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

**Contact: William Barker (barker@bowdoin.edu)**

**Organizer**

**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)**

**SUMMARY**

**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.**

**PURPOSE**

**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.**

**ORGANIZING COMMITTEE**

**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.**

**WORKSHOP ORGANIZATION**

**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.**

**WORKSHOP QUESTIONS**

**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?**

**Technology.**

**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?**

**CONFERENCE ORGANIZATION**

**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.**

**DISSEMINATION**

**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.**

**DATES AND LOCATIONS**

**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.**

**ESTIMATED BUDGET FOR A SINGLE DISCIPLINARY WORKSHOP**

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

Operations

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.

Salaries/Wages

Secretarial Staff (two weeks) 1000.

Benefits (25%) 250.

Total Salary/Wages+Benefits 1250.

Indirect Costs (est. 50%) 625.

Total Salaries/Wages/Benefits/Indirect 1875.

TOTAL ESTIMATED WORKSHOP BUDGET
20875.

**ESTIMATED BUDGET FOR
THE CURRICULUM CONFERENCE**

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

Operations

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.

Salaries/Wages

Staff (one month) 2000.

Benefits (25%) 500.

Total Salary/Wages+Benefits 2500.

Indirect Costs (est. 50%) 1250.

Total Salaries/Wages/Benefits/Indirect 3750.

TOTAL ESTIMATED CONFERENCE BUDGET
47500.

**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.**