Journal Article

  • Our primary goal is to design a microworld which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This study reports on a design research study of how students appear to exploit their appreciation of causal control to construct new situated meanings for the distribution of throws and success rates. We provided on-screen control mechanisms for average and spread that could be deterministic or subject to stochastic error. The students used these controls to recognize the limitations of causality in the short term but its power in making sense of the emergence of distributional patterns. We suggest that the concept of distribution lies in co-ordinating emergent data-centric and modeling perspectives for distribution and that causality may play a central role in supporting that co-ordination process.

  • This exploratory study, a one group pretest-posttest design, investigated the development of elementary preservice teachers' understandings of distribution as expressed in the measures and representations used to compare data distributions. During a semester-long mathematics methods course, participants worked in small groups on two statistical inquiry projects requiring the collection, representation, analysis and reporting of data with the ultimate goal of comparing distributions of data. Many participants shifted from reporting descriptive exclusively to the combined use of graphical representations and descriptive statistics which supported a focus on distributional shape and coordinated variability and center. Others gained skills and understandings related to statistical measures and representations yet failed to utilize these when comparing distributions. Gaps and misconceptions in statistical understanding are discussed. Recommendations for supporting the development of conceptual understanding relating to distribution are outlined.

  • Activities that promote student invention can appear inefficient, because students do not generate canonical solutions, and therefore the students may perform badly on standard assessments. Two studies on teaching descriptive statistics to 9th-grade students examined whether invention activities may prepare students to learn. Study 1 found that invention acitivities, when coupled with subsequent learning resources like lectures, led to strong gains in procedural skills, insight into formulas, and abilities to evaluate data form an argument. Additional, an embedded assessment experiment crossed the facets of instructional method by type of transfer test, with 1 test including resources for learning and 1 not. A "tell-and-practice" instructional condition led to the same transfer results as an invention condition when there was no learning resource, but the invention condition did better than the tell-and-practice condition when there was a learning resource. This demonstrates the value of invention activities for future learning from resources, and the value of assessments that include opportunities to learn during a tests. In Study 2, classroom teachers implemented the instruction and replicated the results. The studies demonstrate that intuitively compelling student-centered activities can be both pedagogically tractable and effective at preparing students to learn.,

  • We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we embarked on data exploration of our students' responses on these assessments. We observed various trends regarding their understanding of the concepts including results that were consistent with research completed previously (by other authors) for algebra-based introductory level statistics students. We also used the information obtained from our data exploration and our experiences in the classroom to examine and conjecture about possible reasons for our results.

  • This study uses the Attitudes Toward Statistics (ATS) scale (Wise 1985) to investigate the attitudes toward statistics and the relationship of those attitudes with short- and long-term statistics exam results for university students taking statistics courses in a five year Educational Sciences curriculum. Compared to the findings from previous studies, the results indicate that the sample of undergraduate students have relatively negative attitudes toward the use of statistics in their field of study but relatively positive attitudes toward the course of statistics in which they are enrolled. Similar to other studies, we find a relationship between the attitudes toward the course and the results on the first year statistics exam. Additionally, we investigate the relationship between the attitudes and the long-term exam results. A positive relationship is found between students' attitudes toward the use of statistics in their field of study and the dissertation grade. This relationship does not differ systematically from the one between the first year statistics exam results and the dissertation grade in the fifth year. Thus, the affective and cognitive measures at the beginning of the curriculum are equally predictive for long-term exam results. Finally, this study reveals that the relationship between attitudes toward statistics and exam results is content-specific: We do not find a relationship between attitudes and general exam results, only between attitudes and results on statistics exams.

  • The calculation of the upper and lower quartile values of a data set in an elementary statistics course is done in at least a dozen different ways, depending on the text or computer/calculator package being used (such as SAS, JMP, MINITAB, Excel, and the TI-83 Plus). In this paper, we examine the various methods and offer a suggestion for a new method which is both statistically sound and easy to apply.

  • Part of the history of oil and gas development on Indian reservations concerns potential underpayment of royalties due to under-valuation of production by oil companies. This paper discusses a model used by the Shoshone and Arapaho tribes in a lawsuit against the Federal government, claiming the Government failed to collect adequate royalties. Portions of the case have been settled out of court with compensation paid to the Tribes. Other portions remain pending. This material can be used as a real example in a calculus-based probability and statistics course.

  • This paper describes the components of a successful, online, introductory statistics course and shares students' comments and evaluations of each component. Past studies have shown that quality interaction with the professor is lacking in many online courses. While students want a course that is well organized and easy to follow, they also want to interact with the professor and other students. Interactions in this course took place through small group discussions, emails, weekly announcements and graded exams. The course also contained lecture slides with audio prepared by the professor. As the variety and quantity of interaction increased, student satisfaction with the amount of interaction with the professor increased from 75% the first year of the course to 99% the fifth year. Overall satisfaction with the online course increased from 93% the first year to 100% the fifth year.

  • Stock car racing has seen tremendous growth in popularity in recent years. We introduce two datasets containing results from all Winston Cup races between 1975 and 2003, inclusive. Students can use any number of statistical methods and applications of basic probability on the data to answer a wide range of practical questions. Instructors and students can define many types of events and obtain their corresponding empirical probabilities, as well as gain a hands-on computer-based understanding of conditional probabilities and probability distributions. They can model the rapid growth of the sport based on total payouts by year in real and adjusted dollars, applying linear and exponential growth models that are being taught at earlier stages in introductory statistics courses. Methods of making head-to-head comparisons among pairs of drivers are demonstrated based on their start and finish order, applying a simple to apply categorical method based on matched pairs that students can easily understand, but may not be exposed to in traditional introductory methods courses. Spearman's and Kendall's rank correlation measures are applied to each race to describe the association between starting and finishing positions among drivers, which students can clearly understand are ordinal, as opposed to interval scale outcomes. A wide variety of other potential analyses may also be conducted and are briefly described. The dataset nascard.dat is at the driver/race level and contains variables including: driver name, start and finish positions, car make, laps completed, and prize winnings. The dataset nascarr.dat is at the race level and contains variables including: number of drivers, total prize money, monthly consumer price index, track length, laps completed, numbers of caution flags and lead changes, completion time, and spatial coordinates of the track. These datasets offer students and instructors many opportunities to explore diverse statistical applications.

  • Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs®. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical and prior estimates, and yields posterior predictive simulations used to compare competing extreme strategies.

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