Making statistics a full partner in mathematical sciences programs

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Mar 2002 by Wainwright, Barbara A, Tardiff, Robert M, Austin, Homer W

ADDRESS: Department of Mathematics and Computer Science, Salisbury University, Salisbury MD 21801 USA.

ABSTRACT: We have developed an introductory course that exposes mathematical sciences majors to a full range of issues that most practicing statisticians may face including data acquisition, design of experiments, use of theory, and formal writing.

This new course developed for mathematics majors not only requires the use of the computer in and out of the classroom for demonstrations and assignments, but also has a two hour computer laboratory once a week.

In this paper, we provide a summary of the labs, and share student perspectives on the course. This laboratory-based course can easily be transported to other locations.

KEYWORDS: Statistics, computer laboratory, math major, data-driven, simulation, inference.

1 INTRODUCTION

Most would agree that formal course work in statistics is essential for students majoring in mathematical sciences. Moreover, our department has come to the position that majors should have a four-pronged experience early in their careers; namely, pure mathematics, applied mathematics, computer science, and statistics. This four-pronged approach at the freshman/sophomore level makes statistics a full partner from the beginning.

To meet this need for an early statistics experience for mathematical sciences majors, we developed a laboratory-based freshman/sophomore level course. The course has three hours of lecture and a two-hour lab each week. Our course introduces students to statistics soon enough in their careers to pursue a concentration in statistics if they so desire.

Over the past few years, several articles have appeared in the literature addressing the needs of making the first course in statistics more engaging for students [1, 3, 5, 6, 7, 8] Some of these papers address introductory courses for non-majors; some address the traditional mathematical statistics course for majors. These papers support (to varying degrees) active involvement of students with data, use of real data, use of computing technology, and writing results. About ten years ago our department developed an introductory course in parametric and nonparametric statistics [10] designed primarily for nursing and geography majors. The course is data driven, integrates parametric and nonparametric procedures, and uses the computer to allow students to shift from calculation to interpretation. Our experience with this course over a ten year period gave us a firm basis for designing the introductory course for the majors. The primary differences between this new course and the existing one are the level of mathematical presentation and the addition of a two-hour formal laboratory experience each week.

This introductory course for majors is designed to expose students to the full range of issues that most practicing statisticians might face. Students develop a sense for how experiments are designed, how data is collected and analyzed, how computing and especially graphics enter into an analysis, and how mathematics and probability allow statisticians to assess the performance of procedures. Moreover, since most statisticians are part of a team and teams produce written reports, students learn to address star tistical problems as part of a team. They learn to write reports that are accessible to a professional who may or may not be a statistician.

Courses like the one we developed demand much from both instructors and students. A formal weekly computer laboratory experience necessitates an active learning environment which engages everyone. In this paper we will share our laboratory-based course and some of the insights we have gained from designing this course.

2 THE LABS

2.1 Our Goals

The goals for this course are a direct consequence of the department's philosophy of undergraduate education using the four-pronged approach discussed earlier. The department offers courses which actively involve the students in the learning process. We design courses using the constructivist approach to teaching. In all our courses we incorporate the spirit of the NCTM standards; i.e., an active, hands-on learning environment. Thus, courses have group work, projects, and writing assignments. There is an emphasis on interpretation and communication of results and a de-emphasis on mechanical calculations without explanations. Although all courses contain some lecture, most courses contain minimum lecture. This new statistics course reported here has been designed to include these characteristics.

We want students to know first hand that data is confusing and often messy, and that statistical reasoning offers a way to extract information and begin to assess how reliable the information might be. The content we explore, in both lecture and lab, is not particularly different from typical introductory statistics courses. Our purpose is to have students use this content when actively engaged with data. We want them to develop some sense of where data comes from - whether it be through experiments they perform, from the World Wide Web, or existing data sets in the MINITAB library.