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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).


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)

Committee members:  
   Bill Barker (Chair), Wade Ellis, David Lay, Bill McCallum
   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 

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 

  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 

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 

[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).   


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 

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   
 Articulation of
 calc/la/de reforms  4       5   3                       5

   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
(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  

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
August 1997

William Barker    1/00   
Chair                             Yale University
                                  P.O. Box 208283, 
                                  New Haven, CT  06520-8283
                                  (203) 432-7055

Karabi Datta      1/99  
                                  Northern Illinois University
                                  DeKalb, IL  60115-2854

William Davis     1/98  
                                  Ohio State University
                                  Columbus, OH  43210

Wade Ellis, Jr.   1/98  
                                  West Valley College
                                  14000 Fruitvale Avenue
                                  Saratoga, CA  95070-2200

Susanna Epp       1/00
                                  DePaul University
                                  2219 North Kenmore
                                  Chicago, IL  60614-3504

Martin Flashman   1/99
                                  Humboldt State University
                                  Arcata, CA  95521

Sheldon Gordon    1/00
                                  61 Cedar Road
                                  East Northport, NY  11731-4128
                                  (Suffolk Community College)

Margret Hoft      1/99
                                  University of Michigan, Dearborn
                                  Dearborn, MI  48128-1491

Herbert Kasube    1/99
                                  Bradley University
                                  1501 W. Bradley Avenue
                                  Peoria, IL  61625-0001

Linda Kime        1/00
                                  University of Massachusetts at Boston
                                  Harbor Campus
                                  Boston, MA 02125

David Lay         1/00
                                  University of Maryland, College Park
                                  College Park, MD  20742-0001

William McCallum  1/00
                                  University of Arizona
                                  Tucson, AZ  85721

Donald Small      1/98
                                  U.S. Military Academy
                                  West Point, NY  10996

August 1997

Jack Bookman  
Sue Ganter    
Bill Haver    
Deborah Hughes-Hallett
Don Kreider      
Rafael Martinez-Planell
David Smith      
Elizabeth Teles
Tom Tucker