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Mathematics for Elementary Teaching II

1. Catalog Description

MATH 327, 328, 329 Mathematics for Elementary Teaching I, II, III (4) (4) (4)

Introduction to set theory, number theory, real numbers, probability, statistics and geometry.
Computer applications. 2 lectures, 2 activities. MATH 327 prerequisite: Completion of ELM
requirement, and passing score on appropriate Mathematics Placement Examination, or MATH
118 or equivalent. MATH 328 prerequisite: MATH 327 with a grade of C- or better or consent of
instructor. MATH 329 prerequisite: MATH 328.

2. Required Background or Experience

Math 118 or equivalent, and completion of Math 327 with a grade of C- or better.

3. Learning Objectives

Mathematical Content
• Rational and Real Numbers

The student will understand:
a. Fundamental relations (greater than, less than, equal to) and operations (addition, subtraction,
multiplication, and division) on rational numbers and real numbers. This includes both the
ability to write word problems as well as the ability to solve those problems using multiple
representations, standard algorithms, and nonstandard algorithms.
b. The special roles of the unit and equivalence in the rational number system.
c. The rational numbers as fractions, decimals, and percents including how to convert from one
form into another.
d. Algorithms with non-terminating repeating decimals, and to order decimals.
e. Proportions and ratios.
f. The connections between probabilities, ratios, proportions, decimals and percents.
g. The properties of irrational numbers including their similarities and differences with the rational numbers.

• Probability and Counting
The student will:
a. Understand a variety of representations for probabilities of one and two stage experiments,
appealing to notions of complementary, mutually exclusive, dependent, and independent events.
b. Understand basic counting techniques including the use of trees and organized lists.
c. Use different counting techniques to calculate theoretical probabilities.

• Statistics
The student will:
a. Collect, organize, and represent data through graphs and tables, and given a representation of
data, the student will be able to interpret and draw conclusion about the data considering
possible effects of bias.
b. Understand how mean, median, mode, and range describe a set of data.

• Other
The student will:
a. Identify errors in given calculations and identify typical error patterns found in children’s
mathematical thinking.

Mathematical Understanding
• Students will deepen their understanding of mathematics by:
a. Experiencing concrete, investigative experiences in mathematics.
b. Estimating and approximating to check the reasonableness of a solution.
c. Developing and comparing physical, pictorial, and symbolic languages for representing
mathematical ideas.
d. Explaining why mathematics makes sense by integrating the English language with
conventional mathematical notation, mathematical definitions, and concrete representations.
e. Writing and solving mathematical problems and exercises.
f. Watching and analyzing videos of young children solving mathematics problems.
g. Addressing the fears and apprehensions of many people towards mathematics.

4. Text and References

Billstein, Rick, et al., Mathematics for Elementary School Teachers, 9th ed., Addison Wesley, 2006.

5. Minimum Student Materials

Required text, and activity materials provided by instructor.

6. Minimum University Facilities

Mathematics education classroom equipped with materials and technology.

7. Content and Method

Topic   Lecture/Activity
Chapter 5: Rational Numbers as Fractions
The Set of Rational Numbers
Addition and Subtraction of Rational Numbers
Multiplication and Division of Rational Numbers
Chapters 6: Decimals, Percents, and Real Numbers
Introduction to Decimals
Decimals in Other Bases (optional)
Operations on Decimals
Operations on Decimals in Other Bases (optional)
Nonterminating Decimals
Real Numbers
Chapter 7: Probability
How Probabilities Are Determined
Multistage Experiments with Tree Diagrams and Geometric Probabilities
Using Simulations in Probability
Odds, Conditional Probability, and Expected Value
Using Permutations and Combinations in Probability
Chapter 8: Data Analysis/Statistics (optional)
Statistical Graphs of Categorical and Numerical Data
Measures of Central Tendency and Variation
Abuses of Statistics



Lecture, discussion, and activity.

8. Methods of Assessment

Class activities, homework and lab assignments, term projects, midterm tests or quizzes, final examination.