This course is designed to help preservice elementary school teachers develop a conceptual framework for mathematics, especially for those aspects normally experienced in elementary school. Through their work in the course the students study the main themes of mathematics throughout the curriculum, considering both mathematical and pedagogical content issues in teaching mathematics. Topics include sets, logic, informal geometry, numeration systems, properties of real numbers and an introduction to probability and statistics. Prerequisite: Grade of C or higher in MATH 104, or higher MATH course; or a score of 19 or above on the math portion of the ACT; or 460 or above SAT score; or a passing score on the Columbia College math placement exam.
Prerequisite(s) / Corequisite(s):
Grade of C or higher in MATH 104 or higher MATH course; or a score of 19 or above on the math portion of the ACT; or 460 or above SAT score; or a passing score on the Columbia College math placement exam.
Course Rotation for Day Program:
Most current editions of the following:
Mathematics for Elementary Teachers: A Conceptual Approach
By Bennett and Nelson (McGraw-Hill) Recommended
A Problem Solving Approach to Mathematics for Elementary School Teachers
By Billstein, Libeskind, and Lott (Pearson/Addison-Wesley) Recommended
Mathematics for Elementary Teachers
By O’Daffer, Charles, Cooney, Dossey, and Schielack (Pearson/Addison-Wesley) Recommended
To understand and demonstrate confidence in personal ability to do mathematics.
To become a persistent and successful mathematical problem solver.
To learn to reason and justify mathematically.
To learn to communicate mathematically.
To become an independent learner.
To learn to read mathematics for understanding.
To understand the role of language and precision in mathematics, in particular, the importance of defining mathematical terms.
To learn to choose and use representations (verbal, symbolic, visual, material, manipulative, technological) to enhance mathematical understanding.
To understand and master the topics of sets, sets of numbers and their structure, geometry and constructions, systems of numerations, probability statistics and logic.
Explain the concepts of whole numbers, integers, fractions, real numbers, ratio, proportion and percent.
Demonstrate the usual and some alternative algorithms for operations on whole numbers, fractions, decimals, integers and real numbers.
Justify and use estimation procedures.
Illustrate the relations of equality and inequality with whole numbers, integers, rational numbers and real numbers.
Apply basic number theory concepts to problem situations.
Organize and interpret data.
Calculate measures of central tendency and dispersion.
Solve problems involving probability.
Apply basic counting techniques to problem situations.
Identify and analyze 2- and 3-dimensional geometric figures.
Calculate 2- and 3-dimensional measurements of geometric figures.
Measure in the metric and customary units.
Justify the similarity or congruency of figures.
Demonstrate knowledge of the skills required for problem solving.
Use a variety of manipulatives to develop number and concepts, geometric concepts, spatial relationships and probability.
Use technology (calculator and computer) as a learning and teaching tool for mathematics.
Basic set theory
Whole numbers and numeration
Operations with whole numbers (addition, subtraction, multiplication and division), including the use of mental math, estimation, calculators and written algorithms
Primes, composites, and tests for divisibility
Factors, greatest common factor, and least common multiple
The set of fractions and operations with fractions
Decimals and operations with decimals
Integers and operations with integers
The real number system
Collecting, organizing, picturing, and analyzing data
Basic probability, including simple and complex experiments
Counting techniques, including the combinations and permutations
Recognizing and analyzing 2-dimensional and 3-dimensional geometric shapes
Lines and angles
Measurement with nonstandard and standard units
Length and area
Surface area and volume
Congruence and similarity of triangles
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.