Striving for mathematical thinking

ABSTRACT

Computer science and software engineering are young, maturing disciplines. As with other mathematically based disciplines, such as the natural sciences, economics, and engineering, it takes time for the mathematical roots to grow and flourish. For computer science and software engineering, others have planted these seeds over many years, and it is our duty to nurture them. This working group is dedicated to promoting mathematics as an important tool for problem-solving and conceptual understanding in computing.

REFERENCES

• 1: Baldwin, D, and Henderson, P., math-thinking discussion group web site http://www.math-in-cs.org/
• 2: Doug Baldwin , Greg Scragg , Hans Koomen, A three-fold introduction to computer science, Proceedings of the twenty-fifth SIGCSE symposium on Computer science education, p.290-294, March 10-12, 1994, Phoenix, Arizona, United States
• 3: Janet L. Bailey , Greg Stefaniak, Industry perceptions of the knowledge, skills, and abilities needed by computer programmers, Proceedings of the 2001 ACM SIGCPR conference on Computer personnel research, p.93-99, April 2001, San Diego, California, United States [doi>10.1145/371209.371221]
• 4: Jon Bentley, Programming pearls, ACM Press, New York, NY, 1986
• 5: Frederick P. Brooks, Jr., No silver bullet: essence and accidents of software engineering, Computer, v.20 n.4, p.10-19, April 1987 [doi>10.1109/MC.1987.1663532]
• 6: D. F. Butcher , W. A. Muth, Predicting performance in an introductory computer science course, Communications of the ACM, v.28 n.3, p.263-268, March 1985 [doi>10.1145/3166.3167]
• 7: Edmund M. Clarke , Jeannette M. Wing, Formal methods: state of the art and future directions, ACM Computing Surveys (CSUR), v.28 n.4, p.626-643, Dec. 1996 [doi>10.1145/242223.242257]
• 8: Cox, B. D., "The rediscovery of the active learner in adaptive contexts: a developmental-historical analysis of transfer of training." Educational Psychologist, vol. 32, pp. 41 - 55.
• 9: Emanuele Ciapessoni , Piergiorgio Mirandola , Alberto Coen-Porisini , Dino Mandrioli , Angelo Morzenti, From formal models to formally based methods: an industrial experience, ACM Transactions on Software Engineering and Methodology (TOSEM), v.8 n.1, p.79-113, Jan. 1999 [doi>10.1145/295558.295566]
• 10: DIMACS, http://dimacs.rutgers.edu/Education/
• 11: Keith Devlin, Viewpoint: the real reason why software engineers need math, Communications of the ACM, v.44 n.10, p.21-22, Oct. 2001 [doi>10.1145/383845.383851]
• 12: Devlin, K., "The Language of Mathematics : Making the invisible visible", W. H Freeman and Company, 2000, p.3.
• 13: Paul De Palma, Viewpoint: Why women avoid computer science, Communications of the ACM, v.44 n.6, p.27-30, June 2001 [doi>10.1145/376134.376145]
• 14: Susanna S. Epp, Discrete mathematics with applications, Wadsworth Publ. Co., Belmont, CA, 1990
• 15: "Formal Methods Education Resources" http://www.cs.indiana.edu/formal-methods-education/
• 16: Erich Gamma , Richard Helm , Ralph Johnson , John Vlissides, Design patterns: elements of reusable object-oriented software, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1995
• 17: Judith L. Gersting, Mathematical Structures for Computer Science, W. H. Freeman & Co., New York, NY, 1998
• 18: David Ginat, Colorful examples for elaborating exploration of regularities in high-school CS1, Proceedings of the 5th annual SIGCSE/SIGCUE ITiCSEconference on Innovation and technology in computer science education, p.81-84, July 11-13, 2000, Helsinki, Finland
• 19: Ginat, D., "Early algorithm efficiency with design patterns", Computer Science Education, June 2000, (11:1), pp. 1-21.
• 20: Robert L. Glass, A New Answer to "How Important is Mathematics to the Software Practitioner?", IEEE Software, v.17 n.6, p.136, November 2000
• 21: Graham, M., Carpenter, J., Cutlip, M., Pintar, A., and Puszynski, J., Chemical Engineering Report to the CUPM Curriculum Foundations Workshop in Engineering, July, 2000, http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum Foundations/
• 22: David Gries, The Science of Programming, Springer-Verlag New York, Inc., Secaucus, NJ, 1987
• 23: David Gries , Fred B. Schneider, A logical approach to discrete math, Springer-Verlag New York, Inc., New York, NY, 1993
• 24: Gunstra, Neal, "Universities aren't serving the IT workforce", Potomac Tech Journal, July 9, 2001 http://www.potomactechjournal.com
• 25: Cordelia Hall , John O'Donnell, Discrete mathematics using a computer, Springer-Verlag New York, Inc., New York, NY, 2000
• 26: Hatano, G., "A conception of knowledge acquisition and its implications for mathematics education," in Theories of Mathematical Learning, Steffe, L. P. and Nesher, P., eds., Lawrence Erlbaum Associates, Mahwah, NJ. 1996.
• 27: Henderson, P., "'Foundations of Computer Science 1' Stony Brook Alumni Survey", http://www.sinc.sunysb.edu/cse113/survey/
• 28: Henderson, P., Unpublished, Informal Survey of Students and Alumni, SUNY Stony Brook, 1998.
• 29: Henry, R., Hoit, M., Katz, L., Keshawarz, S., Hart, F., Ohland, M., Sill, B., and Thompson, D., Chemical Engineering Report to the CUPM Curriculum Foundations Workshop in Engineering, July, 2000, http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum_Foundations/
• 30: Kelemen, C., Tucker, A. B, Henderson, P. B, Bruce, K., Astrachan, O., Baldwin, D., Skrien, D., Van Loan, C., Computer Science Report to the CUPM Curriculum Foundations Workshop in Physics and Computer Science, http://www.cs.swarthmore.edu/~cfk/cupm2.pdf
• 31: Charles Kelemen , Allen Tucker , Peter Henderson , Owen Astrachan , Kim Bruce, Has our curriculum become math-phobic? (an American perspective), Proceedings of the 5th annual SIGCSE/SIGCUE ITiCSEconference on Innovation and technology in computer science education, p.132-135, July 11-13, 2000, Helsinki, Finland
• 32: Kelemen, C., Tucker, A. B, ITiCSE audience survey, http://www.cs.geneseo.edu/~baldwin/math-thinking/ITiCSE-survey.html
• 33: Donald E. Knuth, The Art of Computer Programming Volumes 1-3 Boxed Set, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1998
• 34: John Konvalina , Stanley A. Wileman , Larry J. Stephens, Math proficiency: a key to success for computer science students, Communications of the ACM, v.26 n.5, p.377-382, May 1983 [doi>10.1145/69586.358140]
• 35: Peter Gorm Larsen , John Fitzgerald , Tom Brookes, Applying Formal Specification in Industry, IEEE Software, v.13 n.3, p.48-56, May 1996 [doi>10.1109/52.493020 ]
• 36: Denis M. S. Lee , Eileen M. Trauth , Douglas Farwell, Critical skills and knowledge requirements of IS professionals: a joint academic/industry investigation, MIS Quarterly, v.19 n.3, p.313-340, Sept. 1995 [doi>10.2307/249598]
• 37: Timothy C. Lethbridge, What Knowledge Is Important to a Software Professional?, Computer, v.33 n.5, p.44-50, May 2000 [doi>10.1109/2.841783 ]
• 38: Lethbridge, Timothy, Software Engineering Education Relevance survey, http://www.site.uottawa.ca/~tcl/edrel/
• 39: Barbara Liskov , B. Liskov, Program Development in Java: Abstraction, Specification, and Object-Oriented Design, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 2000
• 40: Long Island Consortium for Interconnected Learning, http://www.licil.org
• 41: Mathematical Association of America, MAA, http://www.maa.org/
• 42: "Mathematics Equals Opportunity" http://www.ed.gov/pubs/math/
• 43: McGibbon, T., "A Business Case for Software Process Improvement Revised: Measuring Return on Investment from Software Engineering and Management", http://www.dacs.dtic.mil/techs/roispi2/
• 44: Mechanical Engineering Report to the CUPM Curriculum Foundations Workshop in Engineering, July, 2000, http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum Foundations/
• 45: Oni, B., Butz, B., Froyd, J., and Talley, R., Electrical Engineering Report to the CUPM Curriculum Foundations Workshop in Engineering, July, 2000, http://academic.bowdoin.edu/faculty/B/barker/dissemination/Curriculum Foundations/
• 46: Pedagogical Resources, http://www.cs.geneseo.edu/~baldwin/math-thinking/examples.html
• 47: Shari Lawrence Pfleeger , Les Hatton, Investigating the Influence of Formal Methods, Computer, v.30 n.2, p.33-43, February 1997 [doi>10.1109/2.566148 ]
• 48: Pressley, M., Woloshyn, V., Lysynchuk, L. M., Martin, V., Wood, E., and Willoughby, T., "A primer of research on cognitive strategy instruction: the important issues and how to address them". Educational Psychology Review, vol. 2, pp. 1 - 58.
• 49: Anthony Ralston, The first course in computer science needs a mathematics corequisite, Communications of the ACM, v.27 n.10, p.1002-1005, Oct 1984 [doi>10.1145/358274.358280]
• 50: Eric Roberts , Russ Shackelford , Rich LeBlanc , Peter J. Denning, Curriculum 2001: interim report from the ACM/IEEE-CS task force, The proceedings of the thirtieth SIGCSE technical symposium on Computer science education, p.343-344, March 24-28, 1999, New Orleans, Louisiana, United States
• 51: Eric Roberts , Gerald Engel , C. Fay Cover , Andrew McGettrick , Carl Chang , Ursula Wolz, Computing curricula 2001 how will it work for you?, Proceedings of the thirty-second SIGCSE technical symposium on Computer Science Education, p.433-434, February 2001, Charlotte, North Carolina, United States
• 52: Ann E. Kelley Sobel, Empirical results of a software engineering curriculum incorporating formal methods, Proceedings of the thirty-first SIGCSE technical symposium on Computer science education, p.157-161, March 07-12, 2000, Austin, Texas, United States
• 53: Allen B. Tucker , Charles F. Kelemen , Kim B. Bruce, Our curriculum has become math-phobic!, Proceedings of the thirty-second SIGCSE technical symposium on Computer Science Education, p.243-247, February 2001, Charlotte, North Carolina, United States
• 54: Tucker, Allen B., "From Rigor to Rigor Mortis: Avoiding the Slippery Slope", Keynote address at SIGCSE Technical Symposium on Computer Science Education, Charlotte, North Carolina, Feb. 21-25, 2001, (http://www.bowdoin.edu/~allen)
• 55: Wilkinson, J., Bob Matthew, R. and Earnshaw, H., "Engineers Need Mathematics But Can We Make It Interesting?", In Proceedings of the International Conference on Engineering Education, August 2001, Session 7D3, pp. 15-20.
• 56: Brenda Cantwell Wilson , Sharon Shrock, Contributing to success in an introductory computer science course: a study of twelve factors, Proceedings of the thirty-second SIGCSE technical symposium on Computer Science Education, p.184-188, February 2001, Charlotte, North Carolina, United States
• 57: Computing Curricula 2001, Steelman Draft (August 1, 2001) http://www.acm.org/sigcse/cc2001/steelman/
• 58: Vicki L. Almstrum , C. Neville Dean , Don Goelman , Thomas B. Hilburn , Jan Smith, Support for teaching formal methods, ACM SIGCSE Bulletin, v.33 n.2, June 2001 [doi>10.1145/571922.571962]