This paper discusses both the mathematical and social importance of the study of discrete mathematics topics and themes, including combinatorics, graph theory, iteration and recursion, algorithms, and optimization. Specific expectations within these areas, illustrated by applications and activities, are presented for each of the grade bands, and an argument made for their explicit inclusion in the upcoming final version of the National Council of Teachers of Mathematics' (NCTM) Standards 2000. The paper outlines an additional discrete mathematics standard for grades Pre-K-12, advocating more specific treatment and earlier introduction of combinatorics, graph theory, and recursion.
The paper also addresses the treatment of discrete mathematics topics in the discussion draft of the Standards 2000. The paper points to a need for emphasis on discrete mathematical modeling, algorithmic thinking, and optimization in the existing problem solving and representation standards across the grade bands. It additionally suggests some areas in the existing standards where crucial connections to discrete ideas have been overlooked. While the language of discrete mathematics appears scattered throughout the document, and some topics receive considerable attention, the paper presents a case for selecting a few of these topics for more focused development.
The author cites research that demonstrates the accessibility of the topics selected for discussion to children of all ages and abilities. The activities reflect a wide range of applications and connections within and outside of mathematics and incorporate the major themes of problem solving, representation, communication, and reasoning. All three topics begin in Pre-K-2 and develop in depth and complexity throughout the grade band progression. The discussion of discrete mathematics in the paper attempts to mirror and support the overall structure and treatment of other ideas presented in the discussion draft of the Standards 2000.
Discrete Mathematics: The Missing Standard Pre-K-12
Treatment of Discrete Mathematics in the Principles and Standards for School Mathematics: Discussion Draft (NCTM, 1998)
Suggested
Changes
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Separate Discrete Mathematics Standard: A Rationale
A Proposal for Standard 11: Discrete Mathematics
Pre-K-2 Focus Areas Pre-K-2 Discussion
Grades 3-5 Focus Areas Grades 3-5 Discussion
Grades
6-8 Focus Areas
Grades 6-8
Discussion
Grades
9-12 Focus Areas
Grades
9-12 Discussion