SPRING 2002

 

SU DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE SYLLABUS (Tentative)
MATH 510 Mathematical Reasoning

 

 

Background:

This course is designed for middle/secondary teachers of mathematics and others who wish to enhance their capabilities in mathematical reasoning and problem solving.  We consider topics from discrete mathematics such as sets, logic and proof, relations, graphs, recursion, and cominatorics and we emphasize the construction of well-organized arguments and justifications.

Objectives:
  • To develop the ability to think mathematically,
  • To develop the ablity to construct conjectures, agruments, and proofs.
  • To develop a variety of problem-solving strategies,
  • To gain success in solving non-routine problems, and
  • To become skillful in explaining and justifying conjectures, arguments, proofs, and problem solutions, both orally and in writing.
  • To develop units/lessons addressing K-12 learning objectives related to mathematical reasoning.

The class will focus on content as well as teaching techniques that are aligned with NCTM recommendations.

 

Intended Audience:

Pre-service and in-service middle school and secondary teachers of mathematics and others wishing to strengthen their mathematical background.

 

Prerequisite:

Approval of the department.

 

Texts: 

National Council of Teachers of Mathematics (NCTM), Discrete Mathematics Across the Curriculum, K-12, 1991 Yearbook of the NCTM, 1991.

Solow, D,, “How to Read and Do Proofs,” 3r Edition, Wiley, 2001

Technology:

Excel, Graphing Calculator

 

 

Hours

Weeks 1-3:  Problem Solving.   Problem solving approaches and strategies, mathematical representations, inductive and deductive thinking, generalizations, closed-form solutions, recursive thinking.  Sample problems related to discrete structures and number systems.

9

Weeks 4-7:  Mathematical Logic and Proof.   Direct and indirect proofs, proof by contradiction, and proof by mathematical induction.  Sample theores derived from discrete structures and number systems.

12
Weeks 8-12:  Problem Solving & Proof in Discrete Math.    Further investigation of topics in set theory, the study of functions and relations, graph theory, and combinatorics.

15

Weeks 14-15:  Presentations.  Project presentations based on units/lessons developed, or adapted, to adddress K-12 learning objectives.

6
                                                                                                                                            Total

45
EVALUATION

Assignments & Group Work

20%

Mid-Term Examination

20%

Portfolio

20%

Project

20%

Final Examination

20%

Total

100%