|Deborah Nolan (USA)||firstname.lastname@example.org|
We have developed a course that teaches undergraduate mathematical statistics through in-depth case studies. That is, we motivate topics in mathematical statistics via real-life examples, which lead to an integration of statistical theory and practice in a way not common in an undergraduate course. Each case study centers around a scientific question, and it contains a dataset to address this question. To answer the question, we develop statistical theory. There are three salient aspects in our case studies approach to teaching mathematical statistics: 1. The problem central to the case is introduced first, and background information on the problem and a data description are provided before any theoretical statistics are discussed. 2. The solution to the problem in the case is not provided to the students. In fact, there are many possible solutions at many different levels of analyses. 3. The student must play the role of a consultant, analyst, government official, textbook author, etc. in developing and presenting the solution to the problem.
We have found that there are many advantages to incorporating case studies in this way in the advanced mathematical statistics course. For example, solving a case gives the student experience with how statistics can be used to answer scientific questions, and it helps him or her develop statistical thinking. The student also becomes practiced in communicating his or her ideas, and he or she becomes versed in the use of statistical software. However, the instructor faces many challenges when incorporating case studies in the mathematical statistics course, challenges which are different from the familiar ones faced in teaching the course in a more traditional style. The challenges include determining the following: effective formats for class meetings that balance the development of the application and theoretical material; out-of-class interactions with students to manage group work; assistance for students to develop effective writing and data presentation skills; ways to assist students in their data analysis without turning assignments into cookbook analyses; tools for teaching statistical software quickly; fair, informative, and time efficient evaluation of student reports and analyses. In this paper we plan to explore these and other challenges, and provide examples of approaches for meeting them.
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