Literature Index

This article presents two statistical tasks, one on comparing data sets, another on repeated sampling, both of which have powerful connections to proportional reasoning. Students' work and reasoning on these tasks are included, as well as suggestions for ways to use these tasks with middle school students to connect statistical thinking to proportional reasoning.

A study to investigate students' facility with proportions has been undertaken by the author and Fay Sharples of the University of Waikato in New Zealand over the period 1989 to 1992. The initial study was done during 1989 and 1990 and 64 students at the University of Waikato and 57 at Brunel University in the UK took part. Some results of this study have been reported elsewhere. We made some changes to our questionnaire after studying the results of the initial study. In the Spring of 1992, 127 students in New Zealand and 29 students in the UK, all of whom were taking statistics as a service course, completed the revised version of the questionnaire. As with the previous study, the results in this follow-up were interesting and not always what we expected. This paper discusses the results on three questions.

The purpose of the study was to identify the important aspects of statistical knowledge needed for teaching at the middle school level and to assess prospective teachers' conceptions and misconceptions of statistics related to teaching data analysis. An analytic study of the current literature, including state and national standards, was conducted to identify the important aspects of statistical knowledge for teaching. A written assessment instrument was developed and administered to a sample of 42 prospective middle school teachers. The purpose of the instrument was to gather data in order to describe teachers' conceptions for teaching data analysis and statistics. A subset of the sample (n = 7) was interviewed to provide deeper insight into their conceptions and to assure reliability of the instrument.<br><br>Results show that state and national standards differ greatly on their expectations of what students and teachers should know about data analysis and statistics. The variation is also large for the emphasis or importance given to the content. The average emphasis of all the documents reviewed is given to the selection and proper use of graphical representations of data, and measures of center and spread. Important aspects of knowledge applied to teaching are proper selection and use of teaching strategies and inferring students' understanding from their work and discourse.<br><br>Prospective teachers that participated in this study performed better at the level of pure statistical knowledge than at the level of application of this knowledge to teaching. In particular, they showed abilities on reading, interpreting, and constructing graphical representations, and computing measures of center and spread. Difficulties were shown in judging students' comments and identifying students' mistakes.

Although there is consensus among statistics educators that student data collection projects are of substantial value, we feel that the planning and piloting phases of data collection are often neglected. We ask our students to write protocols or detailed plans for how the data will be collected, and to plan and conduct pilot studies before embarking on full scale data collections. We present examples and results from situations including college freshman introductory statistics courses, graduate statistics courses, and teacher training workshops.