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Reform and The First Two Years
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CUPM Subcommittee on
Calculus Reform and the First Two Years (CRAFTY)
Below you will find detailed minutes of our meeting in Atlanta along
with comments added since that time. Also attached is a complete
summary of the questionnaire results you furnished concerning interest
in our various initiatives.
I welcome your comments on these minutes (and will circulate them to all
committee members unless requested otherwise).
Bill
CUPM Subcommittee on
Calculus Reform and the First Two Years (CRAFTY)
Minutes, Atlanta, Saturday, August 2, 1997, 1:00pm - 3:30pm
Notes produced by Bill Barker, August 20, 1997
(Edited by M. Flashman for www publication)
Attendance.
Committee members:
Bill Barker (Chair), Wade Ellis, David Lay, Bill McCallum
Visitors:
David Smith (Chair Emeritus), Rafael Martinez-Planell (NSF)
(1) Introduction.
The Chair started the meeting by reminding the members of the original
charge to the committee: to monitor ongoing developments and to make
general recommendations concerning the first two years of collegiate
mathematics. He also suggested that committee members think about how
to maximize the impact of our efforts:
Events at meetings reach only a limited number of people.
Publications reach a wide audience but are time consuming to produce.
Sponsoring or organizing conferences can take a great deal of time.
Recommendations to MAA leadership and committees can be appropriate.
We should think of ourselves as a conduit for information and a catalyst
for action.
(2) "AFTY" Initiatives.
A discussion ensued of what CRAFTY can and should do about the non-
calculus portion of its mandate. It was observed that much is being
done in the other areas by other groups --- e.g., in linear algebra and
differential equations there are groups engaged in developing and
disseminating reform materials --- and that perhaps our most important
function is to monitor these activities and help disseminate information
about them to a wider audience.
In keeping with this general philosophy, we decided to take the
following actions:
1. We will ask specific CRAFTY members to monitor education
developments in the relevant subjects, with the charge to report their
findings to the committee.
2. Bill Barker will discuss with Martin Flashman, the CRAFTY
WebWizard, the possibility of establishing links on the (developing)
CRAFTY web page to sites with information about educational innovations
in the relevant areas. The CRAFTY links might also contain paragraph-
length descriptions of the nature of the contents of the linked sites.
Although CRAFTY's role in the college algebra reform was not discussed
at length in our meeting, Linda Kime's written comment is relevant to
these minutes:
"[My] major interest would be in working on the college algebra reform
issues. I would be willing to undertake a major effort on this
initiative. I am interested in it from the point of view of what is
happening in the arena of courses that involve large numbers of
undergraduates who will not in general be going on in mathematics. I'd
like to know what impact reform is really having on these courses, on
the impact of what seems to be a bifurcation of these courses into
terminal and non-terminal parallel courses (are we 'opening windows only
to close doors' on future career paths). Are the all the 'reform' ideas
being implemented only in terminal courses?"
Further discussion will take place on this issue in Baltimore.
(3) CRAFTY/MER/AMS Calculus Reform Special Session at Baltimore.
The Committee members voiced no opposition to the revised description of
the session, as reproduced below:
What should be the guiding principles and goals of the revision of
calculus instruction? What objective measures do we have for success
in calculus instruction? And can honest and open debate on these
questions be conducted in an atmosphere of cooperation and mutual
respect?
The Chair reported that Deborah Hughes-Hallett had accepted our
invitation to speak at the session, leaving us with two more slots to
fill. He further suggested that we ask XXX and XXX to fill these slots. No
opposition was voiced to these choices.
[UPDATE: XXX was subsequently invited but had to decline due to other
commitments. I have decided to invite XXX to fill this slot, partially on
the basis of his article xxx Another person who I intend to consider is
XXX (see the next item) --- he could give a very good talk about research
in mathematics education as related to calculus reform.]
(4) CRAFTY Panel on Research in Mathematics Education at Baltimore.
XXX was invited but cannot participate (he has to leave
Baltimore before the panel takes place). XXX has been invited
but has yet to reply. (However, we have heard that XXX's health is
not good, and this may prevent him from making a trip to Baltimore from
XXX). No other people have as yet been invited.
Suggestions were then solicited for other invitations. A number of
names were offered, but the consensus was to first approach the
following people:
Names deleted
[UPDATE: XXX has tentatively accepted. According to XXX the
only possible problem is financial. He also had some suggestions of
interesting ways to structure the panel. Hence we are corresponding
about who else should be invited. Stay tuned for further details.]
(5) CRAFTY Web Page.
As mentioned above in (2), the Committee would like the web page to
contain links to other sites with information on educational innovations
in relevant areas. David Smith volunteered to help with this task.
I will add my own written comments here:
"I think it is a valuable undertaking, even if we keep it relatively
simple (i.e., CRAFTY minutes, pointers to other sources for calc reform,
etc.). However, it needs to be easily found. One way is to have it
accessible via a button in the MAA home page. Another is to have it
easily locatable via the standard search engines (I have no idea how
this is done). Perhaps the way to proceed is to simply set up the
simplest home page as a start (making sure that it is accessible as
noted above), and then see what other folks suggest for additions (or,
better yet, are will to add themselves)."
(6) Client Disciplines Initiative.
Background: In 1995 Shelly Gordon made a preliminary proposal to the
NSF 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. The following specific actions were suggested:
1. The organization of panels, primarily of mathematicians, at
national meetings of each of the client disciplines.
2. The organization of panels, primarily composed of members of the
client disciplines, at the national meetings of mathematics
organizations.
3. A series of articles written by mathematicians for publication in
the journals of client disciplines.
4. The production of a volume in the MAA Notes series composed of
articles from the client disciplines describing the changes that
are taking place in those fields.
At the time of submission Jim Lightbourne of the NSF was very
supportive, but Shelly's workload increased and he was unable to pursue
this initiative. Shelly recently shared the proposal with CRAFTY
members, who have been enthusiastic in their interest in the project.
Seven months ago in Baltimore CRAFTY (i.e., Shelly) organized a panel of
members from client disciplines that was very well received. More
recently, CRAFTY (i.e., Shelly again) organized a panel of
mathematicians at a national engineering meeting --- this too was well
received.
Atlanta Discussion and Action: The assembled CRAFTY members continued
to be supportive of this initiative, though they felt that commitment at
this time to the production of an MAA Notes volume is premature.
However, in support of this initiative, it was decided that two events
will be organized in San Antonio in January 99:
1. "Linear Algebra and Differential Equations in the Client
Disciplines," a panel consisting of members of the client disciplines
who would describe the uses of linear algebra and differential equations
in their respective fields. David Lay agreed to coordinate the
organization of this panel.
2. "Enriching Instruction via Outreach to the Client Disciplines," a
contributed paper session featuring successful examples of course
enrichment via contacts with and contributions from the client
disciplines. (The committee decided NOT to use Wade Ellis's suggested
title of "Contact with the Aliens".) Bill McCallum agreed to coordinate
the organization of this session.
Further discussions on this initiative will take place in Baltimore.
(7) Tulane II --- Possible Conferences on Calculus Reform.
A significant amount of time was devoted to discussing whether or not
CRAFTY should encourage and/or take a leadership role in the
organization of a "Tulane II" conference on the future of calculus
reform. Most members of the committee are extremely interested in this
initiative but need to be convinced that the vision and goals of such a
conference are sufficiently developed and compelling to justify
undertaking such a large project --- we don't need a "nostalgic
reunion." If we cannot solidly convince ourselves of the value of such
a conference we will hardly convince others.
The discussion started with a summary of the conversations Bill Barker
had the previous week with Deborah Hughes-Hallett, one of the
originators of the Tulane II idea. The original idea, as developed in
San Diego by a group headed by Deborah and Bill Haver, was described
earlier in the CRAFTY minutes for its San Diego meeting. As reported by
Deborah, no further actions on this initiative have taken place since
San Diego. In particular, no group was formed to continue planning for
such a conference, leaving the way open for CRAFTY to assume a
leadership role in such an effort.
The ultimate purpose of a Tulane II conference would be to re energize
and refocus the calculus reform movement. Translated into specifics,
this should include the following goals:
** Lessen the rancor that has developed in the current discussion of the
pros and cons of calculus reform, channeling the debate into more
productive directions. The discussion should be more inclusive of a
variety of viewpoints and more professional in its tone.
** Move the calculus reform debate to a higher intellectual plane. With
a few notable exceptions, people who developed calculus reform materials
did not have a theoretical basis for their pedagogical and curricular
revisions other than their own instinctive beliefs as informed by their
teaching experiences. More is now known about how students learn and
think about mathematics. This knowledge should be used to analyze the
various approaches to calculus instruction, both traditional and reform.
** Motivate instructors who are uncommitted to the current calculus
reform movement but who could be influenced to analyze and evaluate
their teaching of calculus. Many should form a major part of the
vanguard for the next level of calculus reform.
** Preserve materials that have been developed during the first stage of
the calculus reform movement. This is an increasing concern in view of
the large number of reform textbooks which have been dropped by
publishers during the past 12 months.
An additional rationale for a national calculus reform meeting at this
time is that a comprehensive report on all available calculus reform
evaluations is in preparation by AERA Research Fellow Sue Ganter for
release this fall (see the next item). Such a report would furnish a
solid factual basis for informed discussion of calculus reform issues
The current thinking is for the Tulane II meeting to be small and
invitational, leading to a second larger, general conference. (This was
the case with the original Tulane event.) Participation in the first
meeting might involve the submission of a paper beforehand and the
reading of all such submitted papers by all the participants before the
meeting. The meeting would then be an in-depth discussion of the
important issues rather than a collection of individual presentations
(though there certainly would be some presentations). One specific goal
of the first meeting would be to plan for the follow-up conference (if
indeed it is decided that such a conference is warranted).
Bill McCallum and Bill Barker will work with these ideas to draft a
coherent statement for the purpose, goals, and organization of a
potential Tulane II conference series. Input by other committee members
will be most welcomed!
(8) Evaluation of the Effectiveness of Calculus Reform.
Time was short when we reached this item so the discussion was not as
detailed as desired. There was some debate as to the importance of data
in furthering calculus reform. One view, advanced by Wade Ellis, was
that data will not further calculus reform for even if data confirmed
the effectiveness of reform, the reform programs are simply viewed by
many instructors as too time consuming for adoption. (Martin Flashman
echoed this sentiment in a written comment: "My own experience leads me
to believe that choices, decisions, and changes are not based on the
results of such studies, but on more or less emotional responses to
information and contexts. The most useful tools for change help prepare
people to be open to change.") On the other hand, Tom Tucker (CUPM
Chair who entered our meeting at this time) observed that since data on
the poor results of traditional calculus instruction were used to
justify the need for a calculus reform movement; it would be
inconsistent to not examine the data surrounding the reform projects to
see if the original concerns have been addressed. Moreover, as Bill
McCallum observed, the existent data show that the reform programs are
clearly no worse in their outcomes than traditional programs, proving
that "calculus reform is NOT a disaster." We may hope to see a more
positive outcome, but that at least puts the lie to the claims of the
more emotional critics of calculus reform.
However, the strong feeling of those present was that CRAFTY should be
heavily involved in evaluation efforts, at least at the level of
monitoring what has been found thus far, and perhaps more heavily
involved in evaluation efforts themselves.
It was noted that Jack Bookman, the primary evaluator for Duke's Project
CALC, was interested in having CRAFTY as a co-sponsor for a proposal to
the NSF to evaluate how calculus reform graduates fare in subsequent
courses. Moreover, Bill Barker and Wade Ellis would be meeting on
Monday morning with Sue Ganter, an AERA Research Fellow currently housed
at the NSF while on leave from WPI, who has been conducting an
exhaustive survey and compilation of all the available evaluation data
for calculus reform programs. She would like input from CRAFTY on her
forthcoming report (a preliminary description was circulated earlier to
committee members), clearly an item of direct relevance to the current
discussion.
[UPDATE: The meeting with Sue Ganter on Monday was extremely valuable.
The report she is organizing will be of great value as it stands and
will point the way to where additional evaluation research is needed.
Sue was highly supportive of a Tulane II conference and was willing to
see her report used in a high-profile way as one rationale for having
such a conference at this time.]
(9) Other Items.
Having raced through the crammed agenda at a break-neck pace and still
going over the allotted two hours, the Committee members all agreed that
having two meetings at the January MAA/AMS meetings in Baltimore would
be advisable (respond quickly if you disagree).
** VOLUNTEER QUESTIONNAIRE / SUMMARY OF RESPONSES
Here are the results of the "Volunteer Questionnaire." In a memo to
follow shortly I will use these numbers to assign various committee
members to various initiatives. Let me know if you wish to change your
numbers!
Interest/willingness to take on responsibility for our various
initiatives. The 1 to 5 scale means the following:
1 = not interested in spending my time on this initiative
3 = willing to work on this initiative
5 = wish to put in a major effort on this initiative
BB KD WE SE MF SG MH HK LK DL BM
Calc Reform Session 5 5 5 2 3 3 3 5 - 2 3
Math Ed Panel 5 1 3 5 1 1 1 4 - 3 3
TULANE II 5 3 - 3 5 5 3 5 - 2 5
Client Disciplines 4 1 3 4-5 2 5 5 2 - 4 5
Eval of Calc Reform 4 2 3 3 3 2-3 1 5 - 2 3
College Algebra 2 4 5 2 3 5 1 3 5 1 3
CRAFTY Web Page 4 1 1 1 5 1 1 1 - 1 3
Other?
Articulation of
calc/la/de reforms 4 5 3 5
IDENTIFICATIONS:
BB --- Bill Barker KD --- Karabi Datta
WE --- Wade Ellis SE --- Suzanna Epp
MF --- Martin Flashman SG --- Shelly Gordon
MH --- Margret Hoft HK --- Herb Kasube
LK --- Linda Kime DL --- David Lay
BM --- Bill McCallum
** OTHER POSSIBLE AREAS FOR ACTION **
(Listed so that we don't lose sight of them.)
Outreach to traditionally black institutions
Distance learning and "electronic academic systems"
Reviews of calculus reform materials
MF: This is a project ... which I feel is particularly
important.... The community needs easier access to better
information about materials, both from a common reviewer's view and
the views of those who have used the materials directly in
instruction.
Multivariable Calculus and Linear Algebra
MF: Reform efforts here need much more articulation, both for
pedagogy, technology, and content/applications. We should be
supporting greater communication amongst the developers here.
Workshop on Change.
MF: I think a workshop on organizing/planning change similar to
the AMATYC Crossroads workshops might be very useful. Faculty need
some tools in the dynamics of change as well as in the kinds of
change that are happening.
CUPM Subcommittee on
CALCULUS REFORM AND THE FIRST TWO YEARS (CRAFTY)
August 1997
William Barker 1/00 bbarker@math.yale.edu
Chair Yale University
P.O. Box 208283,
New Haven, CT 06520-8283
(203) 432-7055
Karabi Datta 1/99 dattak@math.niu.edu
Northern Illinois University
DeKalb, IL 60115-2854
William Davis 1/98 davis@math.ohio-state.edu
Ohio State University
Columbus, OH 43210
Wade Ellis, Jr. 1/98 wade_ellis@wvmccd.cc.ca.us
West Valley College
14000 Fruitvale Avenue
Saratoga, CA 95070-2200
Susanna Epp 1/00 sepp@condor.depaul.edu
DePaul University
2219 North Kenmore
Chicago, IL 60614-3504
Martin Flashman 1/99 mef2@axe.humboldt.edu
Humboldt State University
Arcata, CA 95521
Sheldon Gordon 1/00 sgordon@ccmail.sunysb.edu
61 Cedar Road
East Northport, NY 11731-4128
(Suffolk Community College)
Margret Hoft 1/99 mhoft@umich.edu
University of Michigan, Dearborn
Dearborn, MI 48128-1491
Herbert Kasube 1/99 hkasube@bradley.bradley.edu
Bradley University
1501 W. Bradley Avenue
Peoria, IL 61625-0001
Linda Kime 1/00 kime@umbsky.cc.umb.edu
University of Massachusetts at Boston
Harbor Campus
Boston, MA 02125
David Lay 1/00 lay@math.umd.edu
University of Maryland, College Park
College Park, MD 20742-0001
William McCallum 1/00 wmc@math.arizona.edu
University of Arizona
Tucson, AZ 85721
Donald Small 1/98 ad5712@exmail.usma.edu
U.S. Military Academy
West Point, NY 10996
FRIENDS AND SUPPORTERS
August 1997
Jack Bookman bookman@math.duke.edu
Sue Ganter sganter@nsf.gov
Bill Haver wehaver@vcu.edu
Deborah Hughes-Hallett dhh@math.harvard.edu
Don Kreider Donald..L.Kreider@Dartmouth.edu
Rafael Martinez-Planell rmartine@nsf.gov
David Smith das@math.duke.edu
Elizabeth Teles eteles@nsf.gov
Tom Tucker ttucker@center.colgate.edu