# Proceedings

• ### Using technology to promote students' construction of knowledge

In this talk I will address how the participants in my dissertation research employed technology as a way for students to interact with statistics and focus on how this interaction with statistics through technology allows students to construct their own knowledge and understanding of statistics.

• ### Statistical or quantitative thinking as a fundamental intelligence

This article presents an expanded view of statistics both in the topics embodied and in the way people employ it. Statistics is proposed as one of the fundamental human intelligences and, using the verbal intelligence as a model, a quantitative parallel to speaking is introduced. This spoken form of the quantitative language is part of everyone's everyday activities and has been used throughout our lives. Informal statistical principles are described as providing a foundation for the formal statistics traditionally taught and promulgated. Recommendations for beginning a radical change in what we teach are offered.

• ### A comparative study of two instruments for evaluating primary probabilistic reasoning

Here we approach the complex nature of probabilistic reasoning, even at its most basic level, and its evaluation through written texts. We also present the conclusions of a theoretical and experimental study of two tests (Green, 1983 and Fischbein, 1984) designed to evaluate primary probabilistic intuitions, reaching the conclusion of the need for them to be mutually complementary in order to improve the validity of their content, both for including items from the different components of probabilistic reasoning and from the universe of task and contextual variables.

• ### Identification of misconceptions in the central limit theorem and related concepts and evaluation of computer media as a remedial tool

In this paper, we will break down the central limit theorem into several components, point out the misconceptions in each part, and evaluate the appropriateness of computer simulation in the context of instructional strategies. The position of this paper is that even with the aid of computer simulations, instructors should explicitly explain the correct and incorrect concepts of each component of the CLT.

• ### Learning by problem solving versus examples: The benefits of generating and receiving information

This experiment contrasts learning by solving problems with learning by studying examples, while attempting to control for the elaborations that accompany each solution step. Subjects were given different instruction materials for a set of probability problems. They were either provided with or asked to generate solutions, and they were either provided with or asked to create their own explanations for the solutions. Subjects were then tested on a set of related problems. Subjects in all four conditions exhibited good performance on the near transfer test problems. On the far transfer problems, however, subjects in two cells exhibited stronger performance: those solving and elaborating on their own and those recieving both solutions and elaborations from the experimenter. There also was an indication of a generation effect in the far transfer case, benefiting subjects who generated their own solutions. In addition, subjects' self-explanations on a particular concept were predictive of good performance on the corresponding subtask of the test problems.

• ### Using students' probabilistic thinking to inform instruction

This study addresses the development and evaluation of an instuctional program guided by research-based knowledge of students' probabilistic thinking. In particular, it seeks to (a) use a framework that describes and predicts students' thinking in probability to construct a third-grade instructional program, and (b) evaluate the effect of two different sequences of the instructional program on students' thinking in probability.

• ### Effects of computer assisted instruction on achievement and attitudes toward probability

Courseware (CW) development and its use in the classroom is an issue in Computer Assisted Instruction (CAI). Whatever the modes of CAI, few CW are adequate and effective in teaching particular topics of school mathematics, and they should be tested properly and improved continuously. In the present study, both the process of CW development for teaching some probability concepts to eighth grade students and its effective use in the classroom are described. The results of this study is given briefly.

• ### Bridging the gap between students and statistics: Cognition, affect, and the role of teaching method

Traditionally, the introductory statistics course has been one of the most hated and feared courses on campuses across the country. Simon and Bruce (1991) lament, "probability and statistics continues to be the bane of students, most of whom consider the statistics course a painful rite of passage--like fraternity paddling--on the way to an academic degree..." Over the past 30 years, there has been an increase in the professional literature on how to teach statistics with a continuous call for reform of the introductory statistics course. Virtually every American Statistical Association (ASA) president, in the past 10 years, has addressed the topic of statistics education as a key issue affecting the status and image of statistics as a profession. It is rather interesting that, while many have examined the practice of teaching statistics, very little is known about how students learn statistical concepts and reasoning skills. In addition to presenting a review of the literature on what is known about how students learn statistics and an overview of the suggested classroom reforms, this talk begins to examine the extreme gap that clearly exists between the introductory student and the subject matter of the introductory statistics course.

• ### The middle of what...?: Students' images of mean, median and mode

This talk is to discuss the mental images that certain students appear to articulate while they are engaged in posing and solving problems involving means, medians and modes.

• ### The effects of repeated cooperative testing in an introductory statistics course

This presentation reports the results of a study concerned with the issue of cooperative testing. Cooperative testing is defined as small group discussion of test items on the day of the exam and it's been proposed as a logical extension of cooperative learning. The results of the study showed that: (1) students' attitudes toward cooperative testing became more positive after each test administration, (2) self-reported study time varied among students, (3) students' perceptions of freeloading increased across test administrations, (4) the cooperative testing sections appeared to experience slightly less test anxiety than did the traditional testing section, and (5) testing condition did not appear to affect retention of course material.