The place of discrete mathematics in the school curriculum: An analysis of preservice teachers' perceptions of the integration of discrete mathematics into secondary level courses
The integration of discrete mathematics into the secondary school curriculum (grades 7-12) is an important consideration because the mathematical area is dynamic and interesting, providing students the development of mathematical thinking. Also, it provides for teachers the opportunity to develop innovative mathematics instruction. Since the publication of the document Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), it has been difficult to determine how many schools have integrated discrete mathematics as a separate or as an integrated course in the school mathematics curriculum. Moreover, the mathematics education research community has, for the most part, not focused on teachers' perceptions about teaching and learning discrete mathematics as an area of investigation.
Because of the lack of research in this area, the researcher investigated preservice secondary mathematics teachers' perceptions about discrete mathematics and their reactions to the integration of discrete mathematics into the school curriculum. The researcher purposely selected four preservice secondary teachers who were enrolled in a mathematics course in the fall of 2005. Various data sources were used to get a deep understanding of each participant, including selected coursework, an online survey, and interviews.
Results indicated that these preservice teachers perceive discrete mathematics as meaningful to students, as it emphasizes processes such as problem solving and mathematical thinking, and it provides opportunities to use innovative instruction. Because of this, the preservice teachers believe that discrete mathematics should be integrated in the school mathematics curriculum. In addition, several factors that affect the integration of discrete mathematics in the school were identified. These factors are the state curriculum and testing, the historical emphasis of algebra and calculus in the school curriculum, the National Council of Teachers of Mathematics (1989, 2000) Standards documents' views of discrete mathematics, teachers' views of discrete mathematics, the lack of knowledge of discrete mathematics, and the lack of materials and guidelines for teaching discrete mathematics.