ModelCourses/Math for Elementary Education

Mathematics for Elementary Educators
PREP 2011 Model Course
Prepared by Mike Diehl and Jonathan Duncan

Description

This is a model course for a two-term Mathematics for Elementary Educators course. Below is a list of topics and sub-topics arranged in an order that is common for many texts on the subject.

To Do

• Finish writing/finding problems (have approximately 240, need approximately 30 more)
• Write set header files
• Create PDF files for homework assignments
• Tag written problems for NPL
• Write solutions
• Shamelessly copy Multi-variable Calculus wiki layout

List of Topics

First Term

• Problem Solving Strategies
  • General Strategies
  • Patterns
  • Algebra
  • Logical Reasoning

• Sets and Functions
  • Sets and Set Operations
  • Counting with Sets and Venn Diagrams
  • Functions and Their Properties
  • Function Applications
• Numeration Systems
  • Ancient Numeration Systems
  • The Hindu-Arabic System
  • Bases Other than Ten

• Whole Number Arithmetic
  • Addition
  • Subtraction
  • Multiplication
  • Division

• Number Theory
  • Divisibility
  • Tests for Divisibility
  • Primes and Prime Factorization
  • Greatest Common Divisors and Least Common Multiples

• Integers, Fractions, and Rational Numbers
  • Integer Operations
  • Modeling Fractions
  • Fractional Number Sense
  • Fraction Operations

• Decimals and Real Numbers
  • Irrational and Real Numbers
  • Decimal Computation and Applications

• Proportions and Percents
  • Ratios and Proportions
  • Percents

Second Term

• Coordinate Geometry
  • Cartesian Coordinate System
  • Graphing and Applications
  • Connecting Algebra and Geometry

• Geometric Figures
  • Figures in the Plane
  • Polygons
  • Figures in Space

• Symmetry and Transformations
  • Similarity Transformations
  • Types of Symmetry
  • Tiling the Plane

• Measurement: Length, Area and Volume
  • Units of Measure
  • Area and Perimeter
  • Pythagorean Theorem
  • Similarity
  • Volume and Surface Area

• Statistics
  • Organizing Data
  • Populations and Sampling
  • Measures of Center
  • Measures of Variation
  • Measures of Relative Standing

• Probability
  • Introduction to Probability
  • Principles of Counting
  • Theoretical Probability
  • Random Variables and Expected Value