MATH 204 — Concepts Of Mathematics For Elementary School Teachers I
Course Content Outline
A
Problem solving (Chapter 1: pages 1 to 59)
1
Polya's problem solving model (Section 1-2)
2
Strategies (Section 1-2)
3
Arithmetic Sequences (Section 1-1)
4
Geometric Sequences (Section 1-1)
5
Determining the nth term (Section 1-1)
6
Other Sequences (Section 1-1)
7
Algebraic Thinking (Section 1-3)
B
Sets (Chapter 2: pages 60 to 74)
1
Concepts (Section 2-1)
2
Operations (Union, Intersection, Complement) (Section 2-2)
3
Venn Diagrams (Section 2-2)
C
Whole number models and properties (Chapter 2: pages 85 to 132)
1
Addition (Section 2-3)
2
Subtraction (Section 2-3)
3
Multiplication (Section 2-4)
4
Division (Section 2-4)
5
Order of operations with whole numbers
6
Exponents
D
Numbers and numeration (Chapter 3: pages 133 to 148)
1
Concepts of whole and natural numbers (Section 3-1)
2
The Hindu-Arabic system (Section 3-1)
3
Non-decimal base systems (Section 3-1)
E
Computation of whole numbers (Chapter 3: pages 149 to 185)
1
Estimation (Section 3-4)
2
Mental computation (Section 3-4)
3
Algorithms in base ten and other bases (Section 3-3)
F
Integers (Chapter 4: pages 186 to 201)
1
Concepts (Section 4-1)
2
Operations (Section 4-1 and 4-2)
3
Order and properties (Section 4-1 and 4-2)
G
Number theory (Chapter 3: pages 214 to 264)
1
Primes/composites and unique factorization theorem (Section 4-4)
2
Divisibility (Section 4-4)
3
Greatest common factor (Section 4-5)
4
Least common multiple (Section 4-5)
H
Rational numbers and Fractions (Chapter 5: pages 265 to 317)
1
Concepts (Section 5-1)
2
Operations on fractions (Section 5-2 and 5-3)
3
Properties (Section5-1, 5-2 and 5-3)
4
Estimation and mental mathematics (Section 5-2 and 5-3)
5
Exponents (Section 5-3)
6
Proportional Reasoning (Section 5-4)
I
Decimals, Percents, and Real Numbers (Chapter 6: pages 318 to 372)
1
Decimal notation (Section 6-1)
2
Operations on Decimals (Section 6-2)
3
Scientific Notation (Section 6-2)
4
Rounding Decimals (Section 6-2)
5
Renaming, terminating and repeating decimals as fractions (Section 6-3)
6
Percents (Section 6-4)
7
Irrational numbers (Section 6-6)
Text:
Billstein, Rick, Libeskind, Shlomo, and Lott, Johnny W. A Problem-Solving
Approach to Mathematics for Elementary School Teachers, 8th Edition, Reading MA:
Addison Wesley Publishing
Calculators:
TI-83 plus is required.
Course Objectives:
This is the first of three required mathematics courses (along with Math 205: Functions, Probability,
and Statistics and Math 251:Measurement and Geometry) designed to provide an enriched content
background for a conceptually based approach to the teaching of elementary school mathematics. The
general goal is to provide each student with the competence and confidence to deal with the elementary
school mathematics curriculum of the 21st century. Specifically, by the end of this course, each
student should be able to:
1.
Apply problem solving heuristics to solve a variety of non-standard mathematical problems;
2.
Display flexibility in expressing a given number in different forms; e.g., whole numbers in
historical notation or non-decimal bases, fractions in common, decimal or non-decimal forms;
3.
Discuss the characteristics of historic and current systems of numeration with respect to
whether or not they are positional, use place value, or have a symbol for zero.
4.
Use set language and notation to characterize whole numbers.
5.
Explain how a variety of thinking models may be used to generate the familiar operations of
arithmetic; addition, subtraction, multiplication, division, exponentiation; identify and create
these models and make appropriate use of them (for example, in the development of counting
techniques);
6.
Identify, make appropriate use of or explain the lack of existence of, properties such as
closure, identify, inverse commutativity, associativity, distributivity for arithmetic operations;
7.
Identify properties of zero in addition and multiplication and as an exponent;
8.
Analyze a variety of standard and non-standard algorithms for the four operations on whole
numbers, including estimation and mental methods of calculation; apply these algorithms in
the context of non-decimal bases; distinguish between a model and an algorithm for an
operation;
9.
Generalize the thinking models for the whole number operations to be able, when appropriate,
to apply these operations in the context of integers with respect to the properties of #6.
10. Explain the algorithms for operations on integers or common and decimal fractions in terms of
the models and/or properties.
11. Interpret the order relations "less than" and "greater than" for whole numbers; correctly order
a set of real numbers, where the members of the set may be in whole number, integer,
common or decimal fraction, or radical form; state and correctly use properties of the order
relation in these systems; show that the rational and real number systems have the density
property;
12. Extend the concept of an exponent to rational exponents; describe and use properties of
rational exponents; perform calculations on rational numbers in scientific notation;
13. Correctly use the language, procedures and conventions associated with percent.