**Textbooks:**

Mathematics for Elementary School Teachers, 2^{nd} Edition by P. O’Daffer, R.
Charles, T.

Cooney, J. Dossey, J. Schielack. Addison-Wesley, 2002.

Teaching and Learning Elementary and Middle School
Mathematics, 5^{th} Edition by L. J.

Sheffield and D. E. Cruikshank. Wiley, 2005.

**Prerequisites:** MATH 1030 with a grade of “C” or
better.

**Course Description:** Math 2030 is the second
semester in a three-semester sequence of

integrated content and methods courses for preservice teachers . It is open only
to students

in elementary education pursuing certification levels B – 11 or 10 – 14. (The
course is not

intended for students pursuing certification level 10 – 21.) Topics covered
include

number theory ; composition and decomposition of numbers including primes,
factors,

and multiples ; using physical models to develop concepts of and operations on
rational

numbers; proportional reasoning ; number sense; and selected topics from
statistics.

Throughout the course, students will be expected to explain their reasoning
using

appropriate vocabulary and notation.

**Test-out Policy:** Math 2030 is an integrated content
and methods course for preservice

teachers. Much of the content material will be embedded in in-class activities
that model

a variety of teaching methods. As a result, students will be actively involved
in doing

mathematics during the class period. Because of the significant amount of
in-class

participation, a student will not be allowed to test out of this course.

**Topics to be covered:**

**Number Theory** – Problem solving is a large
component of this course as well as Math

3030. As such, we begin this course with problems solving involving number
theory.

This study of number theory will help develop a foundation for later work with
operation

on rational numbers . Students will be expected to explain their reasoning using

appropriate vocabulary and notation.

• Divisibility

• Prime Numbers

• Composite Numbers

• Prime Factorization

• Greatest Common Divisor

• Least Common Multiple

**Rational Number Concepts **– In order to better
understand the teaching and learning of

rational numbers, we will study some of the fundamental ways in which students

encounter rational numbers. We will also develop some ways to physically model

rational numbers. Students will be expected to explain their reasoning using
appropriate

vocabulary and notation.

• Part-Whole Concept

• Ratio Concept

• Rate Concept

• Measurement Concept

• Modeling Rational Numbers

o Area Models (using Fraction Circles , Fraction Factories, Pattern
Blocks)

o Linear Models (using Fraction Strips)

o Discrete Models

**Modeling Rational Number Operations** – After
developing some models for thinking

about rational numbers we develop ways to model operations on rational numbers.

Students will be expected to explain their reasoning using appropriate
vocabulary and

notation.

• Operations on Fractions

• Operations on Decimal Fractions

**Modeling Rational Number Operations** – After
developing some ways to model

operations on rational numbers, we study in depths some specific contexts where
students

encounter rational numbers. Students will be expected to explain their reasoning
using

appropriate vocabulary and notation.

• Proportional Reasoning Strategies (Build- Up Add -On Equivalent-Fractions,
Factorof-

Change , Unit-Rate)

• Solving Percent Problems

• Converting between Representations of Rational Numbers (Fraction Form

<->Decimal Form<->Percent Form <->Ratio Form)

• Linear Equations