Conference Paper

  • Use of the internet to support instruction in general and the use of statistical software in particular provides instructors and students with an opportunity to improve learning while maintaining effective use of limited classroom time. We have developed a Web site (http://power.education.uconn.edu/) that encompasses instruction in power analysis issues and teaches students and others how to use the nQuery Advisor© software to establish sample size for research designs ranging from the simple to the complex. The evaluation results of our Power Project Web site and materials are promising, and the purpose of this paper is to share our approach and materials with other instructors of statistics and research design.

  • We constructed a web site to support service statistic courses at the University of Talca (http://dta.utalca.cl/estadistica/). The web site was developed around two fundamental ideas: object learning and concept maps. The statistical content was structured based on object learning organized around the scientific method. The object learning is imbedded in concept maps which highlight the structure and connections in statistics. Each concept map links complementary information in various formats. Students have positively evaluated the web page. This work was founded by the Education Ministry of Chile, MECESUP TAL0103 project: "Diversification of strategies for teaching and learning in basic sciences" (Diversificación de las estrategias de enseñanza-aprendizaje en las Ciencias Básicas).

  • Teaching online involves providing an environment that is interactive and engaging. A large part of this is providing suitable learning resources. In this talk we will demonstrate an efficient method for producing conceptual maps of the actual course content, showing the structure of the subject for students in a visual way. The structures that result allows for learning resources to be linked in as required. The maps are developed using PowerPoint but they can be deployed in a web-friendly format or on CD-ROM.

  • Modeling and simulation with the software Fathom has become an important part of an introductory course on probability and statistics for future mathematics teachers at our institution. We describe our conception of modeling and simulation competence that students are supposed to acquire. We use various means such as modeling guidelines, simulation plan and a guidebook with examples for simulations to support students' learning processes. We report on results of empirical studies that made us change and extend our initial educational approach.

  • This paper presents an analysis of the meanings of sampling distribution as supplied by some undergraduate students in a dynamic statistics environment (Fathom). The paper identifies stages in the simulation process where multiple and dynamic representations were crucial to students' understanding of the relationships among sample size, the behavior of sampling distributions and the probabilities of some sample results. One of the foremost difficulties observed in the simulation process was linked to the use of symbolic representations in the software, mainly at the formulation of the population model stage.

  • We compare two methods of recording data and making graphic displays: a standard paper-and-pencil technique and a "data-cards" approach in which students record case information on individual cards which they then arrange to make displays. Students using the data cards produced displays that tended to be more complex and informative than displays made by those in the paper-and-pencil group. We explore plausible explanations for this difference by examining structural aspects of the two approaches, such as the saliency of the case and the use of space in organizing the information. Our results call into question the wisdom of the current practice of introducing young students to particular graph types and of the idea that they need to master handling of univariate data before they move on to multivariate data.

  • Research on discovery learning and simulation training are reviewed with the focus on principles relevant to the teaching of statistics. Research indicates that even a well-designed simulation is unlikely to be an effective teaching tool unless students' interaction with it is carefully structured. Asking students to anticipate the results of a simulation before interacting with it appears to be an effective instructional technique. Examples of simulations using this technique from the project Online Statistics Education: An Interactive Multimedia Course of Study (http://psych.rice.edu/online_stat/) are presented.

  • Many concepts in simple linear regression can be explained or illustrated on scatterplots. Similar diagrams for regression with two explanatory variables require 3-dimensional scatterplots. Appropriate colouring and dynamic rotation on a computer are needed to effectively show their 3-dimensional nature. Concepts such as multicollinearity, sequential sums of squares and interaction have no analogue in simple linear regression, so it is particularly helpful to illustrate them graphically. This paper gives several examples of concepts in multiple regression that can be illustrated well with 3-dimensional diagrams.

  • Science loves replication: We conclude an effect is real if we believe replications would also show the effect. It is therefore crucial to understand replication. However, there is strong evidence of severe, widespread misconception about p values and confidence intervals, two of the main statistical tools that guide us in deciding whether an observed effect is real. I propose we teach about replication directly. I describe three approaches: Via confidence intervals (What is the chance the original confidence interval will capture the mean of a repeat of the experiment?); Via p values (Given an initial p value, what is the distribution of p values for replications of the experiment?): and via Peter Killeen's 'prep', which is the average probability that a replication will give a result in the same direction. In each case I will demonstrate an interactive graphical simulation designed to make the tricky ideas of replication vividly accessible.

  • Technology, and simulation in particular, can be a very powerful tool in helping students learn statistics, particularly the ideas of long-run patterns and randomness, in a concrete, interactive environment. This talk will provide examples of the integration of simulation to enhance topics throughout an introductory statistics course through a combination of Minitab macros and specifically designed applets. Topics will include randomization tests for comparing groups, and sampling distributions of proportions, odds ratios, and regression coefficients. We will also highlight how simulation can motivate students to learn the more mathematical derivations. Feedback and sample work from students will be presented, as well as issues in designing effective simulation investigations.

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