Course Design for Principles of Mathematics I

Prerequisites

MAT 140 or MAT 154 with a grade of "C" or higher or placement test score as established by
District policy

Educational Value

To provide students with a better understanding of the fundamental concepts of mathematics that are
generally taught in an elementary school. To expose students to a variety of mathematical ideas and
methods for teaching elementary mathematics.

Description

Mathematical principles and processes underlying mathematics instruction in grades K-8; problem
solving, number theory , systems of whole numbers, integers, rational numbers , real numbers, ratios,
decimals , and percents.

Textbooks

O'Daffer, Charles, Cooney, Dossey, Schielack Mathematics for Elementary School Teachers Fourth
Edition Addison Wesley 2008. Required.

Supplies

None

Competencies and Performance Standards
1. Investigate mathematical reasoning
Learning objectives
What you will learn as you master the competency:
a. Discuss inductive and deductive reasoning.
b. Apply inductive and deductive reasoning
c. Discuss Polya's four steps in problem solving.
d. Apply a variety of problem solving strategies.
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams.
on a cumulative exam.
Your performance will be successful when:
You can discuss inductive and deductive reasoning.
You can apply inductive and deductive reasoning.
You can discuss Polya's four steps in problem solving.
You can apply a variety of problem solving strategies.

2. Understand sets and set notion
Learning objectives
What you will learn as you master the competency:
a. Understand the basic terminology and notation of sets.
b. Define the set operations intersection , union, and Cartesian product.
c. Determine the intersection, union, and Cartesian product of given sets.
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams
on a cumulative exam
Your performance will be successful when:
You can understand the basic terminology and notation of sets.
You can define the set operations intersection, union, and Cartesian product.
You can determine the intersection, union, and Cartesian product of given sets.

3. Understand the set of Whole Numbers
Learning objectives
What you will learn as you master the competency:
a. Compare and contrast the following numeration systems : tally, Egyptian, Babylonian,Roman, and
Hindu- Arabic.
b. Demonstrate two models for place value.
c. Define the following operations on whole numbers: addition, subtraction, multiplication, and
division.
d. Illustrate addition as a union of sets, and as measures on a number line .
e. Illustrate the take away and comparison meanings of subtraction using sets and measures on a
number line.
f. Illustrate the various meanings of multiplication using sets and measures.
g. Illustrate the various meanings of division using sets and measures.
h. understand and apply the properties of whole number operations.
i. Understand and demonstrate a variety of algorithms for whole number operations.
j. Discuss strategies for mental computation and estimation of whole number operations.
Performance Standards
You will demonstrate your competence:
on assigned activities.
on written exams.
on a cumulative exam.
Your performance will be successful when:
you can compare and contrast the following numeration systems: tally, Egyptian, Babylonian,
Roman, Hindu-Arabic.
you can demonstrate two models for place value.
you can define the following operations on whole numbers: addition, subtraction, multiplication,
division.
you can illustrate addition as a union of sets, and as measures on a number line.
you can illustrate the take away and comparison meanings of subtraction using sets and measures
on a number line.
you can illustrate the various meanings of multiplication using sets and measures.
you can illustrate the various meanings of division using sets and measures.
you can understand and apply the properties of whole number operations.
you can understand and demonstrate a variety of algorithms for whole number operations.
you can discuss strategies for mental computation and estimation of whole number operations.