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The full committee now meets only once a year, so much of this report is a report on its September 26-27, 1997 meeting, based on notes of Monica Foulkes, and on activities pursuant thereto.

**Proposed National Test in Mathematics**

As a result of the request from CSP and CoE to involve more mathematicians in the development of the test, the Department of Education appointed several mathematicians to the numerous advisory panels being set up. Invited to discuss the progress of the project at this meeting were Gary Phillips (director of the test project), Judy Wurtzel and Pat O'Connell Ross (Office of Educational Research and Improvement). Support in Congress for the proposed test has been mixed, and the day before the meeting Secretary of Education Richard Riley issued a statement that development of the test has been halted until a final appropriations bill is signed. There was discussion of the ways mathematicians have been involved in the process and Phillips promised to look into the concerns expressed. CoE members were encouraged to submit names of mathematicians to the Dept. representatives for future involvement. This was done, and a substantial list was sent by the chair to Gary Phillips.

Judy Sunley (NSF) reported on the work of the joint NSF/Department of Education working group on plans for the support needed in conjunction with the test in areas such as teacher preparation and enhancement, development of instructional material, and public information and encouragement. There was discussion of emerging public backlash to the test, and what professional organizations could do to calm the rhetoric. Daniel Goroff reported on the work of the Administration's Office for Science and Technology Policy (OSTP) to support the President's initiative, which was motivated by the poor performance of U.S. 8th grade students in the Third International Mathematics and Science Study (TIMSS). It was President Clinton's intention to "set the bar high" and set world-class standards in the test, in order to "ratchet up the system", rather than produce a test based on an assessment of what current 8th grade students could pass.

Secretary of Education Richard Riley has accepted an invitation to speak to the Joint Mathematics Meeting in Baltimore, January 1998. He is jointly sponsored by COE and CSP.

**NCTM Standards 2000**

Roger Howe, chair of the subcommittee appointed by CoE to act as an Association Resource Group (ARG) to the writing teams working on the revision of the Standards, reported that the ARG had already submitted two reports to the National Council of Teachers of Mathematics. A public report will soon appear in the NOTICES and on the AMS Web site, and a joint panel session with the MAA ARG will be held at the Baltimore meeting. CoE members who are also members of NCTM's writing teams reported that the AMS ARG's comments had been well-received. The subcommittee was thanked for its hard work, which is still ongoing, and thoughtful reports, and CoE will express its appreciation to NCTM for setting up a process to involve the whole mathematical community in the re-writing of the Standards.

**National Science Foundation, Division of Undergraduate Education**

Norman Fortenberry, interim Division Director while Robert Watson is on assignment, informed CoE about the restructuring of DUE programs into a new entity, to be announced December 1. Programs will be: Course, Curriculum and Laboratory Improvement (CCLI), Advanced Technological Education (ATE), and Collaboratives for Excellence in Teacher Preparation. This restructuring reflects the recommendations made in the 1996 Review of Undergraduate Education. N. Fortenberry posed four questions for CoE comments: 1) What can we do to better prepare future mathematics teachers? 2) What can be done to change the institutional climate? 3) Is the MS degree likely to become a more accepted terminal degree in the mathematics community?, and 4) What are your perceptions about the calculus reform backlash, and how do we best address the issues raised? CoE appointed a subgroup, chaired by David Bressoud, to respond.

The subgroup's response is appended below (Appendix A). This report was received with great appreciation by Fortenberry and the staff at NSF.

**National Science Foundation, Division of Mathematical Sciences**

Ann Boyle described the new VIGRE program (Vertical Integration of Research and Education in the Mathematical Sciences) to support departmental, as opposed to individual, activities. This new and complex program will subsume the GIG program (Group Infrastructure Grants) as a response to the recommendations of the 1995 Workshop on Graduate Education. A. Boyle reported that NSF was pleased with the response to the interdisciplinary grants program that provides sabbatical support for mathematicians to work in other departments.

**Preparation of Future Mathematics Teachers**

A common theme in all the above discussions was an increased emphasis on improvements in the preparation of mathematics teachers. C. Lacampagne, Department of Education, reported that funding had been approved for an MAA proposal ("Mathematics Education of Teachers Project") that the Department wished to see expanded to include other mathematical societies. This proposal will be discussed at the December CBMS meeting, and CoE appointed a subgroup to explore AMS involvement and proposals for the design of the project and make recommendations at the CBMS meeting. The report of this subgroup discussion, submitted to CBMS, is appended below (Appendix B). The Department of Education is also interested in developing departmental workshops with AMS and other interested societies.

**New Criteria for Accreditation of Engineering Programs**

William Kelly gave an overview of the Accreditation Board for Engineering and Technology's (ABET) new accreditation criteria, currently in a pilot phase, by 2001 to be compulsory. Kelly did not feel that the new criteria would impact mathematics departments. CoE will continue to monitor the implementation of the new criteria for possible impact.

**COE Focus**

There was discussion of the focus on K-12 mathematics education that had taken up most of CoE's energy recently. In connection with what was felt to be CoE"s core concern - graduate education - there was discussion of data on decreasing enrollments by U.S. students in upper-level and graduate courses and the resultant impact on education. There was also debate about the structure of CoE meetings. CoE has agreed to meet September 11-12, 1998.

**Reports from Other Groups**

Naomi Fisher reported on MER (Mathematicians for Education Reform) projects, including a joint AMS/MER proposal for workshops on professional Master's degrees. Ron Rosier reported that the 1995 CBMS Survey had been published, reporting that enrollments in 4-year college mathematics courses had decreased by 9 percent from 1990 to 1995, but those in 2-year colleges had increased 12 percent. Almost half (46 percent) of all undergraduate mathematics is now taught in 2-year colleges. John Tucker reported plans for the Board on Mathematical Sciences Department Chairs Colloquium, and other projects. Gerald Kulm reported on the American Association for the Advancement of Science Project 2061, concerning middle-school mathematics curriculum. The CoE subcommittee appointed to make recommendations to the Math Reviews Editorial Committee on a possible classification for research in mathematics education is close to a final recommendation. Representatives from other organizations making short presentations included: Mathematical Association of America, Education Development Council, National Association of State Science and Mathematics Coalitions, Joint Policy Board for Mathematics.

**MATH REVIEWS Coverage of Undergraduate Education Research**

A subcommittee of the CoE, chaired by Joan Ferrini-Mundy, is looking into the possibility of MR listings of work in undergraduate education research. It has produced a draft classification scheme, compatible, as required, with that of Zentralblatt. This is currently under review by MREC. Once a classification scheme is adopted, there remains the question of scope of possible coverage by MR.

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**APPENDIX A: Response to N. Fortenberry's Questions**

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October 10, 1997

Norman Fortenberry

Division of Undergraduate Education

National Science Foundation

Dear Norman,

First let me thank you for the very informative presentation that you made to our Committee on Education. You raised a number of important questions to which the committee felt we had inadequately responded. This was not through lack of interest, but because of the crowded agenda, and the fact that we had no opportunity to see and reflect on the questions prior to the meeting.

We were given to believe that you would still be receptive to input on these questions. Accordingly, I appointed a Subcommittee to develop some responses, via e-mail discussion. That Subcommittee was chaired by David Bressoud, and involved the participation of Jim Lewis, Alan Tucker, Alan Schoenfeld, Judy Roitman, and Harvey Keynes. They gave the questions intense and thoughtful attention. The resulting report, which I respectfully submit to you herewith, contains some important, well informed, and broadly held views which I hope you will find valuable in developing policies and programs at the NSF.

Thank you again for your contributions to our meeting.

Sincerely yours,

Hyman Bass,

Chair, AMS Committee on Education

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

AMS Committee on Education

October 10, 1997

This is a summary of the e-mail discussion among the six whose names appear at the bottom of this report.

**1) What can we do to better prepare future mathematics teachers? **

This is a critically important question that a lot of people--including MER, the MSEB, and the MAA through COMET and CUPM--are struggling to answer. We identified two major issues:

- As stated in
*Everybody Counts*, "Reform of Undergraduate Mathematics is the key to revitalizing mathematics education." (p. 40). Part of this is modeling good pedagogy and taking an active, exploratory approach to mathematics in the undergraduate classroom. The other part is designing the curriculum with the needs of preservice teachers in mind. This means real content, but in a context in which future teachers can see how it will relate to the classes they will be teaching.

This is one place where the NSF could play a role. There is a scarcity of good curricular materials that relate undergraduate mathematics courses to the needs of preservice teachers. Judy Roitman mentioned Bob Burns and Bill Barker who have produced materials for undergraduate mathematical analysis. This is the kind of effort that should be actively supported.

We need to involve more mathematicians in thinking about how preservice teachers should be trained, and that raises the issue of lowering the bar to such participation. Most teacher preparation initiatives are massive programs that require a large commitment of time and energy. The NSF needs to find ways to draw in more of the mathematical community. We need to both broaden the base of ideas that can be drawn upon and increase the number of stake-holders in the training of preservice teachers.

We not only need more mathematicians involved in teacher training; we also need more involvement from our best K-12 teachers. These are the ones who can model the enthusiasm and dedication that we want to instill. The goal should be increased contact and eventually collaboration between university mathematicians and K-12 teachers.

But even exemplary programs feel undercut by public attitudes toward teachers. This brings us to the second big issue: - Teachers need to be treated as professionals. This includes respecting the need for proper credentials, improving pay scales and working conditions, and giving teachers control over the broad context of their professional lives. One way of beginning to address this issue is to fund public awareness efforts designed to increase community support for teachers.

One final point was brought up by several of the committee members: that the most critical area for attention is the mathematical preparation of elementary and middle school teachers. To quote Jim Lewis, "The good news here is that I think there is a great opportunity to make a difference. The elementary school teachers I meet tend to have a very positive orientation toward their job and are good with young children. Their shortcomings tend to be content knowledge in math and science. Here NSF could do a great deal if they put enough money behind the issue."

**2) What can be done to change the institutional climate? **

Again, a lot of people are already working on this question. Specific mention was made of the JPBM Task Force and of the continuing work of MER. In fact, one repeated recommendation for the NSF was to make it easier for MER to get continuing funding.

There was praise for some of the new systemic initiative programs, such as VIGRE, that have the potential to create institutional change in a few universities that will then serve as models for others. At the same time, there was concern that NSF not lose sight of the fact that such systemic change is most likely to succeed when it builds upon a rich assortment of ideas and initiatives that have involved a lot of people from across a wide variety of institutions. This was the case of the large calculus reform projects which were preceded by over a decade of small, yeasty grants that got people thinking about the problems of teaching and learning mathematics and then finding innovative solutions.

The NSF also needs to help break down the perceived barrier between teaching and research. We must make it easier to move back and forth between concentrated attention to mathematical research and concentrated attention to educational issues. One way to accomplish this is to help to make it possible for a faculty member involved in research to turn attention to educational issues. You may want to imitate the success of Paul Sally in involving research mathematicians at Chicago by putting clear and tolerable limits on what would be expected of them. At the same time, the NSF could create opportunities for faculty who have been very involved in education to re-immerse themselves in research.

More broadly, we need to break through the current paradigm that is dominated by turf battles. We, the professional community, must identify the principles of our profession and the goals that we seek to achieve. Priorities will have to be set, but they should be based on the desirability of the outcome and the nature of the particular resources that are at hand. And most critically, individuals must be encouraged to play to their own strengths as well as to explore where those strengths might actually lie.

**3) Is the MS degree likely to become a more accepted terminal degree in the mathematics community? **

Several members of the group expressed concern that an MS degree riding on the side of a graduate program whose purpose is to prepare students to do research is unlikely to be able to compete with true professional programs in the mathematical sciences, programs such as statistics and operations research.

There was also recognition that an MS program in mathematics will require a great deal of flexibility. It is not clear where the professional needs will be in ten or twenty years. This suggests that math departments may have an inherent advantage over existing professional programs, provided they can break away from the tight focus of most graduate mathematics programs.

**4) What are your perceptions about the calculus reform backlash, and how do we best address the issues raised? **

No one saw the reported calculus reform backlash as a serious issue. There is some restabilization, but the center of gravity has moved and standard calculus texts are now incorporating many of the assumptions of the reform texts. Judy Roitman summed it up for the entire group when she said, "Even if none of the NSF-funded curriculum projects survives (and this is unlikely) they have changed the face not only of calculus teaching but of much undergraduate teaching. I think this program has been an unqualified success."

There was concern, however, that as textbook publishing houses are consolidating, many of the texts with small audiences are being dropped.

Just as the most adventurous, original, and innovative ideas often come from small grants, so also the textbooks that will lead the way to the next generation of insights will, almost by definition, only be adopted by a small number of instructors. We need to support and encourage this ferment.

David Bressoud, Macalester College

Harvey Keynes, University of Minnesota

James Lewis, University of Nebraska

Judith Roitman, University of Kansas

Alan Schoenfeld, University of California, Berkeley

Alan Tucker, SUNY at Stony Brook

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**APPENDIX B: Message to Conference Board on Mathematical Sciences about the Teacher Preparation Project**

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Date: Mon, 24 Nov 1997 00:43:52 -0400

From: Hyman Bass

Subject: cbms-ep meeting on teacher prep

To: ronrosier@guvax.acc.georgetown.edu

Cc: math-teach@MATH.AMS.ORG

Dear Ron,

Following the presentations at the meeting of the AMS CoEd on the MAA initiated project on the Mathematical Preparation of Teachers, I assembled an e-mail discussion group to generate ideas for the project.

With this message I am transmitting some of the outcome of that discussion.

I would like it to be disseminated (electronically) to the participants ahead of the meeting, so that there is time to reflect on some of the ideas.

On Nov. 18, I sent essentially the following memo to the group:

______________________________________

The agenda for the CBMS EP (Educational Partnership) formulates discussion of the project on The Mathematical Preaparation of Teachers as a kind of sequel to "A Call for Change," with much of the time spent reviewing and refining the "Standards" in the latter document. Those Standards are of a very general nature, and, while admirable in principle, do little to inform academic mathematicians about how they might change practice to improve their contribution to teacher preparation.

From the feedback I have received from several of you, the following possibilities suggest themselves as more substantial and valuable ways to structure the project. For mathematicians, the following appear to be central issues in preparing future teachers. (Of course the answers will differ for elementary, middle, and secondary teachers.)

**1.** What mathematics should be taught?

**2.** How can it be taught so as to connect meaningfully with the actual practice of teaching.

**3.** How can one initiate and successfully pursue the collaborations with teachers and/or School of Education Faculty necessary to design and support such preparation programs?

Mathematicians, working most comfortably alone, tend to focus almost exclusively on 1., with the result that 2. is often not achieved.

This suggests two useful things that the project might aim for.

**I.** A set of authored papers, by mathematicians together with teachers and/or teacher educators, addressing the issues in 2. above. A good example of this genre, though not addressed only to teaching issues, is the article of George Cobb and David Moore in the current Math Monthly, on the nature of statistics. Other items here could describe the use of primary materials (videos of classroom lessons, student work, curricular materials, etc.) as a site for studying the ambient implicit mathematics.

**II.** A set of case studies of some promising teacher preparation programs involving collaboration between mathematicians and educators. These would highlight both the substance of the program, and the efforts and resources needed to establish and sustain the collaborations.

The project might support both kinds of products. The results might appear in some of the organizational journals if not in a report of the project itself. Collectively we know of several interesting candidates of both types I. and II. above.

____________________________________________

Responses from the group generally supported putting this on the table for your consideration. Some elaborations were also suggested. Judy Roitman proposed giving some attention to the articulation between High School and Undergraduate mathematics courses. Alan Tucker urged consideration of connections of mathematics to other disciplines.

In addition, we have received some substantial commentaries on teacher preparation from Al Cuoco, Hung-Hsi Wu, Peter Braunfeld, and Susan Addington. I shall forward these to you following this message. I think that they have much to contribute to the thinking of your meeting participants.

Best wishes,

Hy Bass