Research

  • Students in the first statistics course generally have trouble reasoning about statistics and the concept of probability. The reform movement tin teaching statistics suggests a variety of good practices. In an attempt to increase student learning, we have researched the use of active learning, cooperative groups, and authentic assessment. In this study we have added web-based instructional materials and on-line small group discussion activities. This classroom-based research looks at an aspect of learning we have not studied previously, reasoning about probability. Due to the large size of this section of sophomore level statistics (N=126), student interaction in thinking g through activities was captured electronically through the use of WebCT on-line group discussion. The on-line discussion format had both strengths and weaknesses, which will be discusses. The WebCT content of the group discussions on-line was captured and analyzed to determine how students reasoned through the activity. The purpose of this study was to explore students' reasoning in completing group-based activities on probability.

  • This paper presents a summary of action research I am doing investigating statistics students' understandings of the sampling distribution of the mean. With 4 sections of an introductory Statistics in Education course (n=98 students), I have implemented and evaluated a computer simulation activity (delMas, Garfield, & Chance, 1999) to show students the sampling distribution "in action," as recommended by many authors and statistics professors. Assessments after the activity point to clear deficiencies in student understanding, such as not understanding how sample size affects the shape and variability of sampling distributions. With the addition of the computer simulation, students' understandings are still incomplete. This is most evident as I move forward in class and introduce inferential statistics. My results discuss some of the deficiencies I have identified in student understandings. Also included is a discussion of how the action research cycle will continue to work on these deficiencies.

  • The research literature on affect and statistics consists of many studies that examined the relationships between mathematics and statistical anxiety and achievement, and between statistical attitudes and achievement. However, what has not been looked at is the relationship between mathematics and statistical anxiety and statistical attitudes. This is an important relationship to examine because it may help explain the relationship in these two bodies of research. Therefore, the current study was designed to investigate the relationship between students' pre-course mathematical and statistical anxiety and their post-course statistical attitudes. In addition, gender differences and graduate/undergraduate status differences will be examined to see how they figure into this relationship.

  • This paper begins by summarizing the research on attitudes toward and anxiety about statistics, distinguishing between studies in the two areas. Next, a research project that explores the relationship between attitudes toward statistics and a particular instructional method is described. A discussion of the results is followed by implications and suggestions for future research.<br>There are three main questions that this study addresses.<br>1. Are there differences in attitudes toward statistics for students in classes that use multimedia software, other software, or no technology?<br>2. Are there differences in how students in these settings view the role of technology in doing statistics?<br>3. Are there gender differences in attitudes toward statistics and views of technology in doing statistics?

  • One hundred-eight students in Grades 3, 5, 6, 7, and 9 were asked about their beliefs concerning fairness of dice before being presented with a few dice (at least one of which was "loaded") and asked to determine whether each die was fair. Four levels of beliefs about fairness and four levels of strategies for determining fairness were identified. Although there were structural similarities in the levels of response, the association between beliefs and strategies was not strong. Three or four years later, we interviewed 44 of these students again using the same protocol. Changes and consistencies in levels of response were noted for beliefs and strategies. The association of beliefs and strategies was similar after three or four years. We discuss future research and educational implications in terms of assumptions that are often made about students' understanding of fairness of dice, both prior to and after experimentation.

  • Comments on statistical articles in the popular press by first-year economics students studying statistics in Australia and South=East Asia are analyzed. Three common weakness are described - lack of appreciation of journalistic style, disregarding statistical variation, and incorrect percentage statements. Differences between the groups are described and implications for teaching such courses are discussed.

  • In this experiment, we investigate the correspondence between how graph-readers visually inspect a graph to answer a comparison question about two groups and the justifications they offer. We recorded how people visually inspected graphs using a device that restricted how much data they could see at any given time. Students offered a variety of justifications for why two groups differed (e.g., slices, cut-points, modal clumps), and these appear to correspond to how they visually parsed the data.

  • Statistical communication has become a larger part of statistics pedagogy during the previous decade, particularly for those students who are majoring in the discipline. Students in servicing courses may have less opportunity to develop statistical communication skills, as they usually take only a small number of statistics subjects: it is this group that forms the basis of our present study. Based on analysis of the discourse in interview transcripts, we highlight an interesting disjunction: many students seem to be able to communicate their understanding of statistics to the interviewer, but their statements about their statistical communication imply that they are unaware that they are communicating statistically during this process. We briefly explore the pedagogical implications of our findings.

  • In this study we evaluated the thinking of 3rd-grade students in relation to an instructional program in probability. The instructional program was informed by a research-based framework and included a description of students' probabilistic thinking. Both an early- and a delayed-instruction group participated in the program. Qualitative evidence from 4 target students revealed that overcoming a misconception in sample space, applying both part-part and part-whole reasoning, and using invented language to describe probabilities where key patterns in producing growth in probabilistic thinking. Moreover, 51% of the students exhibited the latter 2 learning patterns by the end of instruction, and both groups displayed significant growth in probabilistic thinking following the intervention.

  • Advancing technology is inexorably shifting the demand for statisticians from being operators of mechanical procedures to being thinkers. Coupled with this is a perceived lack of development of statistical thinking in students. This chapter discusses the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions. It draws on the literature and in-depth interviews, with statistics students and practising statisticians, which aimed at uncovering their statistical reasoning processes. From these interviews from all four exploratory studies, a four dimensional statistical thinking framework for empirical enquiry has been identified. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. There are a number of associated elements such as techniques for thinking and constraints on thinking. The characterisation of these processes through models, that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving, is begun in this chapter. Tools of this form would complement the mathematical models used in analysis. The tools would also address areas of the process of statistical investigation that the mathematical models do not, particularly in areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is<br>"variation." The role of variation in the statistical conception of real-world problems, including the search for causes, is further discussed.

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