Literature Index

"Simulations in Mathematics-Probability and Computing", (SIM-PAC), is a three year project funded by the United States' National Science Foundation's Materials Research and Development program. This paper describes the background and rationale for the project, its goals and objectives and the instructional strategy utilized by SIM-PAC. An example of a typical learning activity and the capabilities of the software are illustrated.

Recently Watkins, Bargagliotti, and Franklin (2014) discovered that simulations of the sampling distribution of the mean can mislead students into concluding that the mean of the sampling distribution of the mean depends on sample size. This potential error arises from the fact that the mean of a simulated sampling distribution will tend to be closer to the population mean with large sample sizes than it will with small sample sizes. Although this pattern does not change as a function of the number of samples, the size of the difference between simulated sampling distribution means does and can be made invisible to observers by using a very large number of samples. It is now practical for simulations to use these very large numbers of samples since the speed of computers and even mobile devices is sufficient to simulate a sampling distribution based on 1,000,000 samples in just a few seconds. Research on the effectiveness of sampling distribution simulations is briefly reviewed and it is concluded that they are effective as long as they are used in a pedagogically sound manner.

This study investigated two statistics classroom environments that a priori apeared to hold promise as being motivationally effective classrooms. One environment (2 classes) was at the high school level and the other environment (4 classes) was at the graduate level. In particular the study measured students' perceived situational interest in the learning environment, individual interest in statistics (with pre and post measures), and mathematics anxiety (with pre and post measures). The results indicate that both environments were high in situational interest, did substantially increase the mean individual interest of students, and had a beneficial but smaller impact in terms of associated decreases in mathematics anxiety. In addition, there did apear to be some gender effects-although these effects across the two learning environments were not consistent. Finally, the environments did appear to be particularly effective for students with previous low individual interests in statistics/mathematics. The study enriches our understanding of the "interest" construct primarily by providing evidence that the situational interest of learning enviornments may have a much greater impact on individual interests than researchers previously thought. While only two specific learning environments are provided as examples, the paper argues that we may need to pay as much attention to the motivational effects of statistics classrooms as we do to the learning effects. Students who have positive affective experiences will be more willing to continue taking mathematics/statistics courses or to use quantitative analysis techniques in their own research.

StatCrunch (www.statcrunch.com) is an online data analysis package that can be used as a low cost alternative to traditional statistical software for introductory statistics courses. StatCrunch offers a wide array of numerical and graphical routines for analyzing data along with several features such as interactive graphics which can be used for pedagogical purposes. StatCrunch has a number of new features related to social data analysis where users may share data sets and associated analysis results via the StatCrunch site. Users may also interact via online discussions related to shared items. This manuscript provides a brief description of the mechanics of uploading and sharing information via the StatCrunch site and then discusses some of the potential benefits that these social data analysis capabilities offer to both students and instructors.