Faculty Professional Development Long-Term Leave, Winter 2006

Ben Hill, Instructor, Mathematics Division

This is the written report on my sabbatical activities during Winter 2006.  In my application for paid sabbatical, I proposed research, writing, and travel activities with two general goals related to teaching statistics.  In addition to my original goals, the sabbatical provided time for me to pursue research of a more purely mathematical nature, reported below under a supplemental third goal. 

GOAL 1: TO RESEARCH THE TOPIC OF STUDENT-CENTERED TEACHING OF STATISTICS.

I read germane books and articles, researched on-line, and consulted with experts in the field of statistics and statistics education.  The materials I read included:             

• Beyond Crossroads: Implementing Mathematics Standards in the First Two Years of College, AMATYC, draft of October 2004.
• Teaching the Data Analysis Craft, Schafer & Ramsey, in Journal of Statistical Education, 2002
• Workshop Statistics: Discovery with Data, Rossman, 1995
• Conquering Statistics:  Numbers without the Crunch, Weaver, 2000
• Teaching Statistics, A Bag of Tricks, Gelman and Nolan, 2002
• Effective Strategies for Cooperative Learning, in Journal of Cooperation and Collaboration in College Teaching, 10(2), 69-75 (2001).
• Navigating the Bumpy Road to Student-Centered Instruction, Richard Felder and Rebecca Brent, College teaching 44, 43-47, 1996.
• Accounting for Individual Effort in Cooperative Learning Teams, Deborah Kaufman, Richard Felder and Hugh Fuller, Journal of Engineering Education, 2000
• Dynamics of Peer Education in Cooperative learning Workgroups, Cynthia Haller, Victoria Gallagher, Tracey Weldon, Richard Felder, Journal of Engineering Education, 2000
• Turning Student Groups into Effective Teams, Barbara Oakley, Richard Felder, Rebecca Brent, Imad Elhajj, New Forums Press, 2004
• Teaching Mathematical Problem Solving: Implementing the Vision, A Literature Review, McIntosh and Jarrett, 2000

The experts I consulted or observed teaching included:

• Thomas Dick, Professor of Mathematics and Director, Math Learning Center, Oregon State University
• Fred Ramsey, Professor of Statistics, Oregon State University
• Daniel Schafer, Professor of Statistics, Oregon State University
• Jennifer Brown, Senior Lecturer in Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

In aggregate, this research significantly extended and updated my knowledge of statistics pedagogy, particularly regarding the use of small group activities as an alternative to lecture.  It also added to my store of examples and data sets for use in teaching.  This contributed to my professional growth and will have an immediate and lasting positive impact on the quality of my teaching.  With regard to developing my abilities for broader contribution at Lane, the experience of speaking with and observing math instructors at New Zealand’s University of Canterbury increased my awareness, by comparison to this very different institution and academic setting, of some of Lane’s greatest strengths and challenges.         

GOAL 2: TO WRITE ON THE TOPIC OF STUDENT-CENTERED TEACHING OF STATISTICS.

This writing took the form of a series of 21 activities for use in promoting active, student-centered learning in an introductory statistics courses, such as Lane’s math 243.  These activities (available by request) will be tested and refined in my Spring 2006 section of math 243.  They will be shared with colleagues in a math colloquium scheduled for 5/24/06 and may also provide the basis for a future article or conference presentation.  Based on the research summarized under Goal 1, there is reason to believe these activities may be of value to the College by contributing to improved student success and retention in math 243. 

GOAL 3 (SUPPLEMENTAL): TO RESEARCH AND WRITE ON THE TOPIC OF PROBABILITY DISTRIBUTIONS FOR CONTRACT BRIDGE HANDS.

In bridge, the card game, players evaluate each 13-card hand by counting points for high cards (typically four points for each ace, three points for each king, two points for each queen, and one point for each jack) and for the distribution of suit lengths as indicated by short suits (typically three points for each 0-card suit, two points for each 1-card suit, and one point for each 2-card suit).  It is easy, using methods taught in Lane’s math 105 and math 243 courses, to show that there are exactly 635,013,559,600 possible bridge hands, but more difficult to find the number of hands with, say, exactly 13 combined high card and suit distribution points.  Calculations of this type are necessary to answer a variety of questions bridge players might pose about the probability of being dealt certain types of hands.

Previous investigators have written computer programs to calculate the number of hands with each possible high card point total, and the number of hands with each possible distribution of suit lengths.  Using excel software, I solved the more general problem of calculating the number of hands of every possible combination of high card points and suit distribution.  I wrote up my results in a manuscript (available by request) that is under review for possible publication in Mathematics Magazine.  

This work is hardly on the cutting edge of math research.  In an abstract I described it as “an intricate application of elementary combinatorics.”  Even so, it is the best piece of original math I have done since coming to Lane, and something I would not have accomplished without paid leave.  Although the benefits to my teaching will be less immediate than those of my research on pedagogy, this part of my sabbatical work will perhaps have the greatest long-term impact on my professional development. 

IN SUMMARY,

I think I accomplished the goals set out in my application and perhaps a few others.  The last few weeks of my leave were spent traveling and hiking in New Zealand, which added elements of cultural learning and physical exercise to my sabbatical experience.  I am grateful for the opportunities afforded by this leave, and I am resuming my regular duties at Lane with renewed vigor and enthusiasm.