Curriculum Foundations for the First Two Years:

Disciplinary Workshops and Curriculum Conference (Draft Proposal June 30, 1999)

Contact: William Barker (


CRAFTY (Calculus Reform And the First Two Years)

A subcommittee of the Committee on the Undergraduate Program in Mathematics (CUPM),

Mathematical Association of America

Planning Committee

William Barker, Chair (Bowdoin College)

Susan Ganter (American Association for Higher Education)

William Haver (Virginia Commonwealth)

Deborah Hughes Hallett (Arizona)

Harvey Keynes (Minnesota)

William McCallum (Arizona)

Donald Small (U.S. Military Academy)


The CUPM is beginning a major analysis of the undergraduate mathematics curriculum. As the subcommittee of CUPM concerned with the first two years of the college mathematics program, CRAFTY will have a major role in analyzing and formulating recommendations concerning the se foundational years in mathematics instruction. Moreover, given the impact of mathematics instruction on the sciences and quantitative social sciences --- especially instruction during the first two years --- there is a need for significant input from these partner disciplines. CRAFTY will gather much of this necessary information over the next year-and-a-half through a series of disciplinary workshops, culminating in a curriculum conference to analyze and synthesize the workshop findings. This effort will constitute CRAFTY's primary involvement with the CUPM curriculum review.


To generate foundation materials, based heavily on the needs of partner disciplines, from which a curriculum for the first two years of a mathematical sciences program will be constructed. The foundational materials (primarily expectations about the nature and desired outcomes of the first two years of undergraduate mathematics instruction) will include:

* expectations on the skills to be attained at the end of the first two years.

* lists of problems that ought to be solvable at the end of the first two years.

* the nature of assessment tools that should be employed.

* the "learning environments" that students should be exposed to.

Examples of how these expectations can be met, primarily in the form of possible courses and course sequences, will also be developed.


After the first two workshops take place in the fall of 1999, the Planning Committee will embed itself in a larger Organizing Committee. The composition of the Organizing Committee will reflect a wide range of views in the mathematics community and will have representation from the partner disciplines. The Organizing Committee will make the major policy decisions, including the selection of organizers for the disciplinary workshops and the selection of participants at the culminating curriculum conference. The Planning Committee would continue to function as the primary "administrative unit" for this initiative, handling the more routine functions.


There will be several disciplinary workshops. The first two will be:

* physics/computer science (Bowdoin College, October 28-31, 1999)

* physics/engineering, focused on calculus (West Point, November 4-7, 1999)

Additional workshops will be organized following Bowdoin and West Point. The Organizing Committee will determine these subsequent workshops. Possible choices are:

* engineering

* chemical and biological sciences

* health sciences and biomedical engineering

* quantitative social sciences

* operations research and statistics

* mathematics education (focused on teacher preparation and instructional issues affecting curriculum)

* mathematics (focused on preparation of mathematics majors)

Each workshop will consist of 20-30 participants, the majority chosen from the disciplines under consideration, the remainder to be chosen from mathematics. At least some members of the Organizing Committee will be among the workshop participants. Each workshop will result in a document, addressing a series of questions specified at the outset of the workshop. The basic set of questions provided to each workshop will be the same, though some discipline-specific questions may be added for each meeting. However, differences between the workshops will be likely, reflecting the specific needs of the disciplines involved and the desires of the workshop organizers.

The Organizing Committee and the workshop organizers will determine who should produce the final written report. The reports so produced will be widely circulated, within both the specific disciplines and the mathematics community, in order to solicit a wide range of comments.

The workshops will be funded by the hosting institutions, though in certain cases an outside funding agency might be appropriate. It is not CRAFTY's intention to seek one funding source for all the workshops. The Organizing Committee may decide to apply for grants to supply some funds for the workshops.


The questions to be posed to each disciplinary workshop will be determined by the Organizing Committee. Here is one proposed set of questions.

Goals and Content.

What topics must be covered in the first two years? What priorities exist between the topics?

What is the optimum balance between theoretical understanding and computational skill?

Are there different student audiences which need different mathematical preparation?


How should technology affect the content and pedagogy of mathematics courses?

What technology skills should be part of mathematics instruction? What are the priorities?

Do different student audiences require different technology choices?

Instructional Interconnections.

What impact does mathematics education reform have on instruction in your discipline?

How should education reform in your discipline affect mathematics instruction?

How can dialogue on educational issues between your discipline and mathematics best be maintained?

Instructional Techniques.

What instructional methods should be emphasized in mathematics education?

What instructional techniques best build theoretical understanding?

Does educational research provide guidance concerning mathematical training in your discipline?


After the disciplinary workshop papers have been circulated and commented upon, an invitational curriculum conference will be convened. This conference, working primarily from the workshop papers, will produce detailed curricular recommendations for the first two years of undergraduate mathematics instruction. This will entail a careful synthesis of the various disciplinary recommendations, striving for a coherent blueprint for the first two years of mathematical instruction. While the primary goal will not be to recommend a specific set of courses , examples of course s and course sequences which embody the recommended outcomes will be formulated.

A dialogue/discussion format will be used throughout the conference: dialogue to develop understanding of the views and opinions of the participants, discussion to arrive at decisions concerning the final set of curricular recommendations.

Forty participants will be invited. Although the majority of the participants will be mathematicians, invitations will cover all the constituencies and partner disciplines for which the first two year of undergraduate mathematics instruction has important consequences. The Organizing Committee will select the participants. At least some representatives from each disciplinary workshop will be chosen as curriculum conference participants.

Participants will discuss and analyze the disciplinary workshop papers and outline a summary report of their conclusions and recommendations. The final report, containing the curriculum recommendations, will be written after the conference ends. This document, along with all the disciplinary workshop papers, will be collected and prepared for publication, most likely as a volume in the MAA Notes series. These materials will constitute CRAFTY's primary contribution to the overall CUPM analysis of the undergraduate mathematical sciences instructional program.


The most immediate, tangible product of the conference will be the publication of the workshop papers and final conference recommendations, most likely as a volume in the MAA Notes series. Publications in this series have played a significant role in the national growth of instructional reform activity.

Presentations communicating the recommendations of the workshops and conference will be organized by CRAFTY at appropriate national meetings such as the joint AMS/MAA meetings each January. CRAFTY has a great deal of experience in organizing panels and presentations, even at meetings of organizations in disciplines other than mathematics.

Ultimately the recommendations of the workshops/curriculum conference would be embodied in the larger CUPM analysis of the undergraduate mathematics program.


The location and date for the first disciplinary workshop is Bowdoin College, October 28-31. This will coincide with the rededication of Searles Hall as the combined mathematics, physics, and computer science building. The keynote speaker will be Tom Banchoff, the current president of the MAA. In keeping with the rededication, the disciplines chosen for the workshop are physics and computer science.

The location and date for the second disciplinary workshop is West Point, November 4-7. This will be part of the "Interdisciplinary Conference on the Role of Calculus," currently being organized by Don Small at the U.S. Military Academy. As the title indicates, the focus of this workshop will be calculus; the chosen disciplines will be physics and engineering.

Our goal will be to have all the workshops occur within 18 months. The intention would be to spread the workshops out across the country, utilizing a variety of sponsoring organizations. Suggestions for locations/sponsoring organizations include XXX. In particular, XXXhas been suggested as a good site for the quantitative social sciences workshop, XXXfor the mathematics workshop, and XXX for the mathematics education workshop.

The target date for the curriculum conference is the first half of 2001. If a winter date in 2001 is chosen, then the site should be in the southern half of the country --- the XXX would be a good candidate. If a late spring or summer date is chosen, then the site should be chosen from the northern half of the country --- good sites would include the XXX. The Organizing Committee will make the final decision on date and location.


The desire is to support twenty workshop participants for a three day workshop.


Participant Costs (20 participants)

Subsistence (3 days @ $25/day) 1500

Lodging (3 days @ $100/day) 6000

Travel Allowance (@ $500 ea) 10000

Total Participant Costs 17500.

Photocopying 1000.

Indirect Costs (est. 50% / 0% on participant) 500.

Total Operations 19000.


Secretarial Staff (two weeks) 1000.

Benefits (25%) 250.

Total Salary/Wages+Benefits 1250.

Indirect Costs (est. 50%) 625.

Total Salaries/Wages/Benefits/Indirect 1875.



The desire is to support forty conference participants for a four day conference.


Participant Costs (40 participants)

Subsistence (4 days @ $25/day) 4000

Lodging (4 days @ $100/day) 16000

Travel Allowance (@ $500 ea) 20000

Total Participant Costs 40000.

Photocopying 1000.

Publication of Proceedings 1500.

Indirect Costs (est. 50% / 0% on participant) 1250.

Total Operations 43750.


Staff (one month) 2000.

Benefits (25%) 500.

Total Salary/Wages+Benefits 2500.

Indirect Costs (est. 50%) 1250.

Total Salaries/Wages/Benefits/Indirect 3750.


NOTES (not part of formal document)

Some names suggested for the Organizing Committee: XXX. We will also need a representative from the two year colleges. The following names were suggested by XXX. All are very busy people. XXX

Names suggested as good organizers for the mathematics education workshop are XXX.

According to XXX, XXX College would be interested in hosting a health sciences/biomedical engineering workshop.

XXX also made the following suggestion for our document. It could take the form of a draft of a letter to the mathematics community describing our preliminary plans and soliciting (1) comments/suggestions, and (2) offers from individuals to participate in some active way in the process. The letter could also include an overview and vision for the project. We could further construct a cover memo to the organizers focusing on procedural questions. This could be used to recruit members of the Organizing Committee. They could be asked to agree to serve and to comment on the "letter". Then to launch the process, we could put the revised letter on lots of WEB pages, mail hard copies to appropriate MAA committees and other relevant organizations, and send e-mail versions to lots of people.

ASSUMPTIONS (not part of formal document)

The workshops and final conference are to be governed by three important assumptions:

(1) There are many paths to achieving an effective learning environment in mathematics, each defined by various choices of goals, content, and instructional methods. There is no SINGLE road to an effective instructional program.

(2) The primary component in an effective learning environment in mathematics is a knowledgeable faculty, dedicated to quality teaching, and supportive of the nature and philosophy of the instructional program. In particular, instructional programs are effective only when faculty members BELIEVE in them and are comfortable with the necessary pedagogical techniques. Hence, when making curricular recommendations, a multiplicity of options and choices is essential in order for programs to be designed that best suit local conditions.

(3) Constructing an effective learning environment is most reliably accomplished by pragmatic, non-ideological decisions based on rationally determined needs, observed results, and quality educational research. Debates based on opinions or anecdotal examples are not persuasive to the general mathematical community.