William A. Marion

Concept inventories in computer science for the topic discrete mathematics

This report describes concept inventories, specialized assessment instruments that enable educational researchers to investigate student (mis)understandings of concepts in a particular domain. While students experience a concept inventory as a set of multiple-choice items taken as a test, this belies its purpose, its careful development, and its validation. A concept inventory is not intended to be a comprehensive instrument, but rather a tool that probes student comprehension of a carefully selected subset of concepts that give rise to the most common and pervasive mismodelings. The report explains how concept inventories have been developed and used in other STEM fields, then outlines a project to explore the feasibility of concept inventories in the computing field. We use the domain of discrete mathematics to illustrate a suggested plan of action.

Discrete mathematics for computer science majors—where are we? How do we proceed?

It has been nine years since Anthony Ralston and Mary Shaw called for a rethinking of the importance of sound mathematical training for undergraduate computer science majors [14]. In their paper they stressed the need to develop a two-year sequence in discrete mathematics for beginning computer science majors. Since that time numerous articles about such a sequence have appeared in both mathematics and computer science journals [4], [9], [12] and [13] and a number of panel sessions at professional meetings of SIGSCE and of the Mathematical Association of America (MAA) have been held. After all this time questions about the place of discrete mathematics in the undergraduate curriculum are still being debated. One question that is no longer being asked is: should discrete mathematics be part of a computer science majors undergraduate program? The questions that are being asked now and for which there are no easy answers are: at what level should discrete mathematics be taught? should there be one course, two courses or even three courses? what should the prerequisites be for these courses? and what topics should be presented in these courses? Computer scientists and mathematicians who have read the literature, listened to the debates, examined the textbooks or taught a course in discrete mathematics or discrete structures know that there appears to be little agreement as to how and what works and when it works best. This paper attempts to analyze the current situation in more detail and to offer a few suggestions to keep the dialogue alive.

Computer science education in the People's Republic of China in the late 1980s

Last year a delegation of international computer professionals with interests in computer science education participated in an information exchange with colleagues in the Peoples Republic of China. The delegations experiences suggest that the Chinese have made substantial progress in some aspects of computer science education since late 1982, but that difficult problems remain to be solved.

Math educators, computer science educators: working together

Mathematics is one of the disciplines that helped give birth to computer science. Over the years, however, as computer science sought its own identity as an applied, professional discipline, it has occasionally lost contact with its roots. Also, the mathematics profession has had problems that are partly responsible for a decline in rigor in undergraduate computer science courses [1,2,3]. Both disciplines are coming to recognize that the bonds between them must be reestablished and strengthened. This is a healthy sign of maturity. In 1999 the Mathematical Association of America’s (MAA) Committee on the Undergraduate Program in Mathematics (CUPM) initiated the Curriculum Foundations Project, a series of disciplinary workshops, to determine the mathematical requirements primarily in the first two undergraduate years of the disciplines they serve. The first Curriculum Foundations Workshop was held at Bowdoin College in October 1999 and included both computer scientists and physicists. Since then a total of eleven workshops have been held with 19 different disciplines plus a final conference that gathered representatives from all previous workshops to discuss common needs. Draft reports from the workshops,

How departments are responding to the mathematics recommendations in CC2001

The Task Force defined a new knowledge area, Discrete Structures, as part of the core body of knowledge that every computer science major must learn, identified a 43-hour block of discrete mathematics material and recommended that this material be taught early in a student’s four-year program so that these concepts can be applied, where appropriate, in later computer science courses. The Task Force presented three models for covering the essential knowledge units in Discrete Structures: a one-semester course, a full-year sequence or an integration of the mathematics topics within an introductory computer science sequence. The Task Force further recommended that additional mathematics in other areas (such as calculus or linear algebra) should also be included in a computer science program, although guidelines for the specific areas or the number of hours that additional mathematics might encompass were not included.