Showing papers in "Statistics Education Research Journal in 2007"

Assessing Students' Conceptual Understanding after a First Course in Statistics.

Abstract: 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.

An Examination of the Levels of Cognitive Demand Required by Probability Tasks in Middle Grades Mathematics Textbooks.

Abstract: 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, & 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.

A Structural Equation Model Analyzing the Relationship of Students' Attitudes toward Statistics, Prior Reasoning Abilities and Course Performance.

Abstract: 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 & 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.

Students' Achievements in a Statistics Course in Relation to Motivational Aspects and Study Behaviour.

Abstract: The present study focuses on motivational constructs and their effect on students’ academic achievement within an existing statistics course. First-year Health Sciences students completed a questionnaire that measures several motivational constructs: dimensions of causal attributions, outcome expectancy, affect, and study behaviour, all with respect to statistics. The results showed that when the cause of negative events was perceived as uncontrollable, outcome expectancy was negative. When the cause of negative events was perceived as stable, affect toward statistics was negative. Furthermore, negative affect toward statistics and limited study behaviour led to unsatisfactory achievements. Path analysis (Lisrel) largely confirmed the causal relations in a model that was based on attributional and learned helplessness theories. The consequences of these findings for statistics education are discussed.

Use of External Visual Representations in Probability Problem Solving.

Abstract: We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use selfgenerated external visual representations while solving probability problems. The types of visual representations used include: reorganization of the given information, pictures, novel schematic representations, trees, outcome listings, contingency tables, and Venn diagrams. The frequency of use of each of these different external visual representations depended on the type of probability problem being solved. We interpret these findings as showing that problem solvers attempt to select representations appropriate to the problem structure, and that the appropriateness of the representation is determined by the problem’s underlying schema.

Evaluation of Distance Learning in an "Introduction to Biostatistics" Class: A Case Study

Abstract: 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.

Students' Expectations of Introductory Statistics Instructors.

Abstract: The purpose of this phenomenological study was to talk to students about their experiences taking introductory statistics. The author met with eleven students individually for four interviews throughout the semester, followed by a memberchecking focus group during the last week of classes. One of the most salient themes to emerge was the students’ reliance on their instructor for feedback about performance, directions on taking notes, and the creation of a classroom environment that motivated them to study. As part of the phenomenological tradition, the author presents his own reflections based on these students’ comments. Conclusions include the encouragement of instructors to be more mindful of students’ reactions to course content, and suggestions for developing a more learner-centered learning environment.