Teaching

• Presentation of quantitative literacy materials in a math education course

I believe that school teachers will benefit from being exposed to QL materials as a part of their undergraduate education. It seems likely that statistical concepts will be included at a local level if a teacher has been exposed to usable materials. The course we have developed is far from perfect. It is too early to tell what the impact will be in the schools where these mathematics teachers will work in the future. I believe that the concept of presenting these QL materials as a part of the undergraduate education is sound. I would encourage others to try to employ such a strategy and to share with others their successes and failures so that we can all improve our curriculum.

This paper concentrates on the "Why?" parts of some of the simpler questions and discusses the usefulness of asking students to give a brief reason as to why they had chosen the answer they gave. Responses given by the UK students are used to illustrate points.

• What should a bridging course bridge?

This paper describes a course aimed at mature age students who are lacking in basic mathematical skills and who are anxious about mathematics but who are required to do a service course in statistics. The course aims to improve basic skills and attitudes to mathematics and, in addition, to move students from a rule-based approach to mathematics and statistics to a more flexible one. Flexibility in mathematical thinking is required if students at a later stage are to be able to consider and assess the relative merits of different ways of analysing batches of data. Basic skills and attitudes both before and after the course have been measured using an author-prepared test for the former and an attitude to mathematics [Fennema] test for the latter. Mathematical thinking has been measured by using material based on the SOLO (Structure of the Learned Outcome) taxonomy. There has been some evidence of a change in basic skills and attitudes to mathematics over the duration of the course, but to date there has not been an accompanying change in the level of mathematical thinking.

• Integrating analyses of data bases into statistical instruction

Students in graduate-level applied statistical courses should be trained to manipulate realistic data bases which are sufficiently large and complex that they provide verisimilitude with respect to thesis studies and other real-world applications. At the University of Maryland, we have been integrating data base manipulation into our intermediate-level statistics instruction for several years. This presentation concentrates on several issues related to the use of data bases in statistical instruction: appropriate course level; desirable characteristics of data bases; the role of mainframe and microcomputer statistical software; integration of data base manipulation skills into instruction on statistical topics; and grading practices.

• Do men have more sisters than women?

The question of what to expect of data collected can be posed to beginners in an introductory probability course.

• Some distributions and expectations - simplified

The purpose of the present paper is, first, to show how the binomial and the hypergeometric distributions could be lent a comparable form. The suggested presentation exhibits the similarity in the structure of the two distributions in accordance with the similarity in the verbal definitions of the random variables. Likewise, the minor dissimilarity in the two formulas reflects the difference in the respective verbal definitions. Next, the law of addition of expectations will be applied in order to compute the expectations of the above two distributions. The two expectations will be shown to be equal and the computation rendered simple. Finally, the power of the addition technique will be illustrated by computing the expectation for the number of runs in a binary random sequence. In an extended application, the expectation of the number of alternations in a random binary two-dimensional table will be computed, bypassing the complex problem of the distribution of that random variable.

• Instruments to Assess Statistical Concepts on the School Curriculum

This paper will document four instruments devised to assess student understanding of statistical concepts. Two are intended for large scale administration and two are for individual interviews.

• Practical statistics in other school subjects

Statistics is a useful and necessary tool required by large numbers of pupils for their project work in other subject areas. But what are these pupils learning in their Mathematics lessons to back up all this practical statistical work? What can the Mathematics teacher provide to develop the necessary skills? Often little consideration is given to the QUALITY of the data collected and the most appropriate method of selecting a sample for a particular purpose. Should the Mathematics teacher consider sampling methods and help pupils to understand the need for a representative sample? Can the microcomputer be utilised for a more practical approach geared to the child's understanding?

• Teaching statistical regression: Simplifying a principle that is hard to understand

Statistical regression to the mean is not an easy concept to grasp, especially by students whose background in statistics and probability is limited. As a source of internal invalidity, however, it is an important concept to understand. It is perplexing to students to simply indicate that extreme scores regress to the mean; it is beyond most students to use a more complex mathematical approach. The procedure described in this paper is sufficiently detailed to show students how regression occurs without presenting complicated math. The procedure is based on earlier suggestions by Cutter and Levin.

• Preparing the statistics coordinator

This paper discusses various recommendations for courses and materials to be evaluated by programme staff.