GRAPH THEORY: A TOPIC FOR HELPING SECONDARY TEACHERS
DEVELOP INNOVATIVE TEACHING STRATEGIES
Melvin (Skip) Wilson (## email not listed ##)
Olgamary Rivera-Marrero (## email not listed ##)
Virginia Polytechnic Institute and State University
Abstract
Discrete mathematics has curricular importance and provides opportunities for teachers to
develop innovative teaching strategies. Arguments from the National Council of Teachers of
Mathematics, recent secondary curriculum materials, and from other prominent mathematicians
and mathematics educators support this position. An activity for a mathematics course for
secondary teachers is described. The activity illustrates some of what is claimed about curricular
importance and innovative teaching. Finally, results of a recent study of secondary teachers’
conceptions provide support for the arguments made.
Purposes
Discrete mathematics not only has curricular importance, it also provides opportunities for
teachers to develop innovative teaching strategies. This paper presents arguments from the
National Council of Teachers of Mathematics (NCTM, 1989, 2000) Standards, secondary
curriculum materials developed to support them, and from other prominent mathematicians and
mathematics educators. It also describes an activity illustrating some of what is claimed about
curricular importance and innovative teaching. Results of a recent study of secondary teachers’
conceptions provide additional support this claim.
The Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989, p. 176)
stated that in grades 9-12, the mathematics curriculum should include topics from discrete
mathematics so that all students can--
•
represent problem situations using discrete structures such as finite graphs, matrices,
sequences, and recurrence relations;
•
represent and analyze finite graphs using matrices;
•
develop and analyze algorithms;
•
solve enumeration and finite probability problems
The Discrete Mathematics standard recommends the inclusion of discrete mathematics in the
9-12 curriculum. The more recent NCTM document, Principles and Standards for School
Mathematics (NCTM, 2000) also emphasizes how discrete mathematics can be implemented and
integrated throughout the secondary curriculum. For example, it stated:
Because students' interests and aspirations may change during and after high school,
their mathematics education should guarantee access to a broad spectrum of career
and educational options. They should experience the interplay of algebra, geometry,
statistics, probability, and discrete mathematics. NCTM, 2000, p. 287.
In the United States, secondary curriculum development projects, such as the Core-Plus
Mathematics Project (CPMP) have developed high school curriculum materials designed to
implement these calls. For example textbooks for both grades nine and ten of the CPMP series
(Coxford, et al., 2003) contain units dealing specifically with graph theory.
Many prominent mathematicians and mathematics educators have argued for the inclusion of
discrete mathematics in the secondary curriculum (e.g., Rosenstein, 1997) partly because it is so
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