# Conference Paper

• ### How students learn

This paper focuses on the theme of statistical education and includes the following topics: 1. Theories of learning: how we think students learn 2. What we would like students to learn: in terms of statistical ideas, concepts, skills and beliefs 3. Research on teaching and learning statistics 4. Research on teaching and learning mathematics that relates to teaching and learning statistics 5. Implications of research for teaching statistics 6. One example: an alternative statistics course 7. What we still need to find out: a research agenda 8. Current projects

• ### Graphical lesson patterns and the process of knowledge development in the mathematics classroom

A method for analyzing mathematics teaching is presented which permits to take into account the different levels of mathematical meaning within teacher-students interactions. Conceptual structures of the development of mathematical knowledge are visualized by means of graphical diagrams.

• ### Computer-oriented techniques and resources used in teaching and testing an objective-based elementary statistics course

Brief description of a course using computers and data examples.

• ### The Use of Multiple Items to Identify Misconceptions in Probabilistic Reasoning

A three stage model was used in developing and evaluating an instructional unit on probability. The focus of this paper is on the first and third stages of the model, both of which depend on the design of ways to identify misconceptions. In previous studies, researchers have used changes in performance on individual items to evaluate the effectiveness of instructional interventions. The instrument used in the present study borrows heavily from earlier research. The instrument differs from previous instruments not in the content of the items but in the way responses to items are analyzed. Pairs of items are designed so that meaningful error patterns can be identified when responses to both items are considered. The identification of error patterns can be identified when responses to both items are considered. The identification of error patterns allows assessment that goes beyond the reporting of gain scores. Once error patterns are identified, an intervention can be evaluated according to the types of misconceptions (i.e., error patterns) that are affected.

• ### Teachers' misunderstandings in statistical reasoning: Evidence from a field test of innovative materials

This article discusses reasons why it is not sufficient to provide teachers with one day workshops or brief refresher courses and expect them to acquire the knowledge they need. It then describes new courses that must be designed to let teachers acquire expertise in statistical problem solving.

• ### Linked visualizations and interactivity: Developing a qualitative understanding of statistics

Computer scientists have been designing and experimenting with interactive, graphical interfaces for several years now. Recently, educational technologists have begun to take advantage of these advances. With funding from the Applications of Advanced Technologies program in the Division of Science and Engineering Education at the National Science Foundation of group of researchers at BBN are designing and developing interactive, graphical mini-laboratories to help students develop a qualitative understanding of statistics. These Macintosh-based mini-labs allow students to explore statistical concepts and processes by manipulating graphical objects.

• ### Use of the Representativeness Heuristic in a Situation of Simulation

The research of psychologists, in particular from Kahneman and Tversky, has shown that in many situations of everyday life, people estimate the probability of random events using certain heuristics, specially representativeness. Much of the subsequent research in this area supports their thesis. Nevertheless, most of this work has used verbal problems as the means of studying people's conceptions and thinking, whether in a questionnaire or in an interview. In this work we present the results of a study of the pupils' use of representativeness in a situation of simulation of one of the classical problems related to the subject. The experience consisted of an individual interview with the students while simulating this situation and graphically representing the results, in order to answer some predetermined questions posed by the researcher. The analysis of student's pattern of responses before and after the realization of the simulation shows a wide variety of conceptions and the influence of the result of this simulation on the initial arguments of the pupils. As a result of this we conclude the didactical possibilities of simulation both as a means of exploring pupil's probabilistic intuitions and as an educational tool to overcome some of the misconceptions concerning these intuitions.

• ### Opening up the black box of recipe statistics: Putting the data back into data analysis

Statistics becomes interesting to non-methodologists only when taught in a research context that is relevant to them. Real data sets supplemented by sufficient background information provide just such a context. Despite this, many textbook authors and instructors of applied statistics rely on artificial data sets to illustrate statistical techniques. In this paper, we argue that artificial data sets should be eliminated from the curriculum and that they should be replaced with real data sets. Towards this end, we describe the rationale for using real data sets and describe the characteristics that we have found make data sets particularly good for instructional use. Having learned that real data sets can present problems for instructors, we discuss the difficulties that we have encountered when using real data and some of our strategies for compensating for these drawbacks. We conclude by presenting two authentic data sets and an annotated bibliography of dozens of primary and secondary data sources.

• ### Students' Understanding of the Significance Level in Statistical Test

In this paper the initial results of a theoretical- experimental study of university students' errors on the level of significance of statistical test are presented. The "a pripri" analysis of the concept serves as the base to elaborate a questionnaire that has permitted the detection of faults in the understanding of the same in university students, and to categorize these errors, as a first step in determining the acts of understanding relative to this concept.

• ### A minitab approach to teaching college statistics

This paper discusses the features of MINITAB and the advantages of using it for teaching college statistics.