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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 155
Course Title: Algebraic Reasoning for Elementary and Middle School Teachers
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

This course introduces some basic concepts of number theory and modern algebra that underlie elementary and middle grade arithmetic and algebra, with a focus on collaborative learning and technology. Prerequisites: MATH 102 and MATH 150 (or higher).

Prerequisite(s) / Corequisite(s):

MATH 102 and MATH 150 (or higher).

Course Rotation for Day Program:

Offered odd Fall.

Text(s): Most current editions of the following:

A TI-84 calculator is required for this course.

Geogebra, a freeware program, is required.

Developing Essential Understanding of Algebraic Thinking; Grades 3-5
By Blanton, M., Levi, L., Crites, T., and Dougherty, B.J. (NCTM)
Developing Essential Understanding of Expressions, Equations & Functions; Grades 6-8
By Lloyd, G., Herbel-Eisenmann, B., and Star, J. R. (NCTM)
Course Objectives
  • To progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction, and formal proof.
  • To use technology (calculator and computer) as a learning and teaching tool for mathematics.
  • To learn the algorithmic approach to problem solving.
  • To display an understanding of the nature of rigorous proof.
  • To write elementary proofs, especially proofs by induction and basic number theory proofs.
Measurable Learning
  • Know the basic properties of the real numbers including commutativity, associativity, identity, distributivity.
  • Use the basic properties of the real numbers to determine equivalent algebraic equations and solve algebraic equations.
  • Use equations to model problem solving situations.
  • Understand and use a variable to generalize a pattern, to represent a fixed but unknown number, to represent a quantity varies in relation to another quantity and that a variable can be a discrete or continuous quantity.
  • Use quantitative reasoning to generalize relationships.
  • Use functional thinking to generalize relationships between covarying quantities and to express those relationships in words, symbols, tables, or graphs and reason with those relationships to analyze function behavior.
  • Represent patterns algebraically.
  • Compare and contrast the concepts of equality or equivalence.
  • Find values that make two expressions equal.
  • Understand that an inequality can describe a relationship between equalities and solve these inequalities.
  • Understand and describe recursive relationships.
  • Classify functions based on the rate at which the variables change and the situations that they model.
  • Solve equations using symbolic, graphical and numerical methods.
Topical Outline:
  • Arithmetic as Context for Algebraic Thinking
  • Equations and Equivalence
  • Variables
  • Quantitative Reasoning and Generalizations
  • Representing Functions
  • The Symbolic Language of Algebra
  • Expressions as Building Blocks
  • Variables for studying varying quantities
  • Equality vs. Equivalence
  • Functions for modeling
  • Rates of change
  • Solving Equations graphically, symbolically and numerically

Recommended maximum class size for this course: 20

Library Resources:

Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

Prepared by: Ann Schlemper Date: May 22, 2014
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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