SPRING 2003

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 combinatorics 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,” 3rd 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%

Take-Home Mid-Term

20%

Portfolio

20%

Project

20%

Take-Home Final

20%

Total

100%

                                                                                                                                                                                                 

 
View the requirements for the Mathematical Reasoning Portfolio.

View the requirements for the Mathematics Reasoning Project.
View the lesson plan format for this course.
View the assignments for this course.
View the course description.
View some of your instructor's policies.

View the Math ADEPT home page.

View Don Cathcart's home page.



 This course was developed under the auspices of the Maryland MATH ADEPT (MD-ADEPT) project at Salisbury University.  Support for MD-ADEPT and two MD-ADEPT courses was provided by the Maryland Higher Education Commission (MHEC) via Eisenhower funds grant 4-31050.  Opinions, findings, and conclusions expressed herin do not necessarily reflect the position or policy of MHEC or the U.S. Department of Education, and no official endorsement should be inferred.

 

For more information about the Allied Delmarva Enhancement Program for Teachers see http://www.salisbury.edu/community/adept/