|
Mathematics
Marshall Cates, Lead Discipline Faculty
CSU Los Angeles
Summary of Identified
Issues
Four areas of concern arose in nearly every meeting:
1. The level of differential equations and linear algebra,
which is sometimes upper division and sometimes lower division.
2. An alternative to IGETC for science/math/engineering
majors.
3. The need for early warning and informal
contacts between community colleges and four year institutions
whenever curriculum changes are planned.
4. The need for a description for discrete
mathematics, a course of great interest for Computer Science.
5. A CAN conference for mathematics.
6. A need for advice to students and counselors.
Identify Trends/Future
Directions
1) Attention needs to be paid to service courses in mathematics.
This is an area that we need to work with CAN to address.
We see this as the next area that needs clarification.
2) Business calculus is losing favor and
is being replaced by finite mathematics or statistics. Usually,
the statistics course taken is not from the Mathematics Department.
Comments from Statewide
Meetings and the General Field.
1) The Computer Science faculty presented their need for a
course in discrete mathematics. Their professional organization
had adopted a list of topics for such a course. At a joint
meeting between mathematics and computer science, the design
of this course was debated. We note that the prerequisite
sets the level of the class. After reviewing the CS CAN descriptor
for discrete mathematics, several community college discretions
and recalling past discussions with CS, we believe there is
a need for two CAN descriptors for discrete mathematics. We
called the one needing calculus Discrete Structures. This
again demonstrates the need for a CAN conference.
2) We continued the discussion on the desirability
of stressing "proofs" at the community college level.
The most likely places within the curriculum are in discrete
mathematics and in linear algebra.
3) Much time was spent on the perfection
of two "advice" letters to be sent to community
college students and counselors. We hope IMPAC will adopt
these letters and undertake their distribution. We ask that
every participant in this year's discussions be given the
opportunity to comment on the letters; it is attached as Appendix
A and appears on the IMPAC Web site.
4) Geometry is listed a prerequisite for
several of the beginning mathematics classes, yet most four-year
institutions do not have a separate geometry class. This presents
problems that need to be addressed by CAN.
Recommendation for the Discipline
1) When possible linear algebra should be taken at the community
college. It plays a pivotal role later on and is an ideal
place to emphasize proofs.
2) We should support the creation of a science
oriented transfer package that is similar to IGETC, but tailored
to meet the needs of science/math/engineering majors. Such
majors need to start on core requirements early, while delaying
some general education courses until the junior and senior
year. During the debate on this proposal, it became clear
that two paths were being pursued: one offering advice on
a core curriculum, the other on the best general education
choices.
3) If a four-year institution's requirement
for differential equations is at the upper division level
and a transfer student has taken a similar course at the lower
division level, the four-year institution should try to give
"content" credit for the course even though they
cannot transfer the course.
4) Four-year institutions should keep in
close contact with their area community colleges. They should
alert them early in the process about proposed changes in
the curriculum including major course modifications. This
is especially important if the proposed changes could affect
articulation agreements. It is proposed that on a regional
basis that there should be a face-to-face meeting at least
once per year. Institutions could rotate hosting such meetings.
We want to explore, with IMPAC's help, the setting up list
serves and regional annual math discipline meetings, perhaps
to augment the ongoing IMPAC project.
Recommendations
for Support Courses
We believe that there are two discrete Mathematics courses.
Both at one time or another a meet the needs of Computer Science.
As a start we suggest:
Discrete Mathematics: Elements of discrete
mathematics with applications; methods of proof including
mathematical induction. Topics include logic, sets, relations,
graphs, trees, combinatorics and Boolean algebra. Prerequisite:
Pre-Calculus
The second version is:
Discrete Structures: Propositional and Predicate
Logic; Methods of proof: Direct, Indirect and Induction; Relations,
Functions, Recursion; Algorithms; Combinatorics; Graph Theory,
Boolean algebra; Applications; Prerequisite CAN Math 18 or
19.
Recommendations to be forwarded to CAN:
Convene a CAN discipline review committee to thoroughly review
CAN descriptors. CAN descriptors for Discrete Mathematics,
and Discrete Structures need to be developed. Our review indicates
that most of the descriptors need some modification. We note
that to be effective, participants need to know that they
will be working on CAN descriptors and that they are representing
their constituents. That is why we choose this route instead
of having IMPAC develop descriptors, especially for the service
courses.
Topics for Further Discussion:
1. The science version of SCIGETC, refined for mathematics.
2. The development of local articulation councils
3. The new structure of CAN.
Outreach:
The ongoing activities of IMPAC are regularly reported to
the Academic Senate of the CSU to the Executive Committee
of the CSULA Academic Senate, and to the participants in the
CAPI program.
Appendix
A
|
