Prefix, Number, and Name of Course:  MAT 521  Math for Teachers: Geometry

Credit Hours:                        3

In-Class Instructional Hours:         3          Labs:  0          Field Work:   0

 

Catalog Description:

Formal and informal geometry; congruence; measurement; constructions; similarity; transformations; coordinate geometry; trigonometric functions.

 

Reasons for revision:

1.     To provide a graduate level course that provides an in-depth study of the

concepts of Geometry contained in the 7-12 bands of the New York State Core Curriculum.

2.     To provide a graduate level course that helps teachers integrate geometry software into the learning of Geometry.

 

Student Learning Outcomes:

 

Students will:

Course Content References:

Assessment:

 

1.   solve problems and write proofs within an axiomatic system

 

I - V

 

1.   Quizzes, group work, classroom activities, individual assignments, exams, projects

 

2.  present formal and informal   arguments using geometric reasoning

 

I - V

 

2.   Quizzes, group work, classroom activities, individual assignments, exams, projects

 

3.   develop techniques of visual and spatial reasoning using principles of synthetic geometry

 

 

II, III, V

 

3.   Quizzes, Group work, classroom activities, individual assignments, exams, projects

 

4.   demonstrate knowledge of planar and solid geometric objects

 

 

II, III, V

 

4.  Quizzes, Group work, classroom activities, individual assignments, exams, projects

 

5.   apply algebraic techniques to solve geometric problems.

 

 

IV, V

 

5.   Quizzes, Group work, classroom activities, individual assignments, exams, projects

Course Content

I.         Formal and Informal Geometry

  1. Undefined Concepts (points, lines, segments, and angles)
  2. Definitions
  3. Postulates / Axioms
  4. Formal and Informal Proofs

II.        Synthetic Geometry Part A – Plane Geometry

  1. Triangles

1.     Congruency Theorems

2.     Triangle Inequalities

3.     Similarity

4.     Properties of Triangles, Medians, Angle Bisectors, Centroids

5.     Right Triangles (Pythagorean Theorem and Generalizations, Trig Ratios, Law of Sine and Cosine)

B.  Parallels

C.  Polygons

1)    Properties of Quadrilaterals

2)    Angle Sum Theorem

3)    Regular Polygons

4)    Tessellations

5)    Area and Perimeter

D. Circles

1)    Theorems Relating Chords, Tangents, and Secants and Angles

2)    Geometric Development of π

3)    Measures of Circumference and Area

4)    Constructions and Loci (Compass and Straightedge / Geometric Software)

III.      Synthetic Geometry Part B – Solid Geometry

  1. Platonic Solids
  2. Prisms, Cylinders, Pyramids
  3. Spheres
  4. Euler’s Theorem
  5. Surface Area and Volume
  6. Cavalieri’s Principle

IV.      Plane Analytic Geometry

  1. Cartesian Coordinates
  2. Equations of Lines and Circles
  3. Locus Problems

V.        Transformations

  1. Isometries
  2. Translations, Rotations, Reflections, Glide Reflections, and their Compositions, Inverses, Invariants
  3. Similarities
  4. Relation to Group Theory

 

Resources:

 

Classic Scholarship in the Field:

Coxeter, H. S. M. &  Greitzer, S. L. (1967). Geometry revisited. New York: Singer.

Coxeter, H. S. M. (1969). Introduction to geometry.  Toronto: John Wiley & Sons, Inc.

Eves, H. (1965). A survey of geometry.  Allyn & Bacon, Inc.: Boston

Martin, G. E. (1982).  Transformation geometry: An introduction to symmetry.  New York: Springer-Verlag.

Moise, E. (1963) Elementary geometry from an advanced standpoint. New York: Addison Wesley.

Current Scholarship in the Field:

Blau, H. I. (2003).  Foundations of plane geometry. Upper Saddle River, New Jersey: Pearson Education, Inc.

Center for Occupational Research and Development (1999),  Cord geometry – Mathematics in context. New York: South-Western Educational Publishing.

Gay, D. (1998).  Geometry by discovery.  New York: John Wiley & Sons, Inc.

Geltner, P. B., & Peterson, D. J. (1995).  Geometry for college students, 3rd Ed. New York: PWS Publishing Company

Henderson, D. W. (2001).  Experiencing geometry.  Prentice-Hall, Inc.: New York: Prentice Hall, Inc.

Smart, J. R. (1998).  Modern geometries  5th Edition. New York: Brooks/Cole Publishing Company.

Periodicals:

The College Mathematics Journal

Mathematics Magazine

The Mathematics Teacher

Teaching Mathematics in the Middle School

Electronic Resources:

Geometer’s Sketchpad,  Key Curriculum Press.

            http://www.keypress.com/sketchpad/