Teaching

  • 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.

  • 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.

  • This paper reports a comparison of two separate studies using the same task and simulation software but with different age groups and abilities of students who have had different curricula experiences. One study examined how middle school students used computer simulation tools to reason between empirical data and theoretical probability. The second study replicated the first with secondary school students who had just completed an Advanced Placement statistics course. This comparison includes the similarities and the differences in the way each group approached the task and used the simulation software, given their background and prior knowledge.

  • The last decade has seen a rapid increase in the use of Geographical Information Systems (GIS) and the analysis of spatial data is an important component of this development. Spatial statistics is a relatively young subject and, although there are useful textbooks on spatial statistics theory, there is virtually no literature on how to teach spatial statistical concepts and techniques. This paper suggests ways of teaching some of spatial statistical analysis without recourse to matrix algebra and vectors. By using the graphical features in Excel it is possible to illustrate and explain the concepts behind the statistical techniques in GIS. The interactive and dynamic features of Excel enable students to investigate the effects of changing the spatial location of the data and to develop an understanding of spatial dependence and its impact on Kriging and regression techniques.

  • Many statistics educators use simulation to help students better understand inference. Simulations make the link between statistics and probability explicit through simulating the conditions of the null hypothesis, and then looking at sampling distributions of an appropriate measure. In this paper we review how we use simulation to help understand hypothesis testing, and lay out the relevant steps. We illustrate how using simulation and technology can make these difficult ideas more visible and understandable, through making processes more concrete, through unifying apparently disparate tests, and through letting the learners construct their own measures to study phenomena.

  • We consider the role of technology in learning concepts of modeling univariate functional dependencies. It is argued that simple scatter plot smoothers for univariate regression problems are intuitive concepts that- beyond their intended usefulness in providing a possible answer to more intricate regression problem - may serve as a paradigm for statistical thinking, detecting structure in noisy data. Simulation may play a decisive role in understanding the underlying concepts and acquiring insight into the relationship between structural and random variation.

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