@article{c98148cf17204eae9fd2855795271525,

title = "From the principle of bijection to the isomorphism of structures: An analysis of some teaching paradigms in discrete mathematics",

abstract = "This paper is concerned with the teaching of Discrete Mathematics to university undergraduate students. Two to three decades ago this course became a requirement for math and computer science students in most universities world wide. Today this course is taken by students in many other disciplines as well. The paper begins with a discussion of a few topics that we feel should be included in the syllabus for any course in Discrete Mathematics, independent of the audience. We then discuss several potential models for teaching the course, depending upon the interests and mathematical background of the audience. We also investigate various educational links with other components of the curriculum, consider pedagogical issues associated with the teaching of discrete mathematics, and discuss some logistical and psychological difficulties that must be overcome. A special emphasis is placed on the role of textbooks.",

author = "Christine Ebert and Gary Ebert and Mikhail Klin",

note = "Funding Information: In the United States, the reform movement in mathematics education began in the 1950{\textquoteright}s with the formation of the UICSM (University of Illinois Committee on School Mathematics) in 1951 and the NSF (National Science Foundation) in 1950. By 1958 after several revisions, courses for the four high school grades were implemented in a dozen pilot schools. These materials were divided into 11 units, which covered all the topics in the usual secondary school program. The two facets of understanding central to the development and the methodology of this curriculum project were the precision of language and the discovery of generalizations. The inclusion of DM topics, such as set terminology and notation, logic, and deductive structure and theory served the purpose of adding clarification and precision rather than of making the mathematics more rigorous. See [Hen63] for a more detailed discussion of this development.",

year = "2004",

month = dec,

day = "1",

doi = "10.1007/BF02655669",

language = "English",

volume = "36",

pages = "172--183",

journal = "ZDM - International Journal on Mathematics Education",

issn = "1863-9690",

publisher = "Springer Verlag",

number = "5",

}