Textbooks:
Mathematics for Elementary School Teachers, 2nd Edition by P. O’Daffer, R.
Charles, T.
Cooney, J. Dossey, J. Schielack. Addison-Wesley, 2002.
Teaching and Learning Elementary and Middle School
Mathematics, 5th 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
