MA151 MATHEMATICS FOR THE ELEMENTARY SCHOOL TEACHER II (4 Cr.)

COURSE DESCRIPTION

Prerequisite: MA150 (Mathematics for the Elementary School Teacher I) with a C or better.

General Introduction and Goals

This second mathematics course for prospective elementary teachers is designed to examine the areas of probability, statistics, geometry, and logical reasoning. Geometry is developed informally through identifying and characterizing, drawing, constructing, and measuring shapes. Transformational geometry and proofs, both informal and formal, are also included in the course.

In this course the students will:

1. study experimental probability and develop the concepts of theoretical probability and simulation;
2. make and use various statistical tables and graphs to describe and summarize data;
3. examine the clustering and dispersion of data and relate these to the "normal" distribution;
4. study plane and three-dimensional figures and their properties;
5. develop logical arguments and formal proof through inductive and deductive reasoning;
6. develop the concept of congruence and similarity;
7. use and analyze transformations;
8. understand the metric system and develop skill in using it;
9. concretely examine perimeter and area and to solve problems involving them;
10. concretely examine the concepts of surface area and volume of three-dimensional object and solve problems involving the concepts;
11. develop the Pythagorean relationship and the distance and midpoint formulas;
12. solve problems in probability, statistics and geometry.
     

Course Content

1. Probability
   1. One stage experiments
   2. Multiple stage experiments
   3. Odds
   4. Mathematical expectation
   5. Simulation
2. Counting
   1. Fundamental principle of counting
   2. Combinations
   3. Permutations
3. Statistics
   1. Constructing different statistical graphs to summarize data
   2. Measures of central tendency, dispersion, and their meanings with respect to the "normal" distribution
   3. The role of statistics in the elementary school curriculum and in interpreting student data
4. Introductory Geometry
   1. Notions of points, lines, angles, planes, and their relationships
   2. Characteristics of polygons, studied through the use of geoboards, LOGO, Geometry Sketchpad and concrete representations
   3. Three-dimensional geometry -- analysis of polyhedra, cylinders, cones, and spheres
   4. Transformations: slides, flips, and turns
5. Congruence
   1. Logical arguments and formal proof of triangle congruence
   2. Construction of congruent segments and triangles with compass and protractor
6. Other Constructions
   1. Parallel and perpendicular lines, angles and segment bisectors
   2. Circle and triangles -- inscribing circles and circumscribing circles
   3. Constructions through transformations (Mira)
7. Similarity
   1. Properties of similar figures
   2. Problem solving using similar figures and proportion
8. Measurement
   1. The metric system
   2. Area and perimeter of polygons and circles
   3. Surface area and volume measures
   4. Mass and temperature
9. Coordinate Geometry
   1. Rectangular coordinate system
   2. Distance and midpoint formulas
   3. Systems of equations and applications.

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