Below you will find (draft) minutes of the CRAFTY meetings in Baltimore
along with updates on developments since that time.
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CUPM Subcommittee on Calculus Reform and the First Two Years (CRAFTY)
Minutes, Baltimore, Wednesday, January 7, 1998, 8:00am - 10:00am
Saturday, January, 11, 1998, 1:00pm - 2:30pm
Notes produced by Bill Barker, June 4, 1998
Attendance.
Committee members:
Bill Barker (Chair), Jack Bookman, Karabi Datta, Wade Ellis,
Susanna Epp, Susan Ganter, Shelly Gordon, Herb Kasube, David Lay,
Bill McCallum
Visitors:
Bill Haver, Deborah Hughes Hallett, Don Small, Frank Wattenberg
We had two meetings in Baltimore in order to deal with a long agenda of
items. I combine the results of the two meetings in the notes that
follow, and also indicate relevant developments which have occurred since
the January meetings.
(1) BALTIMORE EVENTS.
The Chair reminded all present of the two CRAFTY events taking place in
Baltimore:
CRAFTY/MER/AMS Calculus Reform Special Session.
Susan Ganter, Donald J. Lewis, Deborah Hughes Hallett
CRAFTY Panel on Research in Mathematics Education.
"Research in Math Education: Its Importance in Undergraduate Education"
Panelists: Susanna Epp, Kathleen Heid, David Tall
(2) CONTRIBUTED PAPER SESSION FOR TORONTO MATH FEST.
The Chair informed the committee that Martin Flashman had submitted a
proposal for a contributed paper session at Toronto, entitled
"Interactive & Dynamic Visualizations for Precalculus and Calculus," and
that Martin asked if CRAFTY wished to sponsor the session. We agreed to
be the sponsor, and the proposal was subsequently accepted by the
Committee on Sessions of Contributed Papers, chaired by Elizabeth Teles.
"Interactive and Dynamic Visualizations for Precalculus and Calculus"
Organized by Martin Flashman
Sponsored by CRAFTY
Description: Many new applications of technology allow interactive and
dynamic visualization that enhance student understanding of concepts in
both calculus and precalculus courses. Presentations at this session
are invited that discuss and illustrate some of the most recent of
these applications such as those using real data collection techniques
with calculators, animations, and dynamic software such as Geometer's
Sketchpad and Cabri.
(3) CRAFTY WEB PAGE.
The general concensus remains positive on maintaining a web page and on
allowing the Web Page Working Group to decide on the specifics of the
page. Martin Flashman has constructed a draft web page connected to his
own home page. Take a look: http://flashman.neocities.org/.
(4) EVALUATION OF THE EFFECTIVENESS OF CALCULUS REFORM.
As background, recall the following decision made last summer in Atlanta
(excerpted from the minutes of that meeting). "The strong feeling of
those present was that CRAFTY should be heavily involved in evaluation
efforts [of calculus reform], at least at the level of monitoring what
has been found thus far, and perhaps more heavily involved in evaluation
efforts themselves."
(4a) PANEL DISCUSSION:
It was decided to organize a panel discussion at San Antonio in January
1999. (This replaced a previous proposal for a contributed paper
session.) It was suggested that a written product result from the panel,
perhaps posted on MAA OnLine, but no final decision was made. The panel
session was subsequently accepted by the MAA, and as of June 4, the
description of the panel is as follows.
"Effect of Calculus Reform on Student Performance in Subsequent Courses"
Organized by:
Jack Bookman, Duke University
Susan Ganter, American Association of Higher Education
Herbert Kasube, Bradley University
Sponsored by CRAFTY
Description: CRAFTY recognizes that the evaluation of calculus reform
involves not only students' performance in the calculus, but also their
performance in subsequent courses. This panel will bring together
faculty who have spent time evaluating such performance as well as
(possibly) faculty from client disciplines to discuss how well students
who have completed a reformed calculus sequence perform in later
courses as well that have traditionally had a calculus prerequisite.
Panelists:
Herbert Kasube, Bradley University (moderator)
Judith Baxter, University of Illinois at Chicago
Jack Bookman, Duke University
Susan Ganter, Ammerican Association of Higher Education
James Hurley, University of Connecticutt
John Polking, Rice University
Norman Webb, Wisconsin Center for Education Research
(4b) CONTRIBUTED PAPER SESSION:
Martin Flashman submitted a proposal for a contributed paper session in
San Antonio entitled "Ready for Calculus: What does it mean?," and asked
if CRAFTY wished to sponsor the session. We agreed, but with 54 requests
for contributed paper sessions in San Antonio and room for only 13, this
proposal was ultimately not selected.
(4c) PANEL DISCUSSION:
After the Baltimore meetings Don Samll submitted a proposal for another
panel session devoted to calculus: "Forming A Crystal Ball for Calculus,"
and asked if CRAFTY would co-sponsor the event along with the NSF. The
CRAFTY chair readily accepted this invitation, and the panel session was
ultimately approved by the MAA.
"Forming A Crystal Ball for Calculus"
Organized by Don Small, U.S. Military Academy
Sponsored by the NSF and CRAFTY
Panelists:
Chris Arney, U.S. Military Academy (moderator)
Don Small, U.S. Military Academy
David Smith, Duke University
Frank Wattenberg, NSF
Paul Zorn, St. Olaf College
(4d) AERA/NSF REPORT ON EVALUATION IN CALCULUS REFORM.
Susan Ganter, who spent a year as an AERA Research Fellow at the NSF,
reported on the current status of her survey and compilation of
evaluation data for calculus reform programs. The hope is that at least
a subset of the CRAFTY committee will be able to view the report before
its final public release (possibly in the MAA Notes series). [As of June
5 we have not seen the report.]
(5) CLIENT DISCIPLINES INITIATIVE.
The purpose of this initiative is to increase awareness among members of
client disciplines of the reform efforts in undergraduate education
taking place in mathematics, and awareness among mathematicians of the
changes taking place in the client disciplines.
(5a) CONTRIBUTED PAPER SESSION:
On behalf of CRAFTY, Bill McCallum submitted the following proposal to
the Committee on Sessions of Contributed Papers, chaired by Elizabeth
Teles, for a contributed paper session at San Antonio. [I do not
currently know the committee's decision on this session --- I will update
everyone as soon as I have this information.]
"Enriching Mathematics Instruction via Outreach to Client Disciplines"
Submitted by Bill McCallum
Description:
The session would investigate the ways in which material from
disciplines that use mathematics can be used both to enhance
mathematical understanding, and to increase the usefulness of
mathematics courses for students not planning to major in mathematics.
The session would present model examples of how applications of
mathematics in other professions can be incorporated into undergraduate
mathematics courses.
We would invite people from engineering, science, economics, and
computer science to give examples of how they use mathematics, and
example of what sorts of things they expect their students to be able
to do. We would also invite mathematicians who have successfully
incorporated such material into their courses. Collectively the members
of CRAFTY have extensive contacts that would allow them to find
excellent representatives both from within mathematics and from client
disciplines. We are open to suggestions for joint organizers of this
session.
(5b) PANEL DISCUSSION:
On behalf of CRAFTY, David Lay submitted the following proposal for a
panel discussion at San Antonio. [I do not currently know whether or not
this session was placed on the MAA program --- I will update everyone as
soon as I have this information.]
"Linear Algebra and Differential Equations in Client Disciplines"
Organized by David Lay, University of Maryland, College Park
Sponsored by CRAFTY
Description: A distinguished panel of scientists from industry and
faculty from departments of computer science and engineering will
discuss the role of linear algebra and differential equations in their
respective fields. The goal of the session is to stimulate mathematics
faculty to make the content and approach of their linear algebra and
differential equations courses more relevant to the needs and interest
of their students.
Panelists: Still to be determined. More than a dozen contacts have
already been made in the San Antonio and Austin areas. There are some
promising leads to scientists at some of the high tech companies in
Austin.
(5c) PANEL DISCUSSION AT ASEE MEETING IN SEATTLE, July 1998.
The ASEE (American Society for Engineering Education) requested CRAFTY to
organize an extended panel discussion at their annual meeting in Seattle
this July. The title they proposed was "The Freshman Mathematics
Experience." Shelly Gordon organized the session. CRAFTY will be
represented by Martin Flashman and Wade Ellis. They will probably be
joined by Andy Rex, a physicist from the University of Puget Sound who
has been team-teaching a combined reform calculus / introductory physics
course.
(5d) "GENERIC" ARTICLE ON CALCULUS REFORM.
In order to most efficiently and effectively inform other disciplines
about current treads in calculus instruction, Shelly Gordon volunteered
to draft a "generic" article about calculus reform. The intention would
be to alter and expand upon this document whenever the chance arises to
place an article into a client discipline publication. When possible, a
response by a representative of the particular discipline would also be
included. Shelly has produced a draft for such an article and it has
been circulated to several CRAFTY members for comments. The hope is to
have a second draft ready for the CRAFTY meeting in Toronto (should there
be one).
(6) "AFTY" INITIATIVES: COLLEGE ALGEBRA.
On behalf of the College Algebra working group, Don Small (we refused to
let him leave CRAFTY...) submitted the following two proposals to the MAA
for inclusion in the San Antonio program. Both were accepted by the MAA.
(6a) PANEL DISCUSSION:
"College Algebra Reform"
Organized by:
Don Small, U.S. Military Academy
Linda Kime, University of Massachusetts at Boston
Sponsored by CRAFTY
Panelists:
Don Small, U.S. Military Academy (moderator)
Saudi Athanassiou, University of Missouri-Columbia
Kathi Heid, Pennsylvania State University
General Marshall, Huston-Tillotson College
Phil Quatararo, Southern University
(6b) POSTER SESSION:
"College Algebra Reform"
Organized by:
Sarah Bush, Wiley College
Don Small, U.S. Military Academy
Eugene Taylor, Grambling Statue University
Sponsored by CRAFTY
(7) "AFTY" INITIATIVES: LINEAR ALGEBRA & DIFFERENTIAL EQUATIONS.
The San Antonio panel discussion (5b), "Linear Algebra and Differential
Equations in Client Disciplines," is part of this project as well as the
Client Disciplines initiative. No other events were planned for San
Antonio. A number of other suggestions were made for CRAFTY actions in
this area:
* Put information and links to innovative LA and DE projects on the
CRAFTY web page Specific suggestions should be sent to David Lay.
* Help disseminate information about the West Point "7 into 4"
curriculum, perhaps with suggestions as to how it could be replicated
or adopted in environments different from West Point.
* There are some efforts underway to incorporate aspects of linear
algebra and differential equations into the secondary school
curriculum. We should become aware of these projects and form
connections with teachers involved. David Lay requested that names
of relevant high school contacts be sent to him.
(8) TULANE II: POSSIBLE CONFERENCE ON CALCULUS REFORM.
Much time at both CRAFTY meetings was devoted to this project. Summed up
in one sentence, the ultimate purpose of such a conference would be to
re-energize and refocus the calculus reform movement.
The fundamental question discussed at length was the scope of the
proposed conference. Bill McCallum provided a draft statement for a
conference whose scope was wider than just calculus. Such an expanded
view is justified since calculus does not sit alone, completely
independent of the rest of the curriculum, and that reform efforts are
underway in more subjects than just calculus. Moreover, a more civilized
and productive discussion might be possible if the conference does not
focus entirely on calculus reform, a hot-button for many people. An
informal name somewhat humorously suggested for a wider scope conference
was "Math Reform and the First Two Years" (MRAFTY??).
However, some members of CRAFTY, though sympathetic to the above
concerns, felt that broadening the scope much beyond calculus would lose
the sharp focus that is desired, thereby diluting the power of the
conference to significantly affect the direction of calculus reform.
Hence, for the second CRAFTY meeting, Bill Barker distributed a rewrite
of the McCallum draft, narrowing the scope of the proposed conference
back to just calculus
Susan Ganter observed that a narrow scope might be adopted for the first,
smaller invitational conference, while the broader scope might be more
appropriate for the second, larger general participation conference.
After much discussion, a majority of those present at the meeting opted
for the narrower focus (at least for the initial conference), but not
without some misgivings. Until a final statement defining the conference
is adopted, the question of the appropriate scope will likely be further
debated.
A second draft statement has been constructed based on the Baltimore
discussions. It has been circulated separately and is also attached as
an Appendix to these minutes. It will hopefully form the basis for
further discussions in Toronto in July and via e-mail during the summer
and fall.
Suggestions and comments should be sent to both Bill Barker and Bill
McCallum. Many have already been received and will be incorporated
shortly in an updated version of draft two. In particular, how do we
move from the talk stage to the action stage?
(9) CRAFTY/MER/AMS SPECIAL SESSION AT SAN ANTONIO.
Once again CRAFTY will co-sponsor a portion of the MER (Mathematicians
and Education Reform Forum) Special Session at San Antonio. CRAFTY will
co-sponsor and organize a mini-session of three or four twenty-minute
talks, about a theme which has yet-to-be determined (last year the mini-
session was on calculus reform). This is a well-attended special
session, providing a fine opportunity to reach a large audience.
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A draft proposal for consideration by CRAFTY
June 1, 1998
TULANE II
An Invitational Conference on Trends in Calculus Instruction:
What has been learned? What comes next?
A composite of ideas gathered during the
AMS/MAA Joint Meetings, Baltimore, January 1998.
A first draft was developed by Bill McCallum.
The current draft was assembled by Bill Barker.
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** Comments should be sent to both Barker and McCallum. **
** barker@bowdoin.edu and wmc@math.arizona.edu **
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REASONS FOR THE CONFERENCE
* The initial collection of NSF funded calculus projects are now mature,
some producing commercially successive textbooks, others resulting in
programs with more local impact. Moreover, the startup rate for new
projects has markedly decreased during the past five years, leading to a
perception that the current period of revision and experimentation in
calculus instruction is ending. However, at the same time there is a
widespread hope that the knowledge and experience gained from the initial
projects will fuel a second wave of development, improving upon what has
succeeded, discarding what has failed, and forging into new directions.
Tulane I provided a focus for the energy that led to the current period
of calculus activity; Tulane II would provide a focus for the "Second
Wave".
* The effectiveness of the past ten years of calculus projects has been
much debated in the mathematics community. Tulane II would be a forum in
which the issues of the debate could be thoughtfully examined, drawing
proponents of diverse viewpoints into the shaping of future directions of
calculus innovation and experimentation.
* The NSF funded AERA report on the status of calculus innovation
nationwide is nearing release. It provides much data for reflection,
analysis, and use as foundations for further studies. Tulane II would
draw attention to the report and to its value in the efforts to
strengthen calculus instruction.
* During the past decade much knowledge has been gained on how students
learn mathematics, both from innovative curriculum projects and from
research in mathematics education. Tulane II would build on these
developments, emphasizing the importance of systematic reference to such
knowledge when assessing current teaching practices and when designing
new instructional methods.
GOALS
* Foster Respectful Dialogue. Move the national discussion of calculus
instruction to a more constructive level by recognizing shared goals,
identifying and articulating differences in methods and philosophies, and
retaining a respectful and cooperative tone by acknowledging the common
desire of all involved in the debate to provide the best possible
instruction in calculus.
* Reflect and Refocus. Assess the changes that have taken place in
calculus instruction during the last ten years and identify those
instructional issues most widely recognized as in need of continued
attention and improvement.
* Emphasize Research. Analyze statements of belief and opinion against
evaluations of instructional projects and, more generally, against the
best available research on how students master mathematical reasoning.
Determine areas and topics in need of further evaluation and research.
* Increase Involvement. Broaden the collection of voices heard in the
national debate on the teaching of calculus, and motivate more
instructors and institutions to analyze their calculus programs.
* Plan the General Participation Conference. Define the purpose, goals,
and organization for a larger, general participation conference the
following year. Generate discussion and interest during the period
leading up to the larger conference.
ORGANIZATION
* A three day invitational conference in 1999.
* A five person CUPM committee to nominate participants for the
conference.
* Thirty-five participants representing a wide diversity of views.
Include a number of researchers in mathematics education.
Only people who respect and consider other viewpoints.
Representatives from the client disciplines.
* Participants would circulate discussion papers prior to the start of
the conference.
* A publication would result, based on the initial papers and the
subsequent conference discussions.
* Funded by an appropriate agency. (Is the NSF the best choice?)
* To be followed up by a general participation conference in 2000
A SAMPLE OF TOPICS FOR DISCUSSION
* What does evaluation of the calculus projects and, more generally,
research in mathematics education, tell us about the effectiveness of the
various pedagogical techniques used in calculus instruction? In
particular, what methods are best at aligning the "achieved curriculum"
with the "intended curriculum"? Where is more research needed to better
address these questions?
* What has been learned about the best instructional practices for
traditionally disadvantaged students? Have the innovations of the past
decade affected such students in any significant positive manner?
* What do "high standards" mean for calculus instruction, and how can
such "high standards" be achieved?
* What is the appropriate level of mathematical formality in calculus
instruction? More generally, what are the most effective ways to present
mathematical reasoning in calculus instruction in order to prepare
students for more advanced mathematical work?
* How can instructors both serve students in other disciplines and
maintain mathematical integrity in calculus instruction? How can useful
dialogue with the client disciplines be encouraged and maintained?
* What is the appropriate level and role of technology in calculus
instruction?
* How can the mathematics community most effectively support those
faculty members and institutions interested in analyzing and improving
their instruction of calculus? How can more faculty members and
institutions be convinced of the need to examine their approach to
calculus instruction?
* Many of the instruction methods used in the current calculus projects
are time and labor intensive. Do the results of such methods justify the
added costs? Is it realistic or sensible to encourage increased
institutional funding to support such methods?
* Many of the innovative calculus materials developed during the last
decade have not found permanent homes with commercial publishers. How
can these materials be best preserved and disseminated for further
development?
Please send suggestions for improvements and comments to Martin Flashman:flashman@axe.humboldt.edu