CRAFTY Minutes of Baltimore meetings, January 7 & 11, 1998

Below you will find (draft) minutes of the CRAFTY meetings in Baltimore 
along with updates on developments since that time.


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


Committee members:  
   Bill Barker (Chair), Jack Bookman, Karabi Datta, Wade Ellis, 
   Susanna Epp, Susan Ganter, Shelly Gordon, Herb Kasube, David Lay, 
   Bill McCallum
   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.


The Chair reminded all present of the two CRAFTY events taking place in 

  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


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. 


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:


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."

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. 

        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

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.

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
        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

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.]


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.

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 

  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 

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 

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 

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).  


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.


"College Algebra Reform"
  Organized by:
   Don Small, U.S. Military Academy
   Linda Kime, University of Massachusetts at Boston
  Sponsored by CRAFTY
        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


"College Algebra Reform"
  Organized by:
   Sarah Bush, Wiley College
   Don Small, U.S. Military Academy
   Eugene Taylor, Grambling Statue University
  Sponsored by CRAFTY

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.


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 

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?


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.


A draft proposal for consideration by CRAFTY
June 1, 1998

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.

** Comments should be sent to both Barker and McCallum. **
**  and     **


* 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 

* 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.


* 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.


* A three day invitational conference in 1999.

* A five person CUPM committee to nominate participants for the 

* 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


* 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 

* 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 

Please send suggestions for improvements and comments to Martin