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Investigations for Introducing Mathematically Inclined Students to Statistics

Leaders

Allan Rossman and Beth Chance, Cal Poly - San Luis Obispo

Abstract

We present sample investigations from our project to develop curricular materials for a post-calculus introduction to statistical concepts, applications, and methods. Some of the guiding principles behind these investigations are

• to motivate students' interest through real studies and genuine data,

• to emphasize connections among study design, inference technique, and scope of conclusion,

• to conduct simulations as motivation for mathematical derivations,

• to use a variety of computational tools, and

• to experience the entire statistical process over and over in new settings.

Specific topics to be addressed through these examples include randomization tests, random sampling, confidence intervals, and inference for odds ratios.In addition to leading participants through experiences with sample investigations, we will offer suggestions for implementing such activities. We also plan to lead a discussion about appropriate goals of an introductory statistics course for mathematically inclined students.

Bio-Sketches

Beth Chance and Allan Rossman are Associate Professors of Statistics at California Polytechnic State University in San Luis Obispo. They are co-authors of the Workshop Statistics series of coursebooks, served as co-editors of STATS: The Magazine for Students of Statistics, and have given dozens of presentations and workshops on statistics education both nationally and internationally. They are currently serving as co-editors of the proceedings for the Seventh International Conference on Teaching Statistics (ICOTS-7).

Beth received her Ph.D. in Operations Research, with an emphasis in Statistics and a minor in Education, from Cornell University. She taught at University of the Pacific before moving to Cal Poly. She serves on the Test Development Committee for Advanced Placement Statistics and as the Secretary/Treasurer of the ASA Section on Statistical Education. She was the inaugural recipient of the ASA's Waller Education Award, and she received the 2003 Mu Sigma Rho Statistical Education Award.

Allan Rossman received his Ph.D. in Statistics from Carnegie Mellon University. He taught for twelve years at Dickinson College, where he also served as department chair, before moving to Cal Poly. He is President-Elect of the International Association for Statistics Education and has served as Chair of the ASA Section on Statistical Education and of the ASA/MAA Joint Committee on Undergraduate Statistics. He is a Fellow of the ASA.

Results

Handout (PDF)

Presentation (PowerPoint)

Notes

Top three goals:

• Being able to design studies, use data based concepts to solve real problems (as in Stat 101)

• Showing them the connections to math (its really based on some mathematics) - calculus exists outside of the calc textbook

• Expose students to more sophisticated examples of applications of statistics, methods of statistics

• Get them to be the "refs" to analyze the statistics they see in the media and introduce them to the concepts they will see in their college classes

• Spark their interest in statistics so they want to take another course (get them into the way of thinking as well as some proof of the statements)

• Challenge the more mathematically inclined students in a way that the algebra course is not able to/also have these students familiar with the topics in Stat 101 (so they can answer questions coming from the Stat 101 students!)

• Use simulations more to motivate "things"

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