To the Curriculum Foundations Planning Committee, Participants in the Bowdoin Workshop, and all other Supporters of the Project:
The message below from Charles Kelemen describes the first large scale effort by the computer scientists from the Bowdoin Workshop to disseminate their report and to solicite responses. This is an impressive effort --- it establishes a sterling model for all subsequent workshop groups to follow.
On behalf of CRAFTY and the CUPM I thank the CS workshop members for the quality of their report and the speed with which they have taken it to the wider computer science community.
I look forward to hearing the responses to the report.
-------- Original Message --------
Subject: Mathematics for Computer Science
Date: Wed, 16 Feb 2000 10:58:04 -0500
From: Charles Kelemen <email@example.com>
The purpose of this posting is to invite members of the computer education community to discuss the first two years of college level mathematics for computer science, information systems, information technology and software engineering education. This is in response to an initiative by the Mathematical Association of America (MAA), through its Committee on the Undergraduate Program in Mathematics (CUPM), to carefully analyze the undergraduate mathematics curriculum and its implications for client disciplines (see Item B below). We are opening this discussion to SIGCSE members in hopes of stimulating continued discussion at the SIGCSE meeting in Austin and in Curriculum 2001 committees. We plan to accumulate and eventually summarize all postings on this thread for both the CS and mathematics (eg, MAA and CUPM group) educational communities.
As part of the CUPM effort, a number of disciplinary workshops were/are being held. Computer scientists who participanted in the "CUPM Curriculum Foundations Workshop in Physics and Computer Science" held at Bowdoin College October 28-31, 1999 were Owen Astrachan, Doug Baldwin, Kim Bruce, Peter Henderson, Charles Kelemen, Dale Skrien, Allen Tucker, and Charles Van Loan.
The full CS workshop report is available at: http://www.cs.swarthmore.edu/~cfk/cupm2.pdf
The key points of this report are summarized in Item A below.
We invite you to read the full report and post comments to the SIGCSE mailing list or to either Peter Henderson or Charles Kelemen.
For further discussion at SIGCSE in Austin, attend the panel "CS1 and CS2: Foundations of Computer Science and Discrete Mathematics"
Thursday 10:30 A.M. - 12:00 P.M. An alternate forum for discussion is the math-thinking discussion group
Respectfully submitted by:
Peter B. Henderson
Charles F. Kelemen, Professor
Dept of Computer Science Computer Science Program
Butler University Swarthmore College
4600 Sunset Avenue 500 College Avenue
Indianapolis, IN 46208 Swarthmore, PA 19081
==== Item A ================
Our general conclusion is that undergraduate computer science majors
need to acquire mathematical maturity and skills, especially in discrete
mathematics, early in their college education. The following topics are
likely to be used in the first three courses for CS majors:
logical reasoning, functions, relations, sets, mathematical induction, combinatorics, finite probability, asymptotic notation, recurrence/difference equations, graphs, trees, and number systems.
Ultimately, calculus, linear algebra, and statistics topics are also needed, but none earlier than discrete mathematics. Thus, such a discrete mathematics course should be offered in the first semester and the prerequisite expectations and conceptual level should be the same as for the Calculus I course offered to mathematics, science
and engineering majors. Our detailed recommendations respond directly to the series of questions of direct relevance to the CUPM Initiative posed by the Workshop hosts (see Item C below).
The report focuses on the needs of computer science from the first two
years of college mathematics instruction. While the authors have
all been involved in computer science curriculum design in the past, this
report does not represent the position of any official ACM or IEEE sanctioned
curriculum committee. As ususal, it is a compromise that does not
even reflect the exact opinions of any particular member of the workshop.
We hope that it will be informative to the mathematics
community and taken together with other input from the CS community (e.g. a record of the SIGCSE postings on this issue) and other client disciplines help the mathematicians in their planning.
Here is an abridged version of what we received from the mathematics folks.
===== Item B ======================================================
This is the first in a series of disciplinary-based workshops, all part of the CUPM Curriculum Initiative for the Mathematical Sciences. The Workshop at Bowdoin is designed to seek guidance from physicists and computer scientists on the design of modern and effective programs in the mathematical sciences.
The specific goal of the Workshop will be to provide responses to a
series of questions of direct relevance to the CUPM Initiative. The current
versions of the questions are enclosed with this letter.
The primary focus of the Workshop will be on the first two years of
undergraduate mathematics education. This is the most influential portion
of the mathematics curriculum and is the central concern of CRAFTY ("Calculus
Reform And the First Two Years"), the CUPM Subcommittee which is organizing
this series of workshops. However, discussions will not be limited
to the first two years - we hope valuable suggestions will be made for
the full spectrum of mathematics courses as it affects physics and computer
The Mathematical Association of America (MAA), through its Committee on the Undergraduate Program in Mathematics (CUPM), is beginning a major analysis of the undergraduate mathematics curriculum. Historically CUPM curriculum recommendations have had a significant influence in the design of undergraduate Mathematics programs. Last revised in 1982, these important and influential guidelines need to be reconsidered.
Given the impact of mathematics instruction on the sciences and quantitative social sciences - especially instruction during the first two years - there is a need for significant input from these partner disciplines. CUPM will gather much of this necessary information over the next year-and-a-half through a series of invitational disciplinary workshops, culminating in a curriculum conference to analyze and synthesize the workshop findings.
The first of these CUPM workshops will be sponsored and hosted by Bowdoin
College on October 28-31, 1999. The focus will be on the needs of physics
and computer science from the first two years of college mathematics instruction.
After the disciplinary workshop papers have been circulated and commented
upon, an invitational curriculum conference will be convened. This conference,
working primarily from the workshop papers, will produce detailed curricular
recommendations for the first two years of undergraduate mathematics instruction.
This culminating event should take place in 2001.
====== Item C =====================================
A primary goal of the Workshop is to obtain responses from physicists
and computer scientists to the following series of questions. The responses
will help guide the CUPM as it formulates recommendations for programs
in the mathematical sciences for the 21st century. These questions may
not cover all of the issues you believe important and relevant to our goal
- if so, please suggest additional questions or rewordings of those we
Understanding and Content.
What conceptual mathematical principles must students master
in the first two years? What mathematical problem solving skills
must students master in the first two years? What broad mathematical
topics must students master in the first two years? What priorities
exist between these topics? What is the desired balance between theoretical
understanding and computational skill? How is this balance achieved?
What are the mathematical needs of different student populations and how
can they be fulfilled?
How does technology affect what mathematics should be learned in the first two years? What mathematical technology skills should students master in the first two years? What different mathematical technology skills are required of different student populations?
What impact does mathematics education reform have on instruction
in your discipline? How should education reform in your discipline
affect mathematics instruction? How can dialogue on educational issues
between your discipline and mathematics best be maintained?
What are the effects of different instructional methods in mathematics on students in your discipline? What instructional methods best develop the mathematical comprehension needed for your discipline? What guidance does educational research provide concerning mathematical training in your discipline?
The CUPM would also appreciate having examples of the important types
of mathematical problems students should be able to solve after two years
of undergraduate mathematics."