities to become involved in data analysis and informal inference while working in self-selected small group environments. Enables students to explore their own resources for asking questions. (DDR)