A Working Group on
Integrating Mathematical Reasoning* into Computer Science Curricula
* "Mathematical Reasoning": Applying mathematical techniques,
concepts and processes, either explicitly or implicitly, in the solution of
problems -- in other words, mathematical modes of thought that help us to solve
problems in any domain. In its most general interpretation, every problem-solving
activity requires mathematical thinking. For example, basic logic, be it used
explicitly or implicitly is required for all problem-solving activities.
In The Public Eye
- August 2007, ICT Results, "Processor Design Gets Mathematical Sweetener"
- April 2007, "Is Abstraction the Key to Computing?" by Jeff Kramer, Communications of the ACM.
- Nov. 2006, Rensselaer Polytechnic Institute, "Using Mathematics and Computers To Understand the World."
- Nov. 2006, The Epoch Times, "Discrete Math Comes to the Classroom."
- Sept. 2003, USA Weekend Magazine, "The
Numbers Game: Why Math Books are Hot."
- Sept. 2003, Communications of the ACM, special section on "Why Universities
Require Computer Science Students to Take Math."
- Jan. 22, 2002. BusinessWeek, "A
Better Web through Higher Math"
- 1992. The Queen's
Award for Technological Achievement awarded to Oxford University Computing
Laboratory and IBM United Kingdom Laboratories for the development and application
of Z.
Mathematical reasoning is central to computer science. It should therefore
be an integral part of the entire CS curriculum, with special emphasis in the
early courses. This would be a deviation from current practice, requiring systemic
change in CS education. We are a group of computer scientists, mathematicians,
and others interested in fostering such change.
The group "meets" (via
e-mail), to discuss topics related to mathematical reasoning in CS and its
teaching. An archive
of these discussions is available on-line. Possible topics include, but are
not limited to, which mathematical concepts are relevant, when and how they
can/should be introduced and reinforced in the curriculum, how they relate to
practice, pedagogical approaches to teaching math foundations, supporting laboratories,
etc. We are undertaking concrete projects designed to raise awareness of mathematical
reasoning in CS and of ways of teaching it. The exact nature of projects is
determined by members' interests, including such things as working to get a
prominent place for mathematical reasoning in computer science and software
engineering curriculum recommendations; workshops, panels, birds-of-a-feather,
and similar presentations at relevant conferences; and collecting pedagogical
resources for incorporating mathematics into CS courses. Future projects could
include such things as performing studies and otherwise collecting evidence
on the importance of mathematical thinking in CS; contests to increase student
interest in, and faculty awareness of, mathematics as part of CS; etc.
Accomplishments
Math-reasoning related accomplishments of this group or its members include...
- A birds-of-a-feather session on "Mathematical Reasoning in Computer Science" at SIGCSE 2008, led by group members Doug Baldwin and Murali Sitaraman.
- ProofBuilder, a Java program that helps students learn to
do proofs in several different ways. It handles material of a first
course on discrete mathematics, including induction, sets, summations,
O(), mod, and combinatorics. Written and maintained by group member Hugh McGuire.
- The 3-2-1 Approach to Introductory Computer Science at Haverford College, directed by group members Dave Wonnacott and John Dougherty.
- SIGCSE 2006: Members organized several sessions, including
- A workshop on "Hands-On Activities for Learning Discrete Mathematics," run by group members Susanna Epp, Peter Henderson, and Bill Marion.
- A special session presenting the "Final Oral Report of the SIGCSE Committee on the Implementation of a Discrete Mathematics Course," moderated by group members Bill Marion and Doug Baldwin.
- A paper entitled "Discrete Partnership -- A Case for a Full Year of Discrete Math," co-authored by group member Mark LeBlanc.
- A birds-of-a-feather session on "Mathematical Reasoning in Computer Science," led by group members Peter Henderson and Judith Gersting.
- Discrete Mathematics: Curricular Issues, Pedagogy and Nifty Examples, a workshop presented by group members Bill Marion, Susanna Epp, and Peter Henderson, at Messiah College (Grantham, PA), from June 12-16, 2006.
- SIGCSE 2005: Members presented special sessions and
workshops, including
- A special session presenting a "Status Report on the
SIGCSE Committee on the Implementation of a Discrete
Mathematics Course," featuring group members Bill Marion and Doug
Baldwin.
- A workshop on "More
Nifty Examples in Discrete Mathematics," run by group members
Bill Marion, Peter Henderson and Susanna Epp.
- A birds-of-a-feather session on "A Concepts-Based
Approach to Teaching Programming," run by group member Peter
Van Roy.
- A birds-of-a-feather session on "Mathematical Thinking in
Computer Science" offered by group members Peter Henderson
and Judy Gersting.
- A special issue of the ACM Journal on Educational Resources
in Computing (JERIC)
devoted to Software
Support for Discrete Mathematics Teaching, edited
by member Valerie J. Harvey, and Susan H. Rodger.
- An MAA PREP workshop entitled "Nifty
Applications in Discrete Mathematics" was held June 7 to 11, 2004
at Valparaiso University. Organized by group member Bill Marion,
and also featuring presentations by members Doug Baldwin, Susanna Epp and
Peter Henderson.
- Algorithms
and Data Structures: The Science of Computing, a textbook by group
member Doug Baldwin, and Greg Scragg, that integrates mathematical analysis
of algorithms, algorithm design and programming, and empirical analysis
of algorithms.
- Members Peter Henderson and Kim Bruce appeared on a panel "Mathematical
Logic in
Computer Science Education" at the Association
for Symbolic Logic 2004 Meeting on
May 22, 2004.
- SIGCSE 2004:
Members presented special sessions and workshops, including
- Communications of the ACM, September 2003 section on "Why Universities
Require Computer Science Students to Take Math." Members wrote many of
the articles, including...
- SIGCSE 2003:
Members presented workshops, panels, and special sessions related to mathematical
reasoning in computer science, including...
- A workshop by David Gries entitled "Calculational Logic in Discrete
Math Courses"
- A special session chaired by Dan Garcia, and featuring group members
David Ginat and Peter Henderson, entitled "Everything
You Always Wanted to Know about Game Theory"
- A special session chaired by Susanna Epp, Peter Henderson, and Bill
Marion entitled "Math
Educators, Computer Science Educators: Working Together"
- A panel organized by Bill Marion and including Kris Powers, Adrienne
Bloss, and Doug Baldwin entitled "How Departments Are Responding
to the Mathematics Recommendations in CC2001"
- A birds-of-a-feather session on mathematical thinking in computer science,
organized by Doug Baldwin and Peter Henderson
- "Discrete
Mathematics: An Early Foundation for the Study of Computer Science",
an MAA PREP (Professional Enhancement Program) workshop run by Bill Marion,
Susanna Epp, Peter Henderson, and Henry Walker, June 2-6, 2003.
- Programming
Languages: Principles and Paradigms: A textbook by Allen Tucker and Bob
Noonan that takes a rigorous semantics-based approach to programming languages.
- Computing Curriculum
Software Engineering (CCSE): Several members of the group were involved
in various aspects of the CCSE project. Of particular note, Peter Henderson
chaired the "Foundations" knowledge area subcommittee.
- CCSC:NE-2002: Allen
Tucker presented a plenary talk entitled "Ensuring a Rigorous Curriculum:
Practices and Goals" at the Consortium for Computing in Small Colleges:
Northeast conference.
- Computing Curriculum
2001: Kim Bruce, Bill Marion and Henry Walker (Chair) served on the Supporting
Topics and Courses Focus Group. Kim Bruce was chair of the Programming Languages
Focus Group. Several ideas in CC 2001, Section 9.1.1 "Mathematical
Rigor" evolved from member activities.
- A panel on Women,
Math, and Computer Science, organized by Peter
Henderson, and featuring other group members Vicki Almstrum, Orit Hazzen,
and Kim Kihlstrom, presented at SIGCSE 2002. The panel's Web page includes
the speakers' presentations and links to a number of background references.
- SIGCSE 2002:
Members presented a paper, and participated in 3 panels and several birds
of a feather sessions devoted to math thinking.
- SIGCSE
2001: Members presented 2 papers, the keynote address, participated on
3 panels and several birds of a feather sessions devoted to math thinking.
- ITiCSE
2001: The working group "Striving
for Mathematical Thinking"
Publications & Reports
Papers, reports, and invited talks related to mathematical reasoning by members
of this group include...
- Bill Marion and Doug Baldwin, "SIGCSE Committee Report on the Implementation of a Discrete Mathematics Course," Inroads - the SIGCSE Bulletin, June 2007, pp. 109 - 126. Also available at http://www.sigcse.org/DiscreteMathHome.shtml.
- Doug Baldwin, "Effectiveness of a Language Implementation Project in Building Appreciation for Formal Specification," Papers of the Twelfth Annual CCSC Northeastern Conference, Apr. 2007, pp. 173 - 183.
- Valerie J. Harvey et al., eds., Discrete Mathematics Applications for Information Systems Professionals, 2nd ed. (Pearson, 2006), a collection of applications examples and a curriculum guide for teaching discrete mathematics in information systems (IS) and IS Management programs; designed as a supplement to Richard Johnsonbaugh, Discrete Mathematics, 6th ed. (Prentice Hall, 2005).
- "Life-long Learning: Making Discrete Math Relevant for Information Systems Professionals," by David F. Wood, Valerie J. Harvey, and Frederick G. Kohun, IACIS 2005.
- "Insights
from Teaching Discrete Mathematics in Information Systems Programs, A Report
for the Discussion Forum," by Valerie J. Harvey and E. Gregory Holdan,
CoLogNet/Formal Methods Europe Symposium on Teaching Formal Methods, November
2004.
- "Workshop
on Discrete Mathematics for Programs Conforming to ABET Information Systems
Accreditation," by Valerie J. Harvey, Peter Y. Wu, and John C. Turchek,
ISECON, November 2004.
- "Mathematics
for the Exploration of Requirements," by
Michael Huth, SIGCSE InRoads, June 2004.
- "The
Role of Logic in Teaching Proof," by Susanna Epp, in American
Mathematical Monthly, Dec. 2003, which holds the copyright with all rights
reserved.
- "The
Role of Modeling in Software Engineering Education," by Peter Henderson,
presented at the 2003 Frontiers in Education conference.
- "Materials Development in Support of
Mathematical Thinking", the report of an ITiCSE
2002 working group chaired by Peter Henderson, in SIGCSE Inroads,
June 2003.
- "A Small College Response to the Mathematics Recommendations of Curriculum
2001", by Blayne Carroll and Kris Powers, presented at the 2002 Consortium
for Computing Sciences in Colleges Southeastern Conference.
- "Where is Programming Methodology these Days", invited editorial
by David Gries in SIGCSE Inroads, Dec. 2002.
- "Teaching Discrete Structures with SML",
by Christelle Scharff and Andrew Wildenberg, presented at Functional and Declarative
Programming in Education (FDPE02), a one day workshop at PLI'02, October 2002.
- "Functional and Declarative Languages for
Learning Discrete Mathematics", by Peter Henderson, presented at
Functional and Declarative Programming in Education (FDPE02), a one day workshop
at PLI'02, October 2002.
- "Mathematical Reasoning in Software Engineering
Education", an article prepared by Peter Henderson in the September 2003 Communications of the ACM special section on math in computer
science.
- "Why Math?", an article prepared by Kim
Bruce, Scot Drysdale, Charles Kelemen, and Allen Tucker in the September 2003 Communications of the ACM special section on math in computer
science.
- "The
Importance of Mathematics to the Software Practitioner", by Doug
Baldwin and Peter Henderson, in the March/April 2002 issue of IEEE Software.
A response to Robert Glass's essay "A New Answer to 'How Important is
Mathematics to the Software Practitioner'?" (Copyright
2002 by IEEE)
- A paper entitled "Integrating Formal Models into the Programming Languages
Course", by Allen Tucker and Bob Noonan appeared in The 33rd SIGCSE Technical
Symposium on Computer Science Education, 2002.
- Pete Henderson gave a seminar entitled "The Role of
Mathematics the Undergraduate Computer Science Curriculum" at Ohio State
University on Jan. 17, 2002.
- A ITiCSE
2001 working group report "Striving
for Mathematical Thinking" was published in SIGCSE Inroads
(Vol. 33 , No 4, pp. 114-124, Dec. 2001).
- A paper entitled "Our Curriculum has Become Math-Phobic!",
by K. Bruce, C. Kelemen, and A. Tucker was published in The 32nd SIGCSE Technical
Symposium on Computer Science Education, 2001.
- A paper entitled "Has Our Curriculum Become Math Phobic? (An American Perspective)",
by K. Bruce, C. Kelemen, P. Henderson, O. Astrachan and A. Tucker; The 5th
Annual ITiCSE Conference, 2000.
- The MAA CUPM report "Mathematical
Needs of Introductory Computer Science Curricula", 1999.
- A paper entitled "The Propositional Logic Test as a Diagnostic Tool
for Misconceptions about Logical Operations" by Vicki Almstrum, The
Journal of Computers in Mathematics and Science Teaching 18(3), 1999.
- A paper entitled "Investigating Student Difficulties with Mathematical
Logic" by Vicki Almstrum in N. Dean and M. Hinchey (eds.), Teaching
and Learning Formal Methods, Academic Press, 1996.
An important goal for this group is to undertake projects designed to increase
awareness of mathematical reasoning in computer science and computer science
curricula. Our current projects are as follows. Anyone is welcome to contribute
to any of these projects. If one interests you, please contact the project's
organizer.
(If you're a member of the group and want to be listed here, send e-mail to
baldwin@geneseo.edu giving the
information you'd like listed -- e.g., how you want your name to appear, your
affiliation, URL's to home pages, e-mail addresses, or anything else you'd like
included. Only adding people when requested to do so hopefully increases people's
privacy and control over distribution of personal information.)
- Vicki L.
Almstrum (e-mail: almstrum@cs.utexas.edu),
Department of Computer Sciences, University of Texas at Austin
- Hossein
Arsham (e-mail harsham@ubalt.edu),
Information and Quantitative Sciences Department, University of Baltimore
- Doug
Baldwin (e-mail baldwin@geneseo.edu), Dept. of Computer Science, SUNY Geneseo
- Kim Bruce
(e-mail kim@cs.pomona.edu), Dept.
of Computer Science, Pomona College
- Tom Cortina
(e-mail: tcortina@cs.cmu.edu),
Dept. of Computer Science, Carnegie Mellon University
- Venu Dasigi (e-mail
vdasigi@spsu.edu), Department of Computer
Science, Southern Polytechnic State University
- Scot Drysdale (e-mail scot@cs.dartmouth.edu),
Department of Computer Science, Dartmouth College
- Carol Anne Edmondson (e-mail cae@utas.edu.au), School of Computing and Information Systems, University of Tasmania
- Abdol-Hossein Esfahanian, (e-mail esfahanian@cse.msu.edu), Department of Computer Science and Engineering, Michigan State University
- Matthias Felleisen, Department of Computer Science, Northeastern University,
Boston
- Kathi Fisler
(e-mail kfisler@cs.wpi.edu), Department
of Computer Science, Worcester Polytechnic Institute
- S. Jane Fritz (e-mail fritz@sjcny.edu),
Dept. of Mathematics/Computer Science, St. Joseph's College, New York
- Judith Gersting (e-mail gersting@hawaii.edu),
University of Hawaii at Hilo
- Don Goelman
(e-mail don.goelman@villanova.edu),
Department of Computing Sciences, Villanova University
- David Gries, Associate Dean of Engineering, Cornell University
- Valerie J. Harvey (e-mail harvey@rmu.edu),
Department of Computer and
Information Systems, Robert Morris University
- David Hemmendinger
(e-mail hemmendd@union.edu),
Dept. of Computer Science, Union College
- Pete Henderson (e-mail phenders@butler.edu),
Dept. of Computer Science, Butler University
- Lew Hitchner
(e-mail hitchner@csc.calpoly.edu)
Computer Science Dept., Cal Poly State Univ. (CSU San Luis Obispo)
- Gregory Kapfhammer
(e-mail gkapfham@allegheny.edu),
Department of Computer Science, Allegheny College
- Charles Kelemen
(e-mail ckeleme1@swarthmore.edu),
Computer Science Program, Swarthmore College
- Kim Kihlstrom
(e-mail kimkihls@westmont.edu),
Dept. of Mathematics and Computer Science, Westmont College
- Nancy Kinnersley (e-mail kinners@eecs.ku.edu),
Dept. of Electrical Engineering and Computer Science, University of Kansas
- Yana Kortsarts (e-mail yanako@cs.widener.edu),
Computer Science Department,
Widener University,
Chester, PA
- Bill Marion (e-mail: Bill.MarionJr@valpo.edu),
Dept. of Mathematics and Computer Science, Valparaiso University
- Hugh McGuire (e-mail: mcguire@cis.gvsu.edu), School of Computing &
Information Systems, Grand Valley State University, MI
- John O'Donnell
(e-mail jtod@dcs.gla.ac.uk), Computing
Science Department, University of Glasgow
- S. Parthasarathy
(e-mail drparth@gmail.com)
Algologic Research and Solutions, Secunderabad, India
- Hemant Pendharkar (e-mail
hpendharkar@worcester.edu)
Department of Computer Science Worcester State College
- Chuck Riedesel (e-mail riedesel@cse.unl.edu),
Computer Science & Engineering Department, University of Nebraska at Lincoln
- Bob Roos (e-mail robert.roos@allegheny.edu),
Department of Computer Science, Allegheny College
- Christelle Scharff
(e-mail cscharff@pace.edu) Computer
Science Department, Pace University
- Murali Sitaraman (e-mail: msitara@clemson.edu), School of Computing, Clemson University
- Allen Tucker (e-mail allen@bowdoin.edu),
Dept. of Computer Science, Bowdoin College
- Peter
Van Roy (e-mail: pvr@info.ucl.ac.be),
Department of Computing Science and Engineering, Université Catholique
de Louvain at Louvain-la-Neuve, Belgium
Electronic discussions are carried out on mailing list "math-thinking-l@geneseo.edu".
All you have to do to join the group is subscribe to this list -- to do this,
just point a Web browser at
http://mail.geneseo.edu/mailman/listinfo/math-thinking-l/ and fill out the
subscription form in the middle of the page.
(Group members can also maintain their subscription to the mailing list --
change delivery options, unsubscribe, etc. -- at the same URL, using the subscriber
information "access panel" at the bottom of the page.)
Upcoming events, on-line resources, and other miscellaneous items likely to
be of interest to members of this group are listed below. Please send suggestions
for further items to Doug Baldwin.
Events
- ICER '08, the 4th International Computing Education Research Workshop, Sept. 6 - 7, 2008, University of Technology, Sydney, Australia.
- ICFP 2008, 13th ACM SIGPLAN International Conference on Functional Programming, Sept. 22 - 24, 2008, Victoria, British Columbia, Canada.
- LICS 2008, the 23rd Annual IEEE Symposium on Logic in Computer Science, Sept. 24 - 27, 2008, Carnegie Mellon University, Pittsburgh, PA, USA.
- CCSC:MW 2008, the 2008 conference of the Consortium for Computing Sciences in Colleges (Midwestern region), Sept. 26 - 27, 2008, Hope College, Holland, MI, USA.
- CCSC:NW, the 10th annual Consortium for Computing Sciences in Colleges Northwestern conference, Oct. 10 - 11, 2008, Southern Oregon University, Ashland, OR, USA.
- CCSC:E, the 23rd annual Consortium for Computing Sciences in Colleges Eastern conference, Oct. 10 - 11, 2008, Hood College, Frederick, MD, USA.
- CCSC:RM, the 17th annual Consortium for Computing Sciences in Colleges Rocky Mountain conference, Oct. 17 - 18, 2008, Colorado Technical University, Colorado Springs, CO, USA.
- OOPSLA '08, the ACM SIGPLAN Object Oriented Programming Systems and Applications Conference, Oct. 19 - 23, 2008, Nashville, TN, USA.
- CCSC:SE, the 22nd annual Consortium for Computing Sciences in Colleges Southeastern conference, Nov. 7 - 8, 2008, Augusta State University, Augusta, GA, USA.
- FSE-16, the 16th International Symposium on Foundations of Software Engineering, Nov. 9 - 15, 2008, Atlanta, GA, USA.
- POPL 2009, the Symposium on Principles of Programming Languages, Jan. 21 - 23, 2009, Savannah, Georgia, USA.
- CSEE&T09, the 22nd IEEE-CS Conference on
Software Engineering Education and Training,
Feb. 17 - 19, 2009, Hyderabad, India.
- SIGCSE 2009,
The 40th ACM Technical Symposium on Computer Science Education,
March 4 - 7, 2009, Chattanooga, TN USA.
- TERMGRAPH 2009, the
5th International Workshop on
Computing with Terms and Graphs,
March 22, 2009, York, UK.
- CCSC:CP, the 15th annual Consortium for Computing Sciences in Colleges Central Plains conference, April 3 - 4, 2009, Southwest Baptist University, Bolivar, MO, USA.
- CCSC:SC, the 20th annual Consortium for Computing Sciences in Colleges South Central conference, April 24 - 25, 2009, Southeastern Louisiana University, Hammond, LA, USA.
- CCSC:NE, the 14th annual Consortium for Computing Sciences in Colleges Northeastern conference, April 24 - 25, 2009, SUNY Plattsburgh, Plattsburgh, NY, USA.
- PLDI 2009, the ACM SIGPLAN 2009 Conference on
Programming Language Design and Implementation,
June 15 - 21, 2009, Trinity College, Dublin, Ireland.
- ITiCSE 2009, the 14th Annual Conference on Innovation and Technology in Computer Science Education, July 6 - 8, 2009, Université Pierre et Marie Curie, Paris, France.
- CCSC:MW, the 16th annual Consortium for Computing Sciences in Colleges Midwestern conference, Sept. 25 - 26, 2009, St. Xavier University, Chicago, IL, USA.
On-Line Resources
Organizations
Publishers/Conference Sponsors
- Cambridge Journals
Online, the online publishing arm of Cambridge University Press.
- The Frontiers in Education
Conferences' clearinghouse Web page.
- Historia Mathematica,
a journal on the history of mathematics.
- The International
Series in Formal Methods from Academic Press.
- JERIC, the ACM
Journal on Educational Resources in Computing.
- The Journal
of Logic and Computation, from Oxford University Press.
- The Journal of On-Line Mathematics
and its Applications, an on-line journal from the MAA.
- Logical Methods in Computer Science, an open-access, referreed, free, on-line
journal covering logical methods in all areas of computer science.
- National Educational Computing
Association, sponsors of the National Educational Computing Conference.
- Teaching Mathematics
and its Applications, a journal from Oxford University Press.
Funding Sources
- NSF, the U.S. National Science
Foundation.
- FIPSE,
the U. S. Department of Education Fund for the Improvement of Postsecondary
Education.
Directories/Collections
- Bibliographies
for computer science, including sub-collections in areas such as Theory
of Computation and Computational
Mathematics
- Computing
Curricula references and links, maintained by Martin Dickey, University
of Washington.
- CSTC, the Computer Science
Teaching Center.
- Directory of DIMACS
Educational Programs (undergraduate and K-12).
- Formal
Methods Education Resources, maintained by Kathi Fisler, Worcester
Polytechnic Institute.
- Alexander Sakharov's Foundations
of Mathematics, a collection of links
to articles dealing with the foundations of mathematics, organized to form
a coherent "book."
- Interactive Mathematics Miscellany and Puzzles, by Alexander Bogomolny
- MacTutor
History of Mathematics Archive at the University of St. Andrews.
- The Math Archives at the University of Tennessee at Knoxville, a collection
of general mathematics resources.
- The Mathematical Atlas, a collection of introductory articles on areas
of modern mathematics.
- The Math Forum, reference
and educational resources for all levels -- K-12, college, and beyond
- "More Math than Science," a collection of tutorials and tools for miscellaneous topics in pre-calculus mathematics
- The National Science Digital Library (NSDL)
- SIGCSE Education
Links, links to computer science teaching resources
- Teaching Maths the Right Way, a collection of links and commentaries on many aspects of mathematics, maintained by Dr. S. Parthasarathy
- Theoretical
Computer Science on the Web, maintained by Suresh Venkat, Stanford
University.
- The World Library for
Formal Methods, maintained by Jonathan Bowen, at South Bank University
- The World of Mathematics reference
pages at Wolfram Research -- a quick reference source for a great deal of
mathematics.
Position Statements, Articles, Et Cetera
- "Do Software Engineers Need Mathematics?", by Keith Devlin, at MAA Online.
- "Mathematics in Computer Science Curricula",
by Jeannette M. Wing -- slides presented at the Sixth International Conference
on Mathematics of Program Construction, July 2002, Dagstuhl, Germany.
- "What Math is Relevant for a CS or SE Student? An Employer's Perspective" by Dennis J. Frailey, Principal Fellow, Raytheon Company, originally published in SIGSOFT Software Engineering Notes, May 2006.
- "What Should Computer Students Learn from Mathematics" by Y. C. Tay, National University of Singapore. (Also available in SIGACT News, June 2005.)
Post-Secondary Teaching Resources
- The BESEME Project -- "Better Software Engineering through Mathematics Education"
- Susanna Epp's Collection
of Discrete Math Applets
- The Computational Discrete Mathematics course at Carnegie-Mellon University
- Supplemental materials for Peter Van Roy and Seif Haridi's text "Concepts, Techniques, and Models of Computer Programming"
- The Great Theoretical Ideas in Computer Science course at Carnegie-Mellon University.
- David Gries's
Introduction to Teaching Logic as a Tool
- LINK -- Software for manipulating and visualizing discrete math
- An on-line course on Logic and Proofs at Carnegie-Mellon University, part of CMU's Open Learning Initiative
- The Mathematical Experiments in Computer Science course at Stonehill College.
- A Java package for Polynomials over Rings.
- ProofBuilder, a Java program that helps students learn to do proofs for a first course on discrete mathematics, including induction, sets, summations, O(), mod, and combinatorics.
- The Reusable Software Research Group at Ohio State University and Clemson University, studying formally-specified component-based software; includes software tools to help students reason mathematically about software specifications and tests.
- Notes and sources for "Teaching with Original Historical Sources in Mathematics" at New Mexico State University, with a sub-project on "Teaching
Discrete Mathematics via Primary Historical Sources."
K-12 Teaching Resources
- CyberChase, a public television series, with associated on-line and print activities, devoted to showing 8-to-12-year-old children the importance and fun of mathematics.
- The Discrete Math Workshop at Tufts University for K-8 teachers.
- HeyMath, electronic learning resources to support teachers and students in grades 5 through 12
- The Making Math Engaging: Discrete Mathematics for K-8 Teachers Web site
- Math.com, math learning resources for students, teachers, and parents
- MATHmaniaCS, devoted
to "passing on the excitement of mathematics and computer science to
kids of all ages."
- Math for America, an organization of investment bankers, educators, and mathematicians dedicated to improving mathematics education in US public schools.
- The METIP
Project, helping kids appreciate the math behind digital images.
- Computer Science
Unplugged, introducing computer science topics to kids without the need
for computers.
- MegaMath,
bringing important mathematical ideas to elementary schools.
- Magic of Math, "a
forum to communicate and share the delight of mathematics with children"
- Views on High School Mathematics Education, mathematicians' and educators' responses to a set of questions about secondary mathematics education in the United States
- The WebLabs project, aimed at "creating new ways of representing and expressing mathematical and scientific knowledge in European communities of young learners (10-14 years)"
Studies
Contests
This page maintained by Doug Baldwin, baldwin@geneseo.edu,
with help from Peter Henderson.
Last updated October 10, 2008.