Course Essentials

Course Description

Math 106: This course covers the mathematical concepts needed for teaching elementary school mathematics.  Topics include the real number system, geometry, Pythagorean Theorem, measurement in both the English and metric systems, transformations, and symmetry.

Prerequisite: MATH 105 - Concepts and Structures of Elementary Mathematics I 

Upon entering this course, the student should be able to do the following:

1. Perform calculations with place value systems including refined arithmetic skills with fractions, decimals, and percents.

2. Evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances.

3. Apply algorithms from number theory to determine divisibility in a variety of settings.

4. Analyze least common multiples and greatest common divisors and their role in standard algorithms.

5. Explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations; and justify their equivalence.

6. Use concrete examples or appropriate technology to explain mathematical concepts, model mathematical structures, and solve problems contained in the elementary school mathematics curriculum.

7. Analyze the structure and properties of whole, rational, and real number systems; define the concept of rational and irrational numbers, including their decimal representation; and illustrate the use of a number line representation.

8. Develop cognitive reasoning skills through practice and assessment of various types of problem-solving strategies, including problem restatement, problem simplification, working backwards, designing models, guess-test-revise, use of algorithms, and pictures, sets, charts, and graphs.

9. Develop logical skills to demonstrate justifications and basic proofs using evidence and reasoning to reach valid conclusions.

10. Develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation.

11. Develop activities implementing curriculum standards and relate the California academic standards for mathematics education to the mathematical topics contained in this course and the elementary school mathematics curriculum.

REQUIRED MATERIALS AND MINDSET

• A Problem Solving Approach to Mathematics for Elementary School Teachers - 13th ed. by Billstein, Boschmans, Libeskind, Lott (ISBN: 978-0-13-518388-5).  The e-book is available for purchase here for $10.99/month (ISBN: 978-0-13-688014-1).

• Activities Manual for A Problem Solving Approach to Mathematics for Elementary School Teachers - 13th ed. by Dolan.  (ISBN: 978-0-13-499561-8).

• A scientific calculator is required for this course. If you will be purchasing a calculator for this course, one I recommend is the Casio fx-300 ES Plus scientific calculator.  These are less than $20 at the bookstore, but is between $13 and 19 at Target/WalMart/Amazon/etc. 

• Compass and ruler (I will let you know when we will start to need these)

• Determination, hard work, and desire to succeed!

Accessibility Statement 

I have made every attempt to ensure this course is accessible for all students. If you encounter any accessibility-related difficulties with required or optional course materials, please contact me as soon as possible so that we can investigate the matter further and provide equally effective alternatives, if needed.