Discipline: Mathematics
Originator: Kenneth Cramm

# Riverside Community College District Integrated Course Outline of Record

Mathematics 26
 MAT-26 : Math for Elementary School Teachers College: RIV MOV Lecture Hours: 54.000 Outside-of-Class Hours: 108.000 Units: 3.00 Grading Methods: Pass/No Pass Letter Grade
Course Description
Prerequisite: MAT-35or qualifying placement level.
Course Credit Recommendation: Degree Credit

This course is designed for pre-service elementary school teachers. The course will examine five content areas: numeration; number theory; properties of numbers; problem solving; and curriculum standards. 54 hours lecture. (Letter Grade, or Pass/No Pass option.)
Short Description for Class Schedule
This course is designed for students majoring in education.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
1. Solve rational, radical, linear, quadratic, literal equations/applications, linear inequalities/applications by choosing an appropriate method
2. Find the domain of rational, irrational, linear, quadratic, and absolute value relations
3. • Perform operations on functions including composition of functions
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
1. Perform calculations with place value systems.
2. Evaluate the equivalence of numeric algorithms and explain the advantages and disadvantages of equivalent algorithms in different circumstances.
• Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
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.
• Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
6. Analyze the structure and properties of whole, rational, and real number systems.
7. Develop and reinforce conceptual understanding of mathematical topics through the use of patterns, problem solving, communication, connections, modeling, reasoning, and representation.
8. Develop activities implementing curriculum standards.
• Information Competency & Technology Literacy: Students will be able to use technology to locate, organize, and evaluate information. They will be able to locate relevant information, judge the reliability of sources, and evaluate the evidence contained in those sources as they construct arguments, make decisions, and solve problems.
9. Define the concept of rational and irrational numbers, including their decimal representation.
10. Illustrate the use of a number line representation.
11. Analyze the arithmetic algorithms for ratio and decimal representations and justify their equivalence.
Course Content:
1. Numeration systems
1. History
2. Hindu-Arabic numeration system
3. Other place value systems
2. Integers
1. Structure and basic properties
2. Computational algorithms
3. 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
4. Rational numbers
1. Structure and properties
2. Ratio and proportion;
5. Real numbers
1. Structure and basic properties
2. Arithmetic operations
3. Rational and irrational numbers
4. Decimal representation
5. Number line representation;
6. Patterns
1. Identification and characteristics
2. Modeling
3. Finalizing representations
7. Problem solving
1. Communication using symbols and verbal information
2. Types of reasoning
3. Establishing connections
8. California Common Core curriculum standards for elementary school math.
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
• Lectures/discussions/demonstrations with question and answer periods that both disseminate information and pose problems in analyzing the structure and properties of whole, rational, and real number systems.
• Create small group activities in order to provide an opportunity for students to the practice explain the advantages and disadvantages of equivalent algorithms in different circumstances
• Develop and assign class exercises that build mathematical and reasoning skills using algorithms from number theory.
• Show videos/films/computer programs that reinforce conceptual understanding of mathematical patterns, modeling, and reasoning.
• Create group/individual project that identifies strengths and weaknesses of California’s curriculum standards for elementary school math
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
• Oral reports/presentations aimed to demonstrate knowledge of California’s curriculum standards for elementary school math
• Quizzes, examinations, and written assignments designed to assess the progress and ability to accomplish calculations with place value systems, and curriculum.
• Midterm and final examination designed to assess students’ mastery and ability of the concept of rational numbers, algorithms from number theory, and/or pattern recognition.
Sample Assignments:
• Reading of the textbook, handouts, lecture notes on implementing curriculum standards
Outside-of-Class Writing Assignments
• Problem sets requiring students to present complete solutions to algorithms from number theory, using both ratio and decimal representations, and calculations with place value systems
Other Outside-of-Class Assignments
• Review of study guides and homework problems on the advantages and disadvantages of equivalent algorithms in different circumstances
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
• Bassarear. Mathematics for Elementary School Teachers. 5th Houghton Mifflin, 2011.
• Musser, Peterson,Burger. Mathematics for Elementary Teachers. 10th Wiley, 2013.
• Sowder, Sowder, Nickerson. Reasoning About Numbers and Quantities. 2nd W.H. Freeman, 2013.
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: N/A (not in college inventory) (D)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
Board of Trustees Approval Date: 12/09/2014
COR Rev Date: 12/09/2014