for the Topic Discrete Mathematics

- David Klappholz, Stevens Institute of Technology
- Vicki L. Almstrum, The University of Texas at Austin
- Peter B. Henderson, Butler University
- Steven J. Condly, University of Central Florida

The primary purpose of this working group is to set the stage for building a coordinated set of validated instruments to easily and reliably assess student knowledge in discrete mathematics topics essential to computing education. Among the working group goals are to establish the underlying topic list from discrete mathematics, begin to develop a concept inventory and a views instrument related to discrete mathematics, and develop a plan for pilot testing the instruments and beginning to gather data.

To apply for this Working Group, please see the instructions on the ITiCSE 2006 Working Group page.

Many leading figures in computing, such as Gries [6] and Parnas [9], have stressed the importance of mathematics in computing curricula. Formal and informal articles provide evidence that many computing and mathematics educators strongly believe in the importance of discrete mathematics (DM) in the education of software practitioners (e.g., [2, 11]). Curriculum guidelines for the disciplines of Computer Science, Software Engineering, and Information Systems consistently include DM as a key component [12, 13, 5].

In spite of these facts, computing faculty do not agree on which DM topics to include in required DM courses, how to sequence DM courses relative to introductory computing courses, or how to integrate instruction in DM with instruction in computing. In addition, students generally fail to understand or appreciate the relevance of DM to their undergraduate computing studies and to their subsequent careers [3, 4] and may, in fact, never master relevant DM concepts. Finally, many educators bemoan an unfortunate trend in recent computing curricula to “dumb down” mathematical aspects [14].

To begin addressing these issues with evidence based on solid educational research, an NSF-funded project has just been started with the following three goals:

- develop and validate two instruments that focus on discrete mathematics topics required for computing majors: a concept inventory and a views instrument,
- use these instruments to study the relative effectiveness of different approaches to teaching DM, and
- study DM's contribution to performance in introductory computing course(s) under the different approaches.

This project is inspired by pioneering work in physics education that led to the Force Concept Inventory (FCI) [8] and the Views About Science Survey (VASS) [7]. A Concept Inventory (CI) is an instrument for measuring students’ mastery of fundamental concepts (as opposed to a list or taxonomy of topics, as the term “inventory” might suggest). The “Views About” instrument investigates student attitudes relative to the concepts. The FCI and VASS have been key tools in research-based reform that has occurred in high school and college physics curricula over the past 15 years. The success of the FCI and VASS has inspired similar developments in other STEM fields, providing a rich source of ideas for similar work in the computing field.

[1] Almstrum, V.L. *Limitations in the Understanding of Mathematical Logic by Novice Computer Science Students*, Unpublished doctoral dissertation, University of Texas at Austin, Austin, TX.

[2] Baldwin, D., and Henderson, P.B., "The Importance of Mathematics to the Software Practitioner,” *IEEE Software*, Mar-Apr 2002, pp. 112, 110, 111.

[3] Devlin, K., “The Real Reason Why Software Engineers Need Math,” *Communications of the ACM*, Oct. 2001 (44:10) pp. 21-22.

[4] Devlin, K., Editor, Special Issue on "Why Universities Require Computer Science Students to take Math," *Communications of the ACM*, 46-9, Sept., 2003.

[5] Gorgone, J.T., “Model Curriculum and Guidelines for Undergraduate Degree Programs in Information Systems”, http://www.acm.org/education/is2002.pdf

[6] Gries, D. "The Need for Education in Useful Formal Logic", *IEEE Computer*, April 1996, pp. 29-30.

[7] Halloun, I.A., *Student Views about Science: A Comparative Survey*. Beirut: Phoenix Series / Educational Research Center, Lebanese University, 2001.

[8] Hestenes, D., Who Needs Physics Education Research?, *Am. J. Phys*. 66:465-467, 1998

[9] Lutz, M. and Parnas, D.L, “Engineering Mathematics”, *IEEE Computer*, Vol. 29, No. 4, April 1996.

[10] Mathematics Association of America, “Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004,” 2004.

[11] Ralston A., “Do We Need ANY Mathematics in Computer Science Curricula?”, invited editorial, *SIGCSE Bulletin - Inroads*, Vol. 37, No. 2, June 2005.

[12] Roberts, E., Shackelford, R, et al, “Computing Curricula 2001: Computer Science Volume”, http://www.acm.org/sigcse/cc2001/, Dec. 15, 2001.

[13] Sobel, A. (Editor), “Computing Curricula Software Engineering Volume,” http://sites.computer.org/ccse/, August 23, 2004.

[14] Tucker, A. B., Kelemen, C.F., and Bruce, K. B., "Our Curriculum Has Become Math-Phobic! ", *Proceedings of the 32nd SIGCSE Technical Symposium on Computer Science Education*, pp. 243-247, Feb. 2001.