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PALOMAR COLLEGE
 COURSE OUTLINE FOR CREDIT COURSE
 
  • Courses numbered 1 - 49 are remedial or college preparatory courses which do not apply toward an A. A. Degree and are not intended for transfer.
  • Courses numbered 50-99 apply toward an AA Degree, but are not intended for transfer.
  • Courses numbered 100 and higher apply toward an AA Degree and/or are intended for transfer to a four-year college or university.
 
Course Number and Title: MATH 105 Concepts of Elementary Mathematics I
 

Unit Value: 3  

Lecture Hours Per Week: 3  

Lab Hours Per Week:  

Lecture/Lab Hours Per Week:  

 

Grading Basis: Grade/Pass/No Pass
 
Basic Skills Requirements: Appropriate Language and/or Computational Skills.
 
Requisite(s)
To satisfy a prerequisite, the student must have earned a letter grade of A, B, C or P(Pass) in the prerequisite course, unless otherwise stated.
Prerequisite:
A minimum grade of 'C' in MATH 56 or A minimum grade of 'C' in MATH 60 or eligibility determined through the math placement process
Corequisite:
None
Prerequisite: Completion of, or concurrent enrollment in
None
Recommended Preparation:
None
Limitation on Enrollment:
None
Catalog Description:
Selected topics from the real number system including properties and operations with integers and rational numbers as fractions and decimals. Additional topics include problem solving, numeration systems, number theory, and topics in logic and set theory. Recommended for prospective teachers.
 
Specific Course Objectives:
Upon successful completion of the course the student will be able to:
  1. Use concrete examples to understand and explain mathematical concepts contained in the elementary school mathematics curriculum.
  2. Use critical thinking skills to analyze and solve problems containing concepts from the elementary school mathematics curriculum.
  3. Use problem-solving skills to deduce valid conclusions.
  4. Evaluate, compare, and contrast mathematical and logical techniques and concepts.
  5. Relate the California academic standards for mathematics education to the mathematical topics contained in this course and the elementary school mathematics curriculum.
  6. Use appropriate technology to research and explore mathematical topics and to solve problems.
 
Methods of Instruction:
Methods of Instruction may include, but are not limited to, the following:
  1. Lecture
 
Content in Terms of Specific Body of Knowledge:

At least the following topics will be covered:

  1. Problem Solving:
    1. Polya's four-step method.
    2. Problem solving strategies.
  2. Sets:
    1. Definitions and relationships: set, proper and improper subset, complement, empty set.
    2. Venn diagrams.
    3. Operations with sets:
      1. Unions and intersections.
    4. Problem solving with sets.
  3. Numeration Systems/Counting:
    1. Early counting systems.
    2. Understanding place value.
    3. Bases other than Base Ten.
  4. Whole Number Operations:
    1. Addition and subtraction:
      1. Ways of thinking about addition and subtraction; children's conceptions and methods.
      2. Standard and nonstandard algorithms; bases other than Base Ten.
    2. Multiplication and division:
      1. Ways of thinking about multiplication and division; children's conceptions and methods.
      2. Standard and nonstandard algorithms; bases other than Base Ten.
    3. Number Sense:
      1. Mental computations and computational estimations.
      2. Using scientific notation for estimating values of very large or very small quantities.
  5. Fractions:
    1. Meanings for fractions:
      1. Meanings of a/b.
      2. Equivalent fractions.
      3. Relating fractions and decimals; rational and irrational numbers.
    2. Operations with fractions:
      1. Ways of thinking about adding and subtracting fractions.
      2. Algorithms for adding and subtracting fractions.
      3. Ways of thinking about multiplying and dividing by fractions.
      4. Algorithms for multiplying and dividing by fractions.
    3. Fractions in Multiplicative Reasoning:
      1. Rates and ratios.
      2. Comparing ratios using proportions.
      3. Percents in comparisons and changes.
  6. Integers:
    1. Ways of thinking about signed numbers.
    2. Operations with integers:
      1. Ways of thinking about adding and subtracting signed numbers.
      2. Adding and subtracting signed numbers.
      3. Ways of thinking about multiplying and dividing signed numbers.
      4. Multiplying and dividing signed numbers.
    3. Algebraic structures:
      1. Field axioms for the rational numbers.
      2. Other numeration systems.
  7. Number Theory:
    1. Primes and composites; factors and multiples.
    2. Prime factorization; determining if a number is prime or composite.
    3. Divisibility tests.
    4. Greatest common factor; least common multiple.
  8. Additional topics may be included at the instructor's discretion. 
Textbooks/Resources:
May Include Textbooks, Manuals, Periodicals, Software, and Other Resources
  1. Sowder, Judith, Larry Sowder, and Susan Nickerson. Reconceptualizing Mathematics for Elementary and Middle School Teachers, Course One: Reasoning with Numbers and Quantities . 3rd ed. San Diego: San Diego State University, 2005.
Required Reading:
Mathematics Content Standards for California Public Schools, Kindergarten Through Grade Five.
 
Suggested Reading:
NCTM, Professional Standards for Teaching Mathematics.
 
Critical Thinking:
Exercises and exams must emphasize the development of insight into the relationships and concepts contained in the mathematics of the elementary school curriculum.
 
Required Writing:
In addition to writing solutions to homework problems using proper mathematical notation and logic, students will write detailed explanations as part of their answers when required to do so.

Students will also write about their analyses of children's errors, the Mathematics Content Standards for Californina Public Schools (K - 5), and other topics relevant to the elementary school mathematics curriculum.
 
Outside Assignments:
Students are expected to spend a minimum of three hours per unit per week in class and on outside assignments, prorated for short-term classes.

Outside assignments include written assignments, reading assignments, review of lecture material, or problem sets as deemed necessary by the instructor.
 
Methods of Assessment:
Methods of Assessment may include, but are not limited to, the following:
  • Class Work
  • Exams/Tests
  • Group Projects
  • Homework
  • Papers
  • Quizzes
 
Open Entry/Open Exit:
No, course is not offered as open entry/open exit.
 
Is Course Repeatable for Reason(s) Other Than Deficient Grade? No
 
Contact Person: Robert N Jones