In recent years many statisticians have become involved in the reform movement in statistical education aimed at improving the teaching and learning of introductory statistics. While instructors are incorporating technology into courses, it is primarily used to support outdated methods even though freely accessible technology for teaching modern statistical approaches is available. Many educators in the reform movement are embracing the power of technological advances to promote statistical thinking through the teaching of statistical computing, especially at the undergraduate level. In conjunction with the NSF-funded Change Agents for Teaching And Learning STatistics (CATALST) curriculum project, the Statistics Teaching Using Resampling and Randomization (STURR) project makes some of these statistical computing approaches accessible to non-statistics majors enrolled in general, non-calculus based introductory statistics courses.
Existing software packages (such as SPSS, Minitab, R, and Fathom) can be programmed to carry out modern methodologies, but the knowledge and skills required to do so are often daunting for most of the undergraduate students who enroll in an introductory statistics course. The primary goal of the STURR project is to develop freely accessible and easy to use tools that provide a Graphic User Interface (GUI) to the R statistical computing environment. The incorporation of these "R Tools" into the CATALST curriculum supports and builds students' conceptual understanding of modern statistical methods, such as resampling and randomization, but without requiring them to learn computer programming or develop other computational skills needed to use R. In this project the research team fully develops and tests the R Tools. They also make modifications and improvements to the tools, and integrate them into the CATALST curriculum, resulting in a more effective CATALST course. Videotaped think aloud interviews with individual students and small groups working together on activities that use the R Tools, along with videotaped class sessions, and results from assessments provides feedback for modifying the R Tools.
The STURR project was designed to develop data analysis tools in R that provided the flexibility needed in the NSF-funded CATALST curriculum project (DUE-0814433). The CATALST curriculum is a college-level introductory statistics course based solely on randomization and resampling methods to develop students’ statistical thinking and understanding of statistical inference. The CATALST course consists of three broad units: Chance Models and Simulation, Models for Comparing Groups, and Exploring Alternative Models. Essentially. The goals of the STURR project were to develop streamlined and efficient analysis tools for the Models for Comparing Groups and the Exploring Alternative Models units of the CATALST course using the R computing environment. The first tool, called the RANDOMIZATION TEST tool, allows students to import any data file that contains data from an experiment with random assignment to treatments and conduct a randomization test to see if there is strong evidence for declaring a difference between two treatment groups. Figure 1 below shows an example where data from a sleep deprivation study has been imported into the RANDOMIZATION TEST tool. The tool displays the observed data plus graphic representations and summary statistics for the dependent variable for both groups. Students can specify the sample summary statistic, the number of randomized trials, and the animation speed. A scroll bar allows students to view each randomized sample in order to see the variability across the samples. A dotplot of the summary statistic highlights summary values that are more extreme than the observed group difference and reports the estimated p-value. The RANDOMIZATION TEST tool also allows students to conduct randomization tests for qualitative response variables (see Figure 2). The second tool, called the BOOTSTRAP tool, allows students to import data and compute a bootstrap interval estimate for the difference in a specified measure between two groups. Figure 3 shows data on airline arrival delay times for two different airlines flying from Chicago to the same five cities that has been imported into the tool. The interface is almost identical to that of the RANDOMIZATION TEST tool to facilitate the transition to the new tool. Notable differences are that plot of summary measures indicates the lower and upper limits of the bootstrap interval estimate instead of reporting the p-value, and that students specify the width of the interval, which can be changed and updated automatically for the same set of bootstrap samples (see Figure 4). As part of the STURR project, problem solving interviews were conducted with three students at the end of Unit 1 during fall 2010, five students at the end of Unit 1 and Unit 2 in spring 2011, and with nine student at the end of each unit in fall 2011. Preliminary results from the spring 2011 problem-solving interviews were presented at the United States Conference on Teaching Statistics (USCOTS) in May, 2011 and at the Statistical Reasoning, Thinking and Literacy (SRTL) research forum in July, 2011, and formed the basis of a research article to be published in ZDM: The International Journal on Mathematics Education (Garfield, delMas & Zieffler, in press). The interviews conducted in fall 2011 will be analyzed during the 2012-13 academic year with an expected publication on the research in fall 2013. The PI presented an invited poster on the STURR project at the 2012 Joint Mathematics Meetings in January, 2012 that was well attended (see delMas, 2012). Two applets were co-developed for the CATALST course by the PI and graduate research assistant as part of the STURR project. The Guessing Game applet (see Figure 5) lets students replicate the conditions for a published psychology experiment where participants try to predict which of two colors will be shown on the next trial. Humans try to match the relative frequencies (75% green, 25% red), whereas research animals tend to always predict the color with the highest relative frequency, outperforming humans. The applet allows students to gather data, and then use the data to simulate the "animal" and "human" strategies. The second applet, WithOrWithout (see Figure 6), was designed to help students understand the difference between sampling with and without replacement. Students are lead through an activity where they make predictions for the different sampling conditions, and then test their predictions with the applet. The PI is currently working an applet that will provide a no-cost alternative to implementers of the CATALST course that is designed specifically for the curriculum to allow students to build and test models. REFERENCES delMas, R. (January 2012). The Statistics Taught Using Resampling and Randomization (STURR) Project. Invited poster presented at the NSF Division of Undergraduate Education session of the Joint Mathematics Meetings (JMM), Boston, MA. Garfield, J., delMas, R., & Zieffler, A. (in press). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM: The International Journal on Mathematics Education.
