UW COLLEGES

DEPARTMENT OF MATHEMATICS

 

COURSE GUIDELINE

 

 

Course Title.  Geometry for Elementary Teachers

Course No.     MAT 132         No. of Credits.  4  

Contact hrs/week.   Lecture/Discussion  4  or Lecture 3/ Lab 2.   

 

Course prerequisites.  A grade of C or better in MAT 105 or MAT 108, or two years of  high school algebra and one year of high school geometry, or cons. instr.

 

Catalog description:

            The course emphasizes geometric concepts.  Topics also may include concepts of algebra, probability and statistics.  Four hours lecture or three hours lecture and two hours laboratory per week. 

Prereq:  a grade of C- or better in MAT 105 or MAT 108, or two

            years of high school algebra and one year of high school geometry, or cons. instr.

 

Course content (list of topics normally covered):

·         NCTM Curriculum and Evaluation Standards

·         Geometric Shapes

                 Recognizing Geometric Shapes and Definitions

                 Analyzing Shapes

                 Properties of Geometric Shapes:  Lines and Angles

                 Regular Polygons and Tessellations

                 Describing Three-Dimensional Shapes

·         Measurement

Measurement with Non-standard and Standard Units, including Unit Conversion

                 Length and Area

                 Surface Area

                 Volume

·         Geometry Using Triangle Congruence and Similarity

                 Congruence of Triangles, including formal proofs using the three postulates

                 Similarity of Triangles

                 Standard Euclidean Constructions – e.g., Construction of an angle bisector, perpendicular bisector, parallel and      perpendicular lines given a line and a point not on it, circumscribed and inscribed circles.

                 Problem Solving Using Triangle Congruence and Similarity

·         Geometry Using Coordinates

                 Distance and Slope in the Coordinate Plane

                 Equations and Coordinates

                 Problem Solving Using Coordinates

·         Geometry Using Transformations

                 Transformations

                 Congruence and Similarity Using Transformations

                 Geometric Problem Solving Using Transformations

 

Content-based department proficiencies:

     Students should be able to

§         Describe, model, draw, compare and classify geometric figures;

§         Visualize and represent geometric figures with special attention to developing spatial

       sense; build and manipulate mental representations of two- and three-dimensional

       objects;

§         Understand and apply geometric properties and relationships;

§         Represent and solve problems using geometric models and a variety of strategies;

§         Predict the results of combining, subdividing, and changing shapes, while working with projections, cross-sections, rotations,        reflections, and translations;

§         Classify figures in terms of congruence and similarity and apply these relationships;

§         Understand and apply the attributes of length, capacity, weight, perimeter, area, volume, and angle measure;

§         Understand the idea of a unit and the need to select a unit appropriate to the attribute being measured, understanding that        measurements are approximate and that different units affect precision;

§         Know the standard systems of units;

§         Make and use measurements in problem and everyday situations; make and use estimates of measurement;

§         Communicate geometric ideas, knowing technical vocabulary and understanding the

       power of precise mathematical terminology;

           

Colleges-wide proficiencies assigned to course:

 

Students should be able to demonstrate the following:

A. Analytical skills Performance Indicators: Students should be able to:

1. Interpret and synthesize information and ideas.

4. Select and apply scientific and other appropriate methodologies.

 

B. Quantitative skills Performance Indicators: Students should be able to:

1. Solve quantitative and mathematical problems.

2. Interpret graphs, tables, and diagrams.

 

Recommended Software:  The Geometer’s Sketchpad, Cabri, or Logo Turtle Graphics

 

Representative textbooks used for the course: (editions change over time)

A Problem Solving Approach to Mathematics for Elementary Teachers (7th Edition) by  Billstein, Libeskind, and Lott. Addison Wesley.

Mathematics for Elementary Teachers (5th Edition) by Musser, Burger and Peterson. John Wiley & Son

            Mathematics for Elementary Teachers (2nd Edition) by Sonnabend.  Saunders College Publishing; Harcourt Brace.

            Mathematics for Elementary Teachers A Conceptual Approach (5th Edition) by Bennett and Nelson. McGraw Hill.

            Geometry for Teachers by Collier

 

 Approved April 22, 2006