COURSE SYLLABUS

Ohio Northern University

College of Arts and Sciences

Department of Mathematics

Date: Fall 2005

Course MATH - 301 Name: Mathematics for Secondary Teachers

Credit hours: 4 Lecture hours/week: 4 Lab hours/week: 0

Instructor: Roepke

Usual student level: Junior/Senior

Course required of students in: secondary mathematics education

Course frequency per quarter/year: 1 section alternate years

Average enrollment per year: (alternate years) 10

This course has a prerequisite: Mathematics 294

This course is a prerequisite for:

Catalogue Description:

To include topics from the theory of arithmetic, numbers systems, theory of equations, functions, inequalities, limits, Euclidean and transformational geometry, coordinate geometry, solids, number theory, numerical methods, applications of mathematics to science and computer studies.

Course Objectives:

The purpose of this course is to allow the pre-service secondary mathematics teacher to re-examine the content he/she will be teaching and/or enrichment topics based on advanced understanding of the nature of mathematics and the nature of proof.

Textbook: Handouts by instructor

Outline of content follows:

(see attached)

Course Outline

MATH - 301

Title: Mathematics for Secondary Teachers

1. Problem Solving - Polya – Tower of Hanoi – sample problems (throughout course) – conjectures and proof

2. Set Theory - Number sets, definitions, Venn diagrams, Numeration and other bases

3. Relations, Functions, Equivalence relations

4. Operations and properties in W, Algorithms and alternate algorithms for operations, mental math and estimation

5. Number Theory – “divides,” primes, composites, divisibility, factors, GCF, LCM

Integers – models for operations, algorithms, properties, ordering

Rationals – Models, Operations, algorithms, ordering – other bases

Reals – irrationals, decimal representations, operations, properties, ordering

6. Some applications of secondary mathematics, Linear programming, Probability applied to baseball, The Birthday problem

7. LOGO – regular polygons, procedures, recursion, Fractals

Three-dimensional geometry, definitions, polyhedra, Euler’s Theorem, Platonic solids

8. Ceva’s Theorem, concurrency points on a triangle, Sketchpad constructions, conjectures, proofs

9. Bisecting an inaccessible angle, Three famous construction problems, inconstructibility arguments, constructing radical lengths, equilangular points, minimum distance problems, Ptolemy’s Theorem

10. Tessellations

11. Golden ratio, section, rectangle – Fibonacci sequence, properties, proofs – Binet form and link to golden ratio