  
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 indepth, 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:
 Perform calculations with place value systems; evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances;
 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;
 Explain the concept of rational numbers, using both ratio and decimal representations; analyze the arithmetic algorithms for these two representations; and justify their equivalence;
 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
 Develop activities implementing curriculum standards.

Special Facilities and/or Equipment  
 Scientific calculator.

Course Content (Body of knowledge)  
  Numeration systems
 History
 HinduArabic numeration system
 Place value systems
 Integers
 Structure
 Basic properties
 Computational algorithms
 Basic number theory
 Divisibility
 Prime and composite numbers
 Prime factorization
 Fundamental theorem of arithmetic
 Least common multiple
 Greatest common divisor
 Rational numbers
 Structure
 Properties
 Ratio and proportion
 Real numbers
 Structure
 Basic properties
 Arithmetic operations
 Rational and irrational numbers
 Decimal representation
 Number line representation
 Curriculum standards for elementary school math
 National
 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  
 Mathematics


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  
  Completing homework problems each week covering subject matter from text.
 Reading textbook and other materials
 Reviewing lecture notes
 Completing a project related to subject matter that requires mathematical discussion, solutions written in accurate mathematical language and notation, and interpretation of mathematical results.
 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.
