# Conference Paper

• ### An examination of the factors structure of Wise's Attitude Toward Statistics Scale

The purpose of the present study was to extent the evaluation of Wise's Attitudes Toward Statistics (ATS) Scale by examining scale responses in relation to (a) its factor structure and (b) the correlation of ATS subscale scores with students' grades in statistics courses at several levels of graduate study, students' sex (which was found to be a useful predictor by Woehlke &amp; Leitner, 1980), and scores on measures of basic mathematics and comprehension of statistical terminology.

• ### What's typical? Children's Ideas about Average

In the research reported in this paper, we address two major sets of questions about children's understanding of average. 1) When they are working with data sets, how do children construct and interpret indicators of center? It's important to examine how children learn to describe data sets in a meaningful, useful, and flexible manner. In particular, we are concerned with the development and use of the idea of "representativeness" in the context of real data sets. The second major question we are addressing deals with the use of the mean in a precise mathematical sense: 2) How do children develop their thinking about the mean as a mathematical relationship? This question moves into the important more general question of how children develop mathematical abstractions, and how they map (or fail to map) these abstractions onto their informal understanding of a concept.

• ### The Use of the Chance-Concept in Everyday Teaching - Aspects of a Socially Constituted Epistemology of Mathematical Knowledge

The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deducted from former more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on introducing the chance concept illustrates this conflict. The interaction between teacher and his students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the chance concept is conceived of as a concrete generalization, which takes "chance" as a fixed and universalized pattern of explanation instead of unfolding potential and variable conceptual relations of "chance" or "randomness" and developing the theoretical mature of this concept in an appropriate way for students' comprehension.

• ### Exploring the Stability of Students' Conceptions of Probability

This paper reports selected results from a larger study designed to investigate the stability of students' conceptions of probability. The "Reasoning About Chance Events" survey was administered to students both before and after the "Coin Toss" unit in order to identify consistent patterns of response as well as to capture changes in responses that might be caused by the instructional unit. Subjects in this study were first and second year college students from three sections of an introductory statistics courses.

• ### Assessment Issues on the Teaching of Statistics

In New Zealand, end-of-course examination based assessment is rooted in our past and while it may have served the past well, it is clear that it does not adequately serve our present needs. In 1991 the Education Subcommittee of the New Zealand Statistical Association suggested that these examinations may not be valid (unbiased) or reliable (have low variability) measures of ability. Further there is a growing concern that our examinations do not function equitably across all groups of students, and that they do not adequately measure either those skills needed by the general population for their everyday needs, or the skills needed to contribute to the country's economic growth. The debate on assessment procedures has, in part, arisen because of the differential performance of girls and boys in traditional mathematics examinations. In New Zealand a number of analyses of secondary school mathematics examination performance have been done (Stewart, 1987; Reilly et al, 1987; Forbes, 1988; Morton et al, 1988 and 1989; Forbes et al, 1990). These results all show a greater range of achievement within each gender than between the genders but typically the top grades are dominated my males. There are a number of forms of assessment in current use in statistics. Some types of assessment may unfairly advantage one group of students over another. A limited amount of research has been done comparing assessment methods to determine those which may best suit women, Maori (indigenous New Zealanders), or ethnic minorities. Women themselves cannot be classified as just one group. Forbes (1992) showed that a reduction in gender differences in performance in mathematics of one group of the New Zealand population (European) does not necessarily lead to a similar reduction in another group (Maori).

• ### Students' understanding of computer-based simulations of random behavior

This paper is motivated by a concern about the increasingly important role being given to computer-based simulations of random behavior in the teaching and learning of probability and statistics. Many curriculum developments in this area make the implicit assumption that students accept the computer algorithm for generating random outcomes as an appropriate representation of random behavior. This paper will outline some reasons for questioning this assumption, and will indicate a need to investigate how students' mental models of random behavior differ from their understanding of the computer representation of randomness.

• ### The success of graphic models to visualize conditional probabilities

Why is training of conditional probabilities necessary? - Conditional probabilities play an important role within the statistics curriculum and in decision making under uncertainty (Bayesian inference). - People often have problems to use conditional probabilities in the right way (many examples in the literature of cognitive psychology). So it is important that - although there exist a lot of didactical suggestions - there has been no empirical research dealing especially with the improvement of the understanding of conditional probabilities. So we made a first try to close this gap.

• ### Solving problems is not enough: Assessing and diagnosing the ways in which students organize statistical concepts

In many statistics courses homework exercises and examinations focus primarily on solving problems. Marks are assigned to students' responses according to the degree to which a problem solution is correct and/or to which a student's procedure employed in the solution is correct. When a statistics course has an applications or data analysis orientation, instructors often find that even though students can solve textbook and examination problems, they are frequently unable to apply probability and statistics to solve "real world" research problems in which judgments have to be made about the technique(s) to be used and in which substantive interpretations of the results of statistical analyses need to be made. The paper reviews several formats of examination questions and assessment procedures which have been used over the years in noncalculus courses in applied statistical methods which focus on data analyses, parameter estimation, and hypothesis testing. Among the types of assessment techniques reviewed are short-answer questions, essay questions, yes-no questions with student-provided justifications, concept-oriented multiple-choice items, masterlist items, analogical reasoning items, graphic inference items, free association tasks, and concept mapping tasks. The paper also reports on a computer-assisted test of knowledge structure called MicroCAM. This test allows students to create on a computer screen a spatial representation of the way in which they perceive key statistical concepts to be linked one to another. The test also permits students to specify the type of relationship which links two or more concepts together. In this way a student's unique knowledge structure is revealed. Implications of these different assessment methods for diagnosing students' learning difficulties and for teaching statistics to mathematically naive students are discussed.

• ### Investigating the relationship between conceptual and procedural errors in the domain of probability problem-solving

The purpose of the study was to investigate the relationships among types of errors observed during probability problem solving.

• ### Evaluating Statistics Texts Used in Education and Psychology

The lack of literature-based guidance for conducting evaluations of statistics texts has likely contributed to some disturbing patterns in published evaluations and studies of statistical texts. Similar patterns probably exist in unpublished evaluations, such as the evaluation (and possible adoption) of a test by an instructor. A critical failing in this area is that published evaluations almost invariably employ criteria for conducting the review that lack any literature-based rationale, being, apparently, experientially based, a failing which is compounded by a lack of empirical evidence supporting the usefulness of the criteria employed in the evaluation. The purpose of these (symposium) papers is to continue and extend the research exemplified by Cobb (1987), Hubety and Barton (1990), Brogan (1980), and others by attempting to construct and pilot criteria for evaluating statistics texts that are grounded in the statistical education and text evaluation literatures. This study is an initial step in a line of research which may result in the establishment, maintenance, and updating of a database containing evaluations of introductory statistical texts similar to (but much smaller in scale) that maintained for educational and psychological tests (e.g., Mental Measurements Yearbooks). Evaluative information of this kind should benefit the direct consumers of these texts, students and instructors.