Journal Article

  • This paper reports one recent study that was part of a project investigating tertiary students' understanding of variation. These students completed a questionnaire prior to, and at the end of, an introductory statistics course and this paper focuses on interviews of selected students designed to determine whether more information could have been gathered about the students' reasoning. Clarification during interviews reinforced researcher interpretation of responses. Prompting assisted students to develop better quality responses but probing was mostly useful for assisting students to re-express reasoning already presented. Cognitive conflict situations proved challenging. The diversity of activities identified by students as assisting the development of their understanding provides a challenge for educators in planning teaching sequences. Both educators and researchers need to listen to students to better understand the development of reasoning.

  • In this paper we first describe the process of building a questionnaire directed to globally assess formal understanding of conditional probability and the psychological biases related to this concept. We then present results from applying the questionnaire to a sample of 414 students, after they had been taught the topic. Finally, we use Factor Analysis to show that formal knowledge of conditional probability in these students was unrelated to the different biases in conditional probability reasoning. These biases also appeared unrelated in our sample. We conclude with some recommendations about how to improve the teaching of conditional probability.

  • Year 11 (15-year-old) students are not exposed to formal statistical inferential methods.<br>When drawing conclusions from data, their reasoning must be based mainly on looking at graph<br>representations. Therefore, a challenge for research is to understand the nature and type of informal<br>inferential reasoning used by students. In this paper two studies are reported. The first study reports on the<br>development of a model for a teacher's reasoning when drawing informal inferences from the comparison<br>of box plots. Using this model, the second study investigates the type of reasoning her students displayed<br>in response to an assessment task. The resultant analysis produced a conjectured hierarchical model for<br>students' reasoning. The implications of the findings for instruction are discussed.

  • We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith, Henningsen, &amp; Silver, 2000). Standards-era textbook series devoted significantly more attention to probability than other series; more than half of all tasks analyzed were located in Standards-era textbooks. More than 85% of tasks for six series required low levels of cognitive demand, whereas the majority of tasks in the alternative series from the Standards era required high levels of cognitive demand. Recommendations for future research are offered.

  • This paper describes the development of the CAOS test, designed to measure students' conceptual understanding of important statistical ideas, across three years of revision and testing, content validation, and realiability analysis. Results are reported from a large scale class testing and item responses are compared from pretest to posttest in order to learn more about areas in which students demonstrated improved performance from beginning to end of the course, as well as areas that showed no improvement or decreased performance. Items that showed an increase in students' misconceptions about particular statistical concepts were also examined. The paper concludes with a discussion of implications for students' understanding of different statistical topics, followed by suggestions for further research.

  • Biostatistics is not universally available in colleges/universities and is thus an attractive course to offer via distance education. However, evaluation of the impact of distance education on course enrollment and student success is lacking. We evaluated an "Introduction to Biostatistics" course at Harvard University that offered the distance option (Spring 2005).We assessed the effect on course enrollment and compared the grades of traditional students with non-traditional students, as well as with historical traditional students (Fall 2004). We further compared course evaluations from the inaugural semester with the distance option to evaluations from the prior semester. No evidence of dissimilarities was noted with respect to overall course grade averages or course evaluations.

  • Recent research in statistical reasoning has focused on the developmental process in students when learning statistical reasoning skills. This study investigates statistical reasoning from the perspective of individual differences. As manifestation of heterogeneity, students' prior attitudes toward statistics, measured by the extended Survey of Attitudes Toward Statistics (SATS), are used (Schau, Stevens, Dauphinee &amp; DeVecchio, 1995). Students' statistical reasoning abilities are identified by the Statistical Reasoning Assessment (SRA) instrument (Garfield 1996, 1998a, 2003). The aim of the study is to investigate the relationship between attitudes and reasoning abilities by estimating a full structural equation model. Instructional implications of the model for the teaching of statistical reasoning are discussed.

  • As we begin the 21st century, the introductory statistics course appears healthy, with its emphasis on real examples, data production, and graphics for exploration and assumption-checking. Without doubt this emphasis marks a major improvement over introductory courses of the 1960s, an improvement made possible by the vaunted "computer revolution." Nevertheless, I argue that despite broad acceptance and rapid growth in enrollments, the consensus curriculum is still an unwitting prisoner of history. What we teach is largely the technical machinery of numerical approximations based on the normal distribution and its many subsidiary cogs. This machinery was once necessary, because the conceptually simpler alternative based on permutations was computationally beyond our reach. Before computers statisticians had no choice. These days we have no excuse. Randomization-based inference makes a direct connection between data production and the logic of inference that deserves to be at the core of every introductory course. Technology allows us to do more with less: more ideas, less technique. We need to recognize that the computer revolution in statistics education is far from over.

  • This paper provides a broad overview of the role technological tools can play in helping students understand and reason about important statistical ideas. We summarize recent developments in the use of technology in teaching statistics in light of changes in course content, pedagogical methods, and instructional formats. Issues and practical challenges in selecting and implementing technological tools are presented discussed, and examples of exemplary tools are provided along with suggestions for their use.

  • The authors' work to develop capabilities for getting data into the data analysis software Fathom&trade; is described. Heuristics of detecting data on a web page allow drag and drop of a URL into a document. A collaboration with the Minnesota Population Center makes possible sampling from census microdata from 1850 through 2000. With direct support for Vernier sensors, students can build a model during the process of realtime data collection. Finally, a survey capability makes it easy for teachers and students to create simple data entry forms hosted on a web site such that the collated data is instantly downloadable for data analysis in Fathom. By taking some of the drudgery out of gathering data, these capabilities carry implications for teaching and curriculum development; namely that students should have experience throughout their learning with data that they individually have chosen to explore. It is argued that the skills they gain by engaging in exploratory data analysis with self-chosen and self-generated data are critically important in our data-driven society and not yet adequately supported in K-14 learning.<br><br>KEYWORDS:

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