By Tom Moore
Readers of FOCUS are well aware of the pedagogical reform that has impacted collegiate mathematics in the past 15 years, especially in calculus. These same readers may be less aware of a similar reform in statistics education, which by and large, the statistics community has embraced. Richard Scheaffer, the past president of the American Statistical Association (ASA), said in 1997, ’With regard to the content of an introductory statistics course, statisticians are in closer agreement today than at any previous time in my career.â? (Moore, D. S. and discussants, ’New Pedagogy and New Content: The Case of Statistics,â? International Statistical Review, 65 (1997), page 156.)
In a seminal 1992 article (’Teaching Statistics,â? in Heeding the Call for Change: Suggestions for Curricular Action, Lynn A. Steen, ed., MAA Notes #22, The Mathematical Association of America, pages 3-43), George Cobb articulated the principles of statistics reform pedagogy that are so much in evidence today:
"More data and concepts, fewer derivations and recipes; automate calculations using a modern statistical package.?
?Emphasize statistical thinking: the omnipresence of variability and the importance of data production.?
?Foster active learning: student projects, group work, activities, writing, oral presentations.?
A recent article (Garfield, J., Hogg, B., Schau, C., and Whittinghill, D. ’First Courses in Statistical Science: The Status of Educational Reform Efforts,â? Journal of Statistics Education, Volume 10, Number 2, (2002), online at http://www.amstat.org/publications/jse/v10n2/garfield.html) surveys the extent to which these recommendations have been implemented.
On October 12-15, 2000, 22 statisticians and 5 mathematicians met for a Curriculum Foundations (CRAFTY) Workshop at Grinnell College. The group included statisticians from academia, business, and government and from two- and four-year colleges and universities.
The workshop considered two sets of questions. The first?considered by all CRAFTY workshops?asked what aspects of the undergraduate math-ematics curriculum are of most value to statistics. The second set came from our belief that statistics?is unique as a partner discipline in that?statistics is a part of the mathematical sciences and should be represented within the curriculum of a mathematics department. Indeed, at many institutions, statistics resides within the mathematics department. So we asked, what is the role of statistics in the mathematics curriculum?
The workshop participants achieved consensus on all issues considered, of which we give here some highlights. The full report can be found at: http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum_Fo....
What do statisticians need from mathematics?
The two highest priority needs of statistics from the mathematics curriculum are to:
(1) Develop skills and habits of mind for problem solving and for gen-eralization. Such development toward independent learning is deemed more important than coverage of any specific content area.
(2) Focus on conceptual understanding of key ideas of calculus and linear algebra, including function, derivative, integral, approximation, and transformation.
Given our principles of good statistics pedagogy, it seems fitting that we would not make strict content demands of the mathematics curriculum. We were much more concerned with conceptual understanding and with the experiences students had in mathematics courses. For example, courses that include some real, applied examples help students learn to draw connections between the language of mathematics and the context of an application, a skill that is invaluable for statistical work and that is better learned incrementally than through a single statistics course. But, including such examples may mean covering fewer topics. Similarly, statisticians routinely turn to technology to explore properties of proposed statistical procedures and so we recommend that early mathematics courses give students experiences in using technology to explore.
What can statistics contribute to the mathematics curriculum?
Here we considered the role of statistics in both the mathematics major and in general education. Regarding general education, we urge mathematics departments to consider that students who take only one college course in quantitative reasoning may be better served by a modern course on introductory statistics than by a traditional college algebra or pre-calculus course.
For the mathematics major, we dusted off an old recommendation from the 1991 CUPM Report, which said: ’Every mathematical sciences major should include at least one semester of study of probability and statistics at a level which uses a calculus prerequisite.’â?¦ The major focus of this course should be on data and on the skills and mathematical tools motivated by problems of collecting and analyzing data.â?¦ any statistics course taught now should use a nationally available software package.â?
Even though this recommendation has been almost universally ignored, our workshop re-affirmed it. We felt there were even more compelling reasons for the recommendation today than there were 10 years ago: (1) Data analysis plays a crucial role in many aspects of academic, professional, and personal life. (2) The job market for mathematics majors is largely in fields (e.g., business) that use data. (3) Future teachers will need knowledge of statistics and data analysis to be current with the new NCTM Standards and with the new and highly popular AP Statistics course. (4) The study of statistics provides an opportunity for students to gain frequent experience with the interplay between abstraction and context that we regard as critical for all mathematical sciences students.
We agreed with the 1991 re-commendation’s emphasis on real data. A first statistics course for majors should adhere to the principles of good statistics pedagogy in order to show students the essence of statistics. We felt strongly, however, that we need not mandate a calculus prerequisite. Those principles leave room for a variety of first statistics courses and in the full report we describe several innovative courses from around the country that differ greatly in their focuses: a time series course, a course that applies statistics to archeology, a course in Bayesian analysis, and a course in experimental design, among others. In other words, just as we argued for development of conceptual under-standing and habits of mind with mathematics courses, we similarly do not believe in prescribing specific content for this statistics course. We hope that relaxing the calculus prerequisite and providing curricular models will enable more institutions to implement this important recommendation. We also trust that this is one way in which statistics and mathematics can cooperate to their mutual benefit.
Tom Moore is in the Dept. of Mathematics and Computer Science at Grinnell College. Roxy Peck and Allan Rossman are in the Dept. of Statistics at California Polytechnic State University at San Luis Obispo. Together they organized the CF Workshop in Statistics at Grinnell College.