Proceedings

• Teaching and assessing statistical reasoning

Statistical reasoning may be defined as the way people reason with statistical ideas and make sense of statistical information. This involves making interpretations based on sets of data, representations of data, or statistical summaries of data. Much of statistical reasoning combines ideas about data and chance, which leads to making inferences and interpreting statistical results. Underlying this reasoning is a conceptual understanding of important ideas, such as distribution, center, spread, association, uncertainty, randomness, and sampling. This chapter begins by distinguishing reasoning from mathematical reasoning, and then outlines goals for students studying statistics. Challenges in assessing statistical reasoning are described and information is provided on a unique paper and pencil instrument, the Statistical Reasoning Assessment. The final section suggests ways teachers may help students develop sound statistical reasoning skills.

• Cooperative learning experiences in introductory statistics

There have been few studies which presented specific cooperative learning techniques for statistics classes (Garfield, 1993; Dietz, 1993; Jones, 1991), but there is a paucity of these. Moreover, not all of the listed studies attempted to quantitatively evaluate effects (academic or otherwise) of the cooperative strategies by using a comparison group. Therefore, the present study piloted some additional cooperative strategies in order to share their content and their strengths and weaknesses among the community of statistics educators. Moreover, the study examined effects of cooperative learning on achievement and attitude by comparing those who received cooperative education with a control group. Finally, the study provided an alternative course opportunity for students. Not everyone has the same learning style and cooperative learning can be a valuable tool for supporting learning by diverse students.

• What's a rubric?: Scoring the open ended questions

This paper provides the scoring rubric used to score the open-ended questions on the advanced placement statistics examination.

• Modeling aspects of students' attitudes and achievement in introductory statistics courses

This report presents a path model of students' attitudes and achievement in statistics; it also presents correlations among attitudinal measures and correlations between attitudinal measures and test performance for both graduate students and undergraduate students.

• Building a theory of graphicacy: How do students read graphs?

This study examined middle grades students' learning of concepts related to the use and interpretation of graphs. We view graphs as part of the process of statistical investigation. A statistical investigation typically involves four components: pose the question, collect the data, analyze the data, and interpret the results, in some order (Graham, 1987). The use of grpahis is linked to the "analyze the data" component of the statistical investigation process. Considering what it means to understand and use graphical representation is a part of what it means to know and be able to do statistics.

• Interpretation of data in a bar graph by students in grades 6 and 8

This study was designed to determine how middle grades students interpret data presented in a bar graph. Of particular interest was the nature of the explanations that students gave to support their answers to various questions. The data reported here are part of a larger study of students' understandings of graphs.

• Students' understanding of the significance level in statistical tests

In this paper the initial results of a theoretical-experimental study of university students' errors on the level of significance of statistical tests are presented. The "a priori" 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.

• Situational interest in the statistics classroom

This study investigated two statistics classroom environments that a priori apeared to hold promise as being motivationally effective classrooms. One environment (2 classes) was at the high school level and the other environment (4 classes) was at the graduate level. In particular the study measured students' perceived situational interest in the learning environment, individual interest in statistics (with pre and post measures), and mathematics anxiety (with pre and post measures). The results indicate that both environments were high in situational interest, did substantially increase the mean individual interest of students, and had a beneficial but smaller impact in terms of associated decreases in mathematics anxiety. In addition, there did apear to be some gender effects-although these effects across the two learning environments were not consistent. Finally, the environments did appear to be particularly effective for students with previous low individual interests in statistics/mathematics. The study enriches our understanding of the "interest" construct primarily by providing evidence that the situational interest of learning enviornments may have a much greater impact on individual interests than researchers previously thought. While only two specific learning environments are provided as examples, the paper argues that we may need to pay as much attention to the motivational effects of statistics classrooms as we do to the learning effects. Students who have positive affective experiences will be more willing to continue taking mathematics/statistics courses or to use quantitative analysis techniques in their own research.

• Graph knowledge: Understanding how students interpret data using graphs

Concepts such as measures of center or graphicacy can be linked to the "analyze the data" component of the statistical investigation process. While a central goal is to understand how students make use of the process of statistical investigation within the broader context of problem solving, it also is necessary that we look at students' understanding related to concepts linked to this process. This has led us to consider what it means to understand and use graphical representations as a key part of what it means to know and be able to do statistics. Specifically, we have engaged in a process of developmental research that permits examination of middle grades learning of concepts related to the use and interpretation of representations. We have looked at how such understanding changes over time and with instructional intervention provided by knowledgeable teachers in order to develop a framework both for looking at students' knowledge of graphing (in the statistical sense) and for developing a research agenda related to this area.

• Teaching introductory statistical methods for understanding: Techniques, assessment, and affect

This paper presentation contains a variety of useful materials for introductory statistics instructors. Kenney discusses the tool box metaphor that she often uses in her class, and she also shares activites and thoughts about issues such as metacognition and portfolio assessment. She includes a survey that she gives to her students in order to gather feedback about study strategies and teaching techniques that seemed to be most helpful to the students. Finally, she includes an anecdotal report from one of the students in her class.