Print Version

Effective: Summer 2013

Prerequisites: Prerequisite: Satisfactory score on the mathematics placement test or MATH 105 or 108 with a grade of C or better.
Advisory: Advisory: Demonstrated proficiency in English by placement as determined by score on the English placement test OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Grade Type: Letter Grade, the student may select Pass/No Pass
Not Repeatable.
FHGE: Non-GE Transferable: CSU/UC
5 hours lecture. (60 hours total per quarter)

Student Learning Outcomes -
  • After instruction, the student will be able to discuss the effects of math anxiety on the learning environment in an elementary classroom
  • After instruction, the student will be able to identify and demonstrate important properties of arithmetic operations.
  • After instruction, the student will be able to describe the mathematical structure of the integers, the rational numbers, and the real numbers.
  • After instruction, the student will be able to design and develop pedagogical strategies to help elementary students learn arithmetic.
Description -
Focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real numbers systems and subsystems. Emphasis is on comprehension and analysis of mathematical concepts and applications of logical reasoning.

Course Objectives -
The student will be able to:
  1. Perform calculations with place value systems; evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances;
  2. Apply algorithms from number theory to determine divisibility in a variety of settings; analyze least common multiples and greatest common divisors and their role in standard algorithms;
  3. Explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations; and justify their equivalence;
  4. 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; and
  5. Develop activities implementing curriculum standards.
Special Facilities and/or Equipment -
Scientific calculator.

Course Content (Body of knowledge) -
  1. Numeration systems
    1. History
    2. Hindu-Arabic numeration system
    3. Place value systems
    4. Integers
      1. Structure
      2. Basic properties
      3. Computational algorithms
  2. Basic number theory
    1. Divisibility
    2. Prime and composite numbers
    3. Prime factorization
    4. Fundamental theorem of arithmetic
    5. Least common multiple
    6. Greatest common divisor
  3. Rational numbers
    1. Structure
    2. Properties
    3. Ratio and proportion
  4. Real numbers
    1. Structure
    2. Basic properties
    3. Arithmetic operations
    4. Rational and irrational numbers
    5. Decimal representation
    6. Number line representation
  5. Curriculum standards for elementary school math
    1. National
    2. California
Methods of Evaluation -
Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.
Representative Text(s) -
Libeskind, Shlomo, Billstein, Rick and Lott, Johnny W., A Problem Solving Approach to Mathematics for Elementary School Teachers, Addison Wesley, 2009. ISBN 0321570553
Beckmann, Sybilla, Mathematics for Elementary Teachers with Activity Manual, Addison Wesley, 2010. ISBN 0321654277

Disciplines -
Method of Instruction -
Lecture, discussion, and collaborative learning exercises.
Lab Content -
Not applicable.
Types and/or Examples of Required Reading, Writing and Outside of Class Assignments -
  1. Completing homework problems each week covering subject matter from text.
  2. Reading textbook and other materials
  3. Reviewing lecture notes
  4. Completing a project related to subject matter that requires mathematical discussion, solutions written in accurate mathematical language and notation, and interpretation of mathematical results.
  5. Extended assessment activities and other nontrivial problems requiring extended responses that are not possible to complete in class. Such activities typically demand that students think critically about the prompts, assimilate knowledge gained in the course, and perhaps apply it in novel situations.