Algebraic Reasoning for Elementary and Middle School Teachers
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.
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) Recommended
Developing Essential Understanding of Expressions, Equations & Functions; Grades 6-8
By Lloyd, G., Herbel-Eisenmann, B., and Star, J. R. (NCTM) Recommended
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.
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.
Arithmetic as Context for Algebraic Thinking
Equations and Equivalence
Quantitative Reasoning and Generalizations
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
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.