Grinnell College

Newsletter for the Section on Statistical Education

Volume 7, Number 1 (Winter 2001)

The Mathematical Association of America (MAA) is undertaking a major curricular review which will result in undergraduate curricular recommendations to the profession in the near future. As part of this process, the MAA asked a diverse collection of client disciplines to conduct workshops to discuss the client's needs of the undergraduate mathematics curriculum, especially the first two years. This series of Curriculum Foundations Workshops was sponsored by MAA's CRAFTY subcommittee; CRAFTY stands for Calculus Reform and the First Two Years.

Grinnell College hosted such a Curriculum Foundations Workshop for statistics on October 12-15, 2000. The ASA provided major funding for this workshop through its ASA Member Initiatives program. This funding paid travel expenses for 27 statisticians and mathematicians representing a wide variety of academic institutions as well as business, industry, and government. Roxy Peck, Allan Rossman, and I organized the workshop. Only 5 of those attending were mathematicians, who were there as observers and as resources.

In framing the agenda for this meeting, we settled on two sets of questions. The first set (called the __CRAFTY Questions__) was a standard set of questions provided to each of the workshops. This set of questions can be summarized succinctly as: "What should the undergraduate mathematics curriculum (esp. first two years) look like to serve the needs of statistics? Consider this question from the perspective of skills, concepts, topics, technology, pedagogy, and methods of assessment."

__A second set of questions__ was proposed by the workshop organizers and concerned the place of statistics within a mathematics curriculum. We developed this second set based upon our understanding that statistics is a *partner discipline* as well as a client discipline of mathematics. By this we mean that statistics is a part of the mathematical sciences and should be represented within the curricular recommendations of the MAA. At most undergraduate institutions, there is no separate statistics department, so that responsibility for statistics offerings typically falls to the mathematics department.

The workshop reached consensus on both sets of questions and issued a report of its recommendations which is available at the web site of CRAFTY chair, Bill Barker: http://academic. bowdoin.edu/math/faculty/barker/dissemination/ Curriculum_Foundations/. You will also find the reports of others curricular foundations projects at this site.

On January 11, 2001, a focus group convened at the annual MAA meeting in New Orleans to discuss an early draft of the CRAFTY Statistics Report. This activity help greatly to shape our final report.

For the first set of questions -- the CRAFTY questions addressing the mathematical (non-statistical) preparation we would like statistics students to obtain in the first two years of undergraduate mathematics -- the workshop reached consensus about the following goals for the undergraduate mathematics curriculum.

- Develop skills and habits of mind for problem solving and for generalization. Such development toward independent learning is deemed more important than coverage of specific content.
- Focus on conceptual understanding of key ideas of calculus and linear algebra, including function, derivative, integral, approximation, and transformation.

The following workshop recommendations are important for achieving these first two goals.

- Emphasize multiple representations of mathematical objects and multiple approaches to problem solving, including graphical, numerical, analytical, and verbal.
- Instruction should be learner-centered and address students' different learning styles by employing multiple pedagogies.
- Insist that students communicate in writing and learn to read algebra for meaning.
- Use real, engaging applications through which students can learn to draw connections between the language of mathematics and the context of the application.
- Instill an appreciation of the power of technology and develop skills necessary to use appropriate technology to solve problems, to develop understanding, and to explore concepts.
- Align assessment strategies with instructional goals.

For the second set of questions, about the place of statistics within a mathematics (i.e., mathematical sciences) curriculum, the workshop endorsed in principle a recommendation submitted by the MAA's own Committee on the Undergraduate Program in Mathematics in 1991 which asserted that all mathematical sciences majors should undertake study of data analysis and statistics. This study need not be at a level requiring a calculus prerequisite, but should adhere to the 1992 ASA/MAA recommendations to emphasize statistical thinking through active learning with more data and concepts, less theory, and fewer recipes. The workshop envisions a diversity of introductory statistics courses that could satisfy this recommendation and our report includes course descriptions of several such courses.

We encourage you to read the CRAFTY Statistics report and we welcome your comments. Please address comments to me at mooret@grinnell.edu.

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