Curriculum Foundations for the First Two Years: 
Disciplinary Workshops and Curriculum Conference

October 21, 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 (Clemson University)

William Haver (Virginia Commonwealth University)

Deborah Hughes Hallett (University of Arizona)

Harvey Keynes (University of Minnesota)

William McCallum (University of Arizona)

Donald Small (U.S. Military Academy, West Point)


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 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 college mathematics 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" in which students should work.

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


The Planning Committee will assemble a larger Steering Committee, with membership reflecting a wide range of views from the mathematics community and the partner disciplines. The Steering Committee will make the major policy decisions of the Curriculum Foundations Project, including approval of organizers for the disciplinary workshops and the selection of participants at the culminating curriculum conference. The Planning Committee will continue to function as the primary "administrative unit" for the project, and will handle the Steering Committee responsibilities until this latter committee comes into existence.


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 (USMA, West Point, November 4-7, 1999)

Additional workshops will be organized following Bowdoin and West Point. Possible choices are:

* engineering

* chemical and biological sciences

* health sciences and biomedical engineering

* quantitative social sciences

* operations research and statistics

* business and finance

* 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 Steering and Planning Committees 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 local workshop organizers, in consultation with the Steering Committee, 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 Steering Committee may decide to apply for grants to supply partial funding forsome of the workshops and for the culminating Curriculum Conference.


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 mathematics instruction. While the primary goal will not be to recommend a specific set of courses, examples of courses 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.

Approximately forty participants will be invited. Although the majority of 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 Steering 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 questions to be posed to each disciplinary workshop will be determined by the Steering Committee. Here are the questions as formulated for the first Workshop at Bowdoin College.

Understanding and Content.

What conceptual mathematical principles must students master in the first two years?

What mathematical problem solving skills must students master in the first two years?

What broad mathematical topics must students master in the first two years?

What priorities exist between these topics?

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

How is this balance achieved?

What are the mathematical needs of different student populations and how can they be fulfilled?


How does technology affect what mathematics should be learned in the first two years?

What mathematical technology skills should students master in the first two years?

What different mathematical technology skills are required of different student populations?

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 are the effects of different instructional methods in mathematics on students in your discipline?

What instructional methods best develop the mathematical comprehension needed for your discipline?

What guidance does educational research provide concerning mathematical training in your discipline?


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 the Searles Science Building 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 the U. S. Military Academy, West Point, November 4-7. This will be part of the "Interdisciplinary Conference on the Role of Calculus.". The focus of this workshop will be calculus; the chosen disciplines are physics and engineering.

The goal is to have all the workshops occur within 18 months, and to spread the workshops out across the country, utilizing a variety of sponsoring organizations. Suggestions for locations/sponsoring organizations include MSRI, IMA (Minnesota), IAS (Princeton), U. of Michigan, Virginia Commonwealth University, and U. of Arizona. In particular, Arizona has been suggested as a good site for the business and finance workshop, VCU for the health sciences and biomedical engineering workshop, IAS for the mathematics workshop, and MSRI 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 will probably be in the southern half of the country --- the University of Arizona 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 University of Michigan or the IMA in Minnesota. The Steering 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 (@ $450 ea) 9000

Total Participant Costs 16500.

Photocopying 1000.

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

Total Operations 18000.


Secretarial Staff (two weeks) 1000.

Benefits (25%) 250.

Total Salary/Wages+Benefits 1250.

Indirect Costs (est. 50%) 625.

Total Salaries/Wages/Benefits/Indirect 1875.

Honorarium for Recorder (produces final report) 500.



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.