JERIC 2004
Special Issue Background Statement
“Software Support
for Teaching Discrete Mathematics”
In
the September 2003 issue of Communications
of the ACM, Keith Devlin, Kim Bruce, Robert Drysdale,
Charles Keleman, Allen Tucker, and Peter Henderson
all seem to agree that the form of mathematics of particular value to computer scientists and software engineers is discrete mathematics.[1]
The
teaching of discrete mathematics is
required to support computer science programs according to the criteria for
ABET computer science accreditation[2]
and must be included in the quantitative analysis requirement for ABET information systems accreditation. [3]
If
discrete mathematics is important to support these areas relating to
information technology, how adequately
is the learning of discrete mathematics (set theory, graph theory, logic
and predicate calculus, state transition diagrams), served by instructional software? Discrete mathematics software
products support not only the information technology curriculum, but also
courses in mathematics and philosophy.
How
convenient is it for a student or an instructor to generate and use a Venn
diagram, overbar negation or complementation
notation, to generate and edit and to demonstrate traversal of a directed graph
(with adjacency matrix articulation) or of a tree, to generate and edit and to
demonstrate a state transition diagram, to generate and edit a Z or VDM
model-based specification, Hasse diagrams, relational
algebra or calculus, BNF, Petri nets, or many other relevant forms of notation?
Are
widely used environments, products, and tools for producing documents and web
pages adequate and convenient for common discrete mathematics needs? Can web
pages with Venn diagrams, graphs, and various kinds of discrete mathematics
notation be created and published easily on the Web? Can students manipulate
symbols and graphs easily and include them in their e-mail messages? To what
extent do the current products support applications
of discrete mathematics (where labeling conventions may be different from those
of A, B, C, etc.)?
There
are a number of discrete mathematics activities supported by major educational
products, but these products might use notations different from those found in
the textbooks or may in other ways be challenging for students beginning the study of discrete math or
doing advanced projects. Are the discrete mathematics resources provided in an
integrated environment, or are they scattered in independent applications? Do
we have appropriate resources for all levels: (1) introductory courses in
discrete mathematics; (2) intermediate exercises to support the teaching of
data structures, data communications and networking, operating systems,
database management, and other topics; and (3) advanced studies and research?
If
discrete mathematics is as important as is indicated in the CACM articles, then we should find ways
to (1) call attention to and facilitate use of and support for current quality
products, (2) seek to strengthen the practice of using software in teaching
discrete mathematics through outcomes assessment, feedback from experience, and
sharing techniques, (3) encourage priority support for discrete mathematics
from the major commercial vendors of mathematics teaching software as well as
support in the widely used computing environments, and (4) assess curricular
requirements and then act to assure that any needed resources lacking are made
available.
--- Valerie
J. Harvey and Susan H. Rodger
Co-Editors,
JERIC 2004 Special Issue
[1] Keith Devlin, “Why Universities Require Computer
Science Students to Take Math,” CACM
49, 9 (September 2003): 37-39; Kim B. Bruce, Robert L. Scot Drysdale,
Charles Keleman, and Allen Tucker, “Why Math?” CACM 49, 9 (September 2003): 40-44;
Peter B. Henderson, “Mathematical Reasoning in Software Engineering Education,”
CACM 49, 9 (September 2003): 45-50;
Diane Crawford, “Editorial Pointers,” CACM
49, 9 (September 2003): 7.
[2]
ACM/IEEE Joint Task Force on Computing Curricula, Computing Curriculum 2001:
Computer Science. http://www.computer.org/education/cc2001/final/index.html;
see also http://www.sigcse.org/cc2001/DS.html
and Peter B. Henderson, “Mathematics and
Computing Curricula 2001 -
Connections” at http://www.cs.geneseo.edu/~baldwin/math-thinking/
under “Current Projects.” Regarding ABET, see http://www.abet.org/criteria_cac.html
for wording of curriculum standard IV-11 under “Criteria for Accrediting Computer Science Programs.”
[3] Criteria
for Accrediting Information Systems Programs (Effective for Evaluations during
the 2002-2003 Accreditation Cycle), Computing Accreditation Commission,
Accreditation Board for Engineering and Technology, Inc., approved