Report for IMPAC Northern California Meeting, January 28, 2005
Martin Flashman, Lead Faculty
Based on Minutes by Robert Hasson
[A list of those attending appears at the end of this report.]
About CAN: CAN is the project for common course numbering
statewide. Course descriptors are attached to the CAN numbers, so
that there is no doubt that a course transferred from a community
college will be accepted as an equivalent CSU course
CAN numbers are used by the community colleges and the CSU’s for
articulation purposes. The UC’s do not use CAN, but they do see
them in student records.
The present CAN descriptors are like catalog descriptions, which means
they are short and lacking detail. CAN is asking disciplines to
provide the list of topics, course outlines, to go with the CAN
descriptors. The purpose is to make the descriptors more specific.
Last year IMPAC recommended a revised descriptor for linear
algebra. CAN is about to receive this descriptor for
consideration and implementation.
A question and proposal: Do we need a special conference,
perhaps outside of the IMPAC meetings, for people teaching the courses
to discuss descriptors and objectives and recommend revisions to
CAN? Hopefully the result would be descriptors that are more
specific and more up to date. About two years ago a revision for
the current descriptors was initiated but was never brought to
CAN for final adoption, so the current Mathematics descriptors in
are not of recent vintage,.
About ASSIST: ASSIST is the website that offers information about
articulation agreements for transfer students. Students can find
there the articulation agreements between the community colleges and
the CSU’s and UC’s. ASSIST also shows the various majors offered
by the universities.
Last year we recommended that ASSIST offer easy access to the
university web sites and departmental web sites. ASSIST decided
the most complete proposal for this feature would be too hard to
maintain, but has made a substantial effort to provide more direct
information connected to majors.
In the current beta version layout of ASSIST related to majors, the
display of the majors at the universities is confusing. It might
be a good idea to have a discipline consultant for each major page.
LDTP: LDTP is the CSU project developing lower division
transfer patterns for the CSU’s. LDTP is now written into state
law. Students who follow the LDTP patterns get a preference for
transfer to a selected CSU campus or campuses. Such a preference
means much less than it sounds, however. The preference doesn’t
help at impacted campuses, and it is unnecessary at non-impacted
campuses. LDTP will target students through the community college
counselors. It was suggested that information about the LDTP be sent to
the CC Mathematics Departments as well.
CSU and Teaching Credentials: The CSU's are developing tighter
secondary credentialing programs (the degree of tightness differing
from CSU to CSU) to be completed in a total of four years without an
additional year for “credential work.”. As a result, at the
community colleges students wishing to follow these more intense
programs must schedule their courses with more care.
In the new secondary integrated programs the credentialing courses and
activities are integrated into the BA with at most one extra semester
needed. (at least at CSU Sacramento)
Liberal studies mathematics programs can no longer be used to waive
examinations for the general elementary teaching credential. This
means that the enrollments in such courses can be expected to be lower
as students take more traditional majors and prepare for the exams
without more general mathematics coursework.
Proof and Bridge Courses:
Background: UC Berkeley’s issues can be seen as an example.
Berkeley has a lot of transfer students, about 40% of the graduating
class in mathematics. It also has several hundred math
majors. The representatives from Berkeley see two problems in
First, some of the transfer students seem to have a lot of trouble
adjusting to the heavy workload at Berkeley. Are the community
colleges demanding enough?
Second, a lot of the transfer students are having trouble adjusting to
the intensive proof nature of upper division math courses at
Berkeley. The Berkeley representatives are concerned that
students are not learning enough proof skills in their work prior to
transfer to help them to survive in the math major. Also sixty percent
of the 500-600 UC Berkeley majors are applied mathematics; and large
related majors such as economics, physics, biological sciences, areas
of computer science, statistics, and operations research are using what
is considered upper division mathematics. Most of these majors require
the same two years of lower division math with theoretical applications
requiring upper division problem solving/writing skills.
This is really part of a larger discussion about the transition from
lower division math courses to upper division courses for majors, a
discussion that includes all the CSU's and UC’s.
Many CSU's offer a bridge course in proof covering issues related as
well to logic and sets as a prerequisite to upper division work in
mathematics. The community colleges don’t offer such a course
because they don’t have enough math majors for an adequate level of
enrollment. UC Berkeley does offer such a bridge course but it is
not required of its native students as these students appear to pick up
proof skills in the lower division mathematics at Berkeley.
At last year’s Northern California IMPAC meeting there was some
sentiment for using the Discrete Mathematics course as the course in
which proof skills would be learned at the community colleges.
Most community colleges now offer a Discrete Math course as a service
to computer science majors, but the content is good for math majors,
too. However, this idea did not survive the state meeting
recommendations primarily because those Universities that offer these
bridge course did not feel confident that there was enough emphasis on
proof writing in the discrete mathematics courses..
The community college representatives were unclear on what they could
do. In a typical calculus class of thirty students at a community
college only one or two students will be math majors, so it is hard to
fashion such courses around the specific needs of math majors. This is
similar to populations of the calculus courses at the CSU’s as well.
Also, it was unclear to the community college representatives how
students are taught proof skills in Berkeley’s lower division math
courses, so they weren’t sure what to try to emulate.
Some felt that communication is a major part of this issue. The
community colleges need better communication with the UC's and the
CSU’s. People offered several ideas for bringing this
about. There could be a regional math day offered by the
universities. One idea was that a UC or CSU could host a meeting
with community college, CSU, and UC faculty. Such a meeting could
rotate between campuses. Students could attend such meetings to
learn more about mathematics, transferring, and see the university
Items from Last Year’s Report:
Course recommendations: The recommendation for the linear
algebra CAN descriptor has the course going more into the structural
aspects of the course (when is something a vector space or not, when is
something a linear transformation or not, etc.). The old
descriptor mentions little about structural aspects. The
recommendation will be presented to CAN soon.
The Math for Managers discussion: At last year’s northern
IMPAC meeting the business people wanted to put together a course that
would essentially combine business calculus and finite math into one
course to replace the traditional two-course requirement.
This idea was modified at the state meeting so that a new “Math for
Managers” course would cover the core areas of finite math plus a very
short discussion of differentiation and integration. Further
discussion of this course is on hold while the new CAN procedures are
coming on line. In parallel it is clear that at some CSU's
business students need a more rigorous grounding in calculus than the
proposed “Math for Managers” course would provide. These schools
will continue to require both Business Calculus and Finite Math.
Also being discussed are the needs of business majors for a required
Elementary Statistics course (or sequence of two courses). It seems
clear that this course should cover regression and hypothesis testing,
but can downplay probability.
The bridge course discussion: The annual report offered a number
of recommendations related to a bridge course. The universities
should offer it in the summer, perhaps as a distance learning
course. With funding from a grant, a consortium of universities
and colleges might offer a summer program on proofs plus undergraduate
research. Students could be recruited from the community
colleges, and a stipend would be offered to the students.
We came up with more ideas. The UC's and/or the CSU's could offer
workshops on styles of proof, learning to prove, and course experiences
that promote the learning of proof. The possibility of involving
MSRI (possibly with solicited NSF support) in these workshops was
suggested, if it could be set up there.
Also it would be useful if someone would put together a report based on
the departmental web sites of who is teaching the bridge course
and what are the course syllabi for these courses. Cindy
Stubblebine and Sean Jackson volunteered to do this. [2-18-05 update:
Cindy has assembled a report listing bridge courses with links to their
descriptions. This report will be posted at the Math- IMPAC web page.]
Finally, it would be good to gather reports on experiences in teaching proof so we can all see what works and what doesn’t.
Computer recommendations for the math major: The UC
Berkeley representatives said it would be great if students were
exposed to a computer language. They strongly recommend C++,
Matlab, or just about anything else. With knowledge of a computer
language a student has a better chance to get research internships and
In Berkeley’s courses, a computer language is used only in the course
in Numerical Analysis, but this course is required for applied math
majors – 60% of Berkeley’s math majors.
At CSU Sacramento some of the teachers of statistics use software in
the course, generally Minitab. The use of Mathematica is
beginning to happen in some other courses.
At Humboldt State math majors are required to take C++, but other
programming languages are acceptable. Students use the language
in Numerical Analysis and Number Theory. Professors in some
courses use Matlab. In calculus, the freeware program WINPLOT is
used in two and three variable calculus.
At this point in time IMPAC funding is less than it was and may even
peter out completely at some time in the future. We used to have
four regional meetings each year, but now we are down to two.
Should we arrange meetings outside of the formal IMPAC
conferences? Possible venues are the annual CMC^3 meeting in
Monterey or the annual Northern California/Nevada/Hawaii MAA meeting,
usually held at a San Francisco Bay Area college or university.
If IMPAC disappears next year (a possibility) then a meeting is still
needed to keep the community college-CSU-UC dialog going. The
universities have a responsibility to give feedback to the community
colleges about transfer and to inform the community colleges about
changes. The community colleges have a responsibility to seek
such feedback and act on it.
Professor College of San
Flashman, Martin Lead Faculty
Positas College firstname.lastname@example.org
Professor College of
San Mateo email@example.com
Instructor Las Positas
Jackson, Shawn Faculty
West Hills College
Keune, Cynthia Instructor
Las Positas College
Loukianoff, Victoria Faculty
Pauling, Catherine SAO
Ramachandran, D. Chair
Stubblebine, Cynthia Instructor
Faculty City College of San
Wagener, Kristine Faculty
Las Positas College
Woo-Hoogenstyn, Yoly Articulation
UC San Diego
Yokoyama, Kevin Chair
Redwoods, College of