ROWAN UNIVERSITY

Department of Mathematics

Department of Mathematics

Syllabus

Math 03.600 — Topics in Elementary Mathematics

CATALOG DESCRIPTION:

Math 03.600 Topics in Elementary Mathematics 3 s.h.

This course is designed to improve the understanding and attitudes of practicing elementary teachers (K-8). Specific topics to be addressed include quantitative reasoning, spatial reasoning, inductive and deductive reasoning, mathematical systems, and communication in mathematics. Students will be expected to do some independent work.

**OBJECTIVES:**

This course is intended to provide students with the opportunity to develop their knowledge of the content and discourse of mathematics, including:

-- knowledge and understanding of mathematical reasoning: quantitative, spatial, inductive, and deductive.

-- analysis of mathematical systems, such as the real numbers, finite geometries, non-Euclidean geometries, or groups, rings, and fields.

-- use of various types and styles of mathematical communication, including explanations, proofs, examples and nonexamples, and problem solutions.

-- application of mathematical concepts to problems in selected situations.

-- understanding and appreciation of the interrelationships of various areas of mathematics, such as algebra, geometry, and analysis.

**CONTENT:**

Topics to be considered in this course will be selected from the following outline, in accordance with students' and faculty interests:

I. Pattern

A. Construction of numerical sequences

B. Construction of geometric sequences and patterns

C. Inductive and deductive reasoning

D. Examples and nonexamples

**II. Dimension**

A. Measuring volumes

B. Fractals

C. Higher dimensions

**III. Quantity**

A. Numbers and operations

B. Variables and relations

C. Procedures

D. Number systems

E. Applications

F. Topics from number theory

**IV. Uncertainty**

A. Estimation, graphing, and counting techniques

B. Data analysis

C. Statistical design

D. Probability

E. Inference

**V. Shape**

A. Classification

B. Symmetry

C. Lattices

D. Representation and visualization

E. Finite geometries

F. Non-Euclidean geometries

**VI. Change**

A. Dynamical systems

B. Underlying concepts of calculus

**VII. Communication in Mathematics**

A. Proof

B. Types and styles of oral and written communication

C. Explanation of concepts and algorithms

D. Examples and nonexamples

E. Problem solutions

**POSSIBLE TEXT(S):**

This course is particularly suitable for the use of multiple texts. Two which have been successfully used together are the following:

On the Shoulders of Giants: New Approaches to Numeracy by Lynn Arthur Steen.

Washington, D.C.: National Academy Press, 1990.

Principles & Standards for School Mathematics

from the National Council of Teachers of Mathematics. Reston, VA: NCTM, 1989.

Rubenstein, Beckmann, Thompson, TEACHING & LEARNING MIDDLE GRADE MATHEMATICS, Key College Pub, 2004

Great Source, MATH ON CALL: A MATHEMATICS HANDBOOK, Houghton Mifflin Co., 1998

Charles Randall, MATHEMATICS:GRADES K-ALGEBRA MATH ACROSS THE GARDENS, Pearson-Prentice Hall, 2005.

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