The design, implementation, and evaluation of a course in discrete mathematics for high school students.

摘要

Purpose. This study focuses on issues centering around the potential role of discrete mathematics in the high school mathematics program. The purpose of this investigation was (a) to design a course in discrete mathematics appropriate for high school students which emphasizes applied problem solving and mathematical modeling, (b) to implement the aforementioned course, and (c) to determine the feasibility of using the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics (1987) to evaluate this course in discrete mathematics. Thus, the investigator addresses the currently unresolved issue of the possible inclusion of discrete mathematics in precollegiate mathematics.;Results. Data analysis showed that the scores of the treatment group in discrete mathematics achievement and mathematical modeling achievement increased significantly over those of the control group. In addition, a highly significant relationship existed between experience in and achievement of mathematical modeling. Both the treatment group and the control group made significant gains in problem-solving achievement and attitudes toward mathematics. Finally, there was no difference in achievement levels of males as compared to females with regard to discrete mathematics achievement, problem-solving achievement, mathematical modeling, and attitudes toward mathematics.;Conclusions. The following conclusions are based on the results of this study: (1) Providing alternative, nonstandard curriculum, such as Discrete Mathematics, to fourth-year mathematics students has no negative effect on Scholastic Aptitude Test (SAT) scores. (2) Giving students the opportunity to apply mathematics in real situations, without formal instruction, appears to enhance achievement in mathematical modeling. (3) Employing the 1987 NCTM Standards as a model for evaluation is feasible.;Methods and procedures. Discrete Mathematics included seven topics: Matrices, Logic, Sets, Counting and Probability, Graphs, Trees, and Recursion. In addition, students gained experience in mathematical modeling by applying mathematics to solve real problems. Data were collected from 203 high school students who had completed the following three courses: Algebra I, Geometry, and Algebra II. In order to assess achievement in discrete mathematics, mathematical modeling, and problem solving, along with attitudes toward mathematics, seven hypotheses were tested.