Table Of Contentfront.qxd 3/16/2005 11:19 AM Page i
Innovations in
Teaching Statistics
Copyright ©2005 by
The Mathematical Association of America (Incorporated)
Library of Congress Catalog Card Number 2005923500
ISBN 978-0-88385-175-3
eISBN 978-1-61444-306-3
Printed in the United States of America
Current printing (last digit):
10 9 8 7 6 5 4 3 2 1
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Innovations
in
Teaching Statistics
Edited by
Joan B. Garfield
University of Minnesota
Published and Distributed by
The Mathematical Association of America
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The MAANotes Series, started in 1982, addresses a broad range of topics and themes of interest to all who
are involved with undergraduate mathematics. The volumes in this series are readable, informative, and
useful, and help the mathematical community keep up with developments of importance to mathematics.
Committee on Publications
Roger Nelsen, Chair
Notes Editorial Board
Sr. Barbara E. Reynolds, Editor
Paul E. Fishback,Associate Editor
Jack Bookman Annalisa Crannell Rosalie Dance
William E. Fenton Mark Parker Sharon C. Ross
David Sprows
MAANotes
11. Keys to Improved Instruction by Teaching Assistants and Part-Time Instructors, Committee on Teaching
Assistants and Part-Time Instructors, Bettye Anne Case,Editor.
13. Reshaping College Mathematics, Committee on the Undergraduate Program in Mathematics, Lynn A.
Steen,Editor.
14. Mathematical Writing, by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts.
16. Using Writing to Teach Mathematics, Andrew Sterrett,Editor.
17. Priming the Calculus Pump: Innovations and Resources, Committee on Calculus Reform and the First Two
Years, a subcomittee of the Committee on the Undergraduate Program in Mathematics, Thomas W. Tucker,
Editor.
18. Models for Undergraduate Research in Mathematics, Lester Senechal,Editor.
19. Visualization in Teaching and Learning Mathematics, Committee on Computers in Mathematics Education,
Steve Cunningham and Walter S. Zimmermann, Editors.
20. The Laboratory Approach to Teaching Calculus, L. Carl Leinbach et al.,Editors.
21. Perspectives on Contemporary Statistics, David C. Hoaglin and David S. Moore,Editors.
22. Heeding the Call for Change: Suggestions for Curricular Action, Lynn A. Steen,Editor.
24. Symbolic Computation in Undergraduate Mathematics Education, Zaven A. Karian,Editor.
25. The Concept of Function: Aspects of Epistemology and Pedagogy, Guershon Harel and Ed Dubinsky,Editors.
26. Statistics for the Twenty-First Century, Florence and Sheldon Gordon,Editors.
27. Resources for Calculus Collection, Volume 1: Learning by Discovery: A Lab Manual for Calculus, Anita E.
Solow,Editor.
28. Resources for Calculus Collection, Volume 2: Calculus Problems for a New Century, Robert Fraga,Editor.
29. Resources for Calculus Collection, Volume 3: Applications of Calculus, Philip Straffin, Editor.
30. Resources for Calculus Collection, Volume 4: Problems for Student Investigation, Michael B. Jackson and John
R. Ramsay, Editors.
31. Resources for Calculus Collection, Volume 5: Readings for Calculus, Underwood Dudley, Editor.
32. Essays in Humanistic Mathematics, Alvin White,Editor.
33. Research Issues in Undergraduate Mathematics Learning: Preliminary Analyses and Results, James J. Kaput and
Ed Dubinsky,Editors.
34. In Eves’Circles, Joby Milo Anthony, Editor.
35. You’re the Professor, What Next? Ideas and Resources for Preparing College Teachers, The Committee on
Preparation for College Teaching, Bettye Anne Case,Editor.
36. Preparing for a New Calculus: Conference Proceedings, Anita E. Solow,Editor.
37. A Practical Guide to Cooperative Learning in Collegiate Mathematics, Nancy L. Hagelgans, Barbara E.
Reynolds, SDS, Keith Schwingendorf, Draga Vidakovic, Ed Dubinsky, Mazen Shahin, G. Joseph Wimbish, Jr.
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38. Models That Work: Case Studies in Effective Undergraduate Mathematics Programs, Alan C. Tucker,Editor.
39. Calculus: The Dynamics of Change, CUPM Subcommittee on Calculus Reform and the First Two Years, A.
Wayne Roberts,Editor.
40. Vita Mathematica: Historical Research and Integration with Teaching, Ronald Calinger,Editor.
41. Geometry Turned On: Dynamic Software in Learning, Teaching, and Research, James R. King and Doris
Schattschneider,Editors.
42. Resources for Teaching Linear Algebra, David Carlson, Charles R. Johnson, David C. Lay, A. Duane Porter,
Ann E. Watkins, William Watkins,Editors.
43. Student Assessment in Calculus: A Report of the NSF Working Group on Assessment in Calculus, Alan
Schoenfeld,Editor.
44. Readings in Cooperative Learning for Undergraduate Mathematics, Ed Dubinsky, David Mathews, and Barbara
E. Reynolds, Editors.
45. Confronting the Core Curriculum: Considering Change in the Undergraduate Mathematics Major, John A.
Dossey,Editor.
46. Women in Mathematics: Scaling the Heights, Deborah Nolan,Editor.
47. Exemplary Programs in Introductory College Mathematics: Innovative Programs Using Technology, Susan
Lenker,Editor.
48. Writing in the Teaching and Learning of Mathematics, John Meier and Thomas Rishel.
49. Assessment Practices in Undergraduate Mathematics, Bonnie Gold,Editor.
50. Revolutions in Differential Equations: Exploring ODEs with Modern Technology, Michael J. Kallaher,Editor.
51. Using History to Teach Mathematics: An International Perspective, Victor J. Katz,Editor.
52. Teaching Statistics: Resources for Undergraduate Instructors, Thomas L. Moore,Editor.
53. Geometry at Work: Papers in Applied Geometry, Catherine A. Gorini,Editor.
54. Teaching First: AGuide for New Mathematicians, Thomas W. Rishel.
55. Cooperative Learning in Undergraduate Mathematics: Issues That Matter and Strategies That Work, Elizabeth
C. Rogers, Barbara E. Reynolds, Neil A. Davidson, and Anthony D. Thomas,Editors.
56. Changing Calculus: AReport on Evaluation Efforts and National Impact from 1988 to 1998, Susan L. Ganter.
57. Learning to Teach and Teaching to Learn Mathematics: Resources for Professional Development, Matthew
Delong and Dale Winter.
58. Fractals, Graphics, and Mathematics Education, Benoit Mandelbrot and Michael Frame, Editors.
59. Linear Algebra Gems: Assets for Undergraduate Mathematics, David Carlson, Charles R. Johnson, David C.
Lay, and A. Duane Porter,Editors.
60. Innovations in Teaching Abstract Algebra, Allen C. Hibbard and Ellen J. Maycock, Editors.
61. Changing Core Mathematics, Chris Arney and Donald Small,Editors.
62. Achieving Quantitative Literacy: An Urgent Challenge for Higher Education,Lynn Arthur Steen.
63. Women Who Love Mathematics: ASourcebook of Significant Writings, Miriam Cooney, Editor.
64. Leading the Mathematical Sciences Department: AResource for Chairs, Tina H. Straley, Marcia P. Sward, and
Jon W. Scott, Editors.
65. Innovations in Teaching Statistics, Joan B. Garfield, Editor.
MAAService Center
P. O. Box 91112
Washington, DC 20090-1112
800-331-1MAA FAX: 301-206-9789
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Forword
George W. Cobb
The modern introductory statistics course has roots that go back a long way, to early books on statistical
methods. R. A. Fisher’s Statistical Methods for Research Workers, which first appeared in 1925, was aimed
at practicing scientists. Adozen years later, the first edition of George Snedecor’s Statistical Methodspre-
sented an expanded version of the same content, but there was a shift in audience. More than Fisher’s
book, Snedecor’s became a textbook used in courses for prospective scientists who were still completing
their degrees: statistics was beginning to establish itself as an academic subject, albeit with heavy practi-
cal, almost vocational emphasis. By 1961, with the publication of Probability with Statistical Applications
by Fred Mosteller, Robert Rourke, and George Thomas, statistics had begun to make its way into the
broader academic curriculum, but here again, there was a catch: in these early years, statistics had to lean
heavily on probability for its legitimacy. During the late 1960s and early 1970s, John Tukey’s ideas of
exploratory data analysis brought a near-revolutionary pair of changes to the curriculum, first, by freeing
certain kinds of data analysis from ties to probability-based models, so that the analysis of data could begin
to acquire status as an independent intellectual activity, and second, by introducing a collection of “quick-
and-dirty” data tools, so that, for the first time in history, students could analyze real data without having
to spend hours chained to a bulky mechanical calculator. Computers would later complete the “data revo-
lution” in the beginning statistics curriculum, but Tukey’s EDA provided both the first technical break-
through and the new ethos that avoided invented examples. 1978 was another watershed year, with the
publication of two other influential books, Statistics, by David Freedman, Robert Pisani, and Roger
Purves, andStatistics: Concepts and Controversies, by David S. Moore. I see the publication of these two
books 25 years ago as marking the birth of what we regard, for now at least, as the modern introductory
statistics curriculum.
The evolution of content has been paralleled by other trends. One of these is a striking and sustained
growth in enrollments. Two sets of statistics suffice here: (1) At two-year colleges, according to the
Conference Board of the Mathematical Sciences, statistics enrollments have grown from 27% of the size
of calculus enrollments in 1970, to 74% of the size calculus enrollments in 2000. (2) The advanced place-
ment exam in statistics was first offered in 1997. There were 7,500 students who took it that first year,
more than in the first offering of an APexam in any subject. The next year more than 15,000 students took
the exam, the next year more than 25,000, and the next, 35,000.
Both the changes in course content and the dramatic growth in enrollments are implicated in a third set
of changes, a process of democratization that has broadened and diversified the backgrounds, interests, and
motivations of those who take the courses. Statistics has gone from being a course taught from a book like
Snedecor’s, for a narrow group of future scientists in agriculture and biology, to being a family of courses,
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viii Innovations in Teaching Statistics
taught to students at many levels, from high school to post-baccalaureate, with very diverse interests and
goals. Ateacher in the 1940s, using Snedecor’s Statistical Methods, could assume that most students were
both quantitatively skilled and adequately motivated by their career plans. Ateacher of today’s beginning
statistics courses works with a very different group of students. Most take statistics much earlier in their
lives, increasingly often in high school; few are drawn to statistics by immediate practical need; and there
is great variety in their levels of quantitative sophistication. As a result, today’s teachers face challenges
of motivation and exposition far greater than those of a half-century ago.
Fortunately for those of us who teach, the changes I have described have been accompanied, especial-
ly over the past quarter century, by an additional set of changes, whose results are represented in this vol-
ume. Not only have the “what, why, who, and when” of introductory statistics been changing, but so has
the “how.” The last 25 years have seen an extraordinary level of activity focused on how students learn
statistics, and on how we teachers can be more effective in helping them to learn. One of the remarkable
features of this enterprise has been the broad-based and vigorous collaboration between those who come
from a background in education research and those who come from a background in statistics. Because of
this felicitous collaboration, statistics education has none of the usual fault lines between theory and prac-
tice. Instead, theory gets quickly translated into classroom practice, and what goes on in class leads back
to a better theoretical understanding.
Until now, the results of this hybrid vigor have been spread mainly by word of mouth, through work-
shops and papers presented at professional meetings, and through written proceedings and articles in the
electronic Journal of Statistics Education. One of the leaders in this process has been Joan Garfield, who
is known both for her education-based research on the learning of probability and statistics, and as one of
a handful of people who have done most to ensure that statisticians and researchers in statistics education
work together. Thinking about statistics education from the point of view of the classroom teacher, Joan
Garfield recognized that something important was missing. We have a number of good textbooks; we also
have a handful of ancillary volumes, on modern content (Perspectives on Contemporary Statistics, edited
by David Hoaglin and David Moore), on activities for the classroom (Activity Based Statistics, by Richard
Scheaffer et al.), and on resources (Teaching Statistics: Resources for Undergraduate Instructors, edited
by Thomas L. Moore). What has been missing is a book of examples of actual classroom practice. Joan
Garfield saw the need, marshaled the resources, assembled a team of outstanding teachers, and coordinat-
ed their writing. Many of the authors are known for their published work about teaching statistics; many
are known from their presentations at workshops and conferences. Now, for the first time, we get a more
personal view of what they do in their own classrooms.
Statistics education has come a long way since Fisher and Snedecor. Moreover, teachers of statistics
across the country have generally been enthusiastic about adopting modern methods and approaches.
Nevertheless, changing the way we teach isn’t always easy. In a way, we are all, teachers and learners
alike, a bit like hermit crabs: In order to grow, we must first abandon the protective shell of what we are
used to, and endure a period of vulnerability until we can settle into a new and larger set of habits and
expectations. In this book you can read the stories of many who have done just that.
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Contents
Forword, George W. Cobb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
1. Introduction,Joan B. Garfield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Section 1: Statistics Teachers in Mathematics Departments
2. Teaching a Data-Oriented, Activity-Based Course,
Allan J. Rossman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
3. Using the PACE Strategy to Teach Statistics
Carl Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
4. Statistics as a Core Course in Liberal Arts
Jerry Moreno . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
5. Teaching a Technology-enhanced Statistics Course in a Liberal Arts Environment
Robin Lock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
6. Teaching a Chance Course
William P. Peterson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Section 2: Statistics Teachers in Two-Year or Community Colleges
7. Teaching Statistics to Under-prepared College Students
Robert C. delMas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
8. Active Learning and Technology in the Community College Classroom
Ruby Evans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Section 3: Statistics Teachers in Departments of Statistics
9. Teaching Interactive Statistics for Understanding,
Martha Bilotti-Aliaga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75
10. Teaching Statistics through an Immersive Learning Environment,
Deborah Rumsey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
11. Becoming an Active Learning Facilitator in the Statistics Classroom,
William L. Harkness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93
12. Integrating Pedagogies to Teach Statistics,
Beth L. Chance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
Section 4: Teaching Statistics to Students in Other Disciplines
13. Teaching Statistics as a Language to Students in Psychology,
Karl N. Kelley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
14. Teaching Statistics to Beginning Researchers in Psychology,
Gary H. McClelland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
15. Teaching Statistics to Business Students,
Jonathan D. Cryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135
ix
