# Conference Paper

• ### Assessing statistics learning

The traditional assessment of students' learning in statistics courses has followed the model used for mathematics and many other subject areas; that is time constrained written examinations. In New Zealand a large proportion of statistics assessment is still of this form. In order to determine whether this is the most appropriate form of assessing statistics learning consideration needs to be given to the following: - fundamental differences between the content of statistics and other courses, - the skills required of statistics learners, - the purpose(s) of assessment, and - whether particular forms of assessment advantage or disadvantage some groups of learners. While this paper raises issues related to the first three points above, the major focus is on the last. Performance in the national examinations sat by secondary school students in New Zealand is analysed for gender and ethnic differences in two different forms of assessment: project based internal assessment and traditional written examination.

• ### Introducing box and whisker plots

Box and whisker plots were introduced to a group of eight students for enrichment and foolow-up sessions as part of a project looking at the ideas that 11 and 12-year-olds have about central tendency and dispersion. This paper reports some tentative findings about the teaching and learning of box and whisker plots to middle-school children.

• ### Children's intuitive understanding of variance

This paper discusses the important pedagogical question of by how much experimental probabilities need to deviate from subjective or symmetric probabilities before children consider revising their subjective probabilities. Many children believe that common random generators like coins and dice are subject to mystical or physical powers, or to be inherently opposed to a child's wishes. Even 9% of Year 11 students have been found to believe that a six is the least likely outcome from tossing a die. Providing experiences which encourage children to revise their opinions is difficult. One reason for this difficulty arises from the mathematics of the situation. There are 2500 tosses of a coin necessary to obtain a relative frequency of between 0.48 and 0.52 with 95% confidence. This makes it very difficult to attempt a classroom confirmation of any theory.

• ### An Empirical Study Comparing Five Statistics Texts in Education and Psychology

This study attempted to provide evidence about two questions (1) Can criteria be developed for evaluating introductory statistics texts which are based on the statistical education and text evaluation literature? (2) Using the criteria from (1), how do several introductory statistics texts used in schools and colleges of education compare to one another?

• ### Establishing objective criteria for evaluating statistics texts

In the course of research conducted with Michael Harwell of the University of Pittsburgh, we have developed a series of five instruments intended to explore several aspects of statistics textbook selection. It should be noted that many of the categories of questions in these instruments were inspired by the previously named articles, and our debt to their groundwork is extensive. However, choosing a statistics text for social science students is not as straightforward a task as choosing a text for students in their major field of study, and therefore warrants a specialized series of instruments. The instruments we have developed range from a general survey for instructors and students who are currently using a statistics textbook in a course, to particular instruments are designed so that data obtained from their administration could be useful to broad-range researchers, to departments trying to choose a textbook, or to writers and publishers of new statistics texts. The five instruments are reproduced in whole in the appendix. These are: 1) a student survey for currently-used textbooks, 2) an instructor survey for currently-used textbooks, 3) an instructor survey of what an ideal statistics textbook would be like, 4) an expert evaluation instrument that may be used on any statistics textbook, and 5) an instrument covering relevant objective information about any statistics textbook.

• ### Judgments of Association in Scatterplots: An Empirical Study of Students' Strategies and Preconceptions

In this paper an experimental study of students' strategies in solving a judgment of association in scatter plots is presented. The classification of these strategies from a mathematical point of view allows us to determine concepts and theorems in action and to identify students' conceptions concerning statistical association in scatter plots. Finally, correspondence analysis is used to show the effect of task variables of the items on students' strategies.

• ### On Teaching the Big Ideas of Statistics: a Project-Based Approach

Students of Statistics, whether they plan to be statisticians, or only to use statistics as a tool in their professions, often fail to grasp the big ideas of statistics from their courses. "Service" courses concentrate on methods, while "mainstream" courses emphasize mathematical structure, and in both types of course, the powerful concepts most useful in practice are not given much emphasis. The textbooks that guide our teaching style do not seem to include a broad appreciation of statistical ideas among their objectives. Statistics courses that do provide some pedagogic emphasis to the big ideas, may still fail to convey these ideas if the examination does not require their comprehension. In this paper, I give some examples of "big ideas" and exam questions that would assess students' comprehension of them, and argue that even though they are the most important aspects of a course, that they will not be absorbed from courses following currently available textbooks. I suggest the use of a project-based teaching technique with which I have had some experience and success, and how to use traditional textbooks as support for such a project-based course.

• ### Understanding of Probability Concepts Among South African Children

During the period 1991 to 1993 a new junior high school curriculum was introduced in many South African schools. This curriculum is fairly strongly constructivist in design. A study of probability was included for the first time in any ordinary South African curriculum, this being at the Standard 7 (Grade 9) level. The approach is initially experimental but continues into the more formal presentation in terms of sample spaces. This situation presented the researchers with an opportunity of looking at the unschooled understanding of probability concepts amongst South African children before the curriculum was actually implemented. Data were also collected once some of the children had been taught about probability according to the new curriculum. It was anticipated that analysis of results would enable the researchers to identify prevalent misconceptions; to ascertain the effects of the reaching of probability according to the new curriculum; to compare the intuitive understanding of various groups (male and female, urban and rural); to offer suggestions for teaching on the basis of the findings and to compare the intuitive understanding of South African children with that of children from other countries such as Britain, Canada and Brazil. In this paper we look at the pre- and post-testing done in a selection of schools in the Johannesburg region and, for the Johannesburg and Umtata samples, present an innovative analysis of data from a selection of items from the instrument used.

• ### Building on and Challenging Students' Intuitions about Probability: Can we Improve Undergraduate Learning?

Students in our first year probability and statistics course typically experience problems in learning formal probability. They also often fail to grasp the logic behind confirmatory methods. The premise of this paper is as follows: to enable students to understand and be comfortable with inferential (or even exploratory) statistics, they must be allowed to (1) experience the omnipresence of variation and (2) experience probability as a means to describe and quantify that variation. A pilot study to investigate the understanding of variability and probability of a small group of students enrolled in the 1994 course is described. These students have a strong tendency to think deterministically (especially in real world settings); they have little understanding of variability and its relationship to sample size; and they are generally unable to reconcile their intuitions with the formal probability they are taught. There were some initial indications that allowing students to experience variation personally made aware of their over-emphasis on causal explanations of variability. Lastly, it appears that students' awareness about probabilistic thinking can be raised by actively challenging and discussing their tacit intuitive models about chance.

• ### Functions and Statistics with Computers at the College Level

An experimental college level course, Functions and Statistics with Computers, was designed using the textbook Functions Statistics and Trigonometry with Computers developed by the University of Chicago School Mathematics Project. A case study of this course and its influence on a more traditional course is described. Students in the experimental course were compared with students in the traditional course based on attitude toward mathematics and achievement in mathematics. Experimental course students showed a significant gain in confidence about learning and performing well in mathematics. Final grade distributions for the experimental and traditional courses were similar, although experimental course students entered the course with somewhat weaker mathematical backgrounds. On a course evaluation document, students in the experimental course reported that computer laboratory activities helped them understand course material. Based on an analysis of the attitude, achievement and course evaluation data, the traditional course was modified to deemphasize algebraic manipulation, emphasize modeling and applications and to include computer laboratory activities.