Mathematics for Elementary Teachers I

MTH 115W

Course Description

Prerequisite: MTH 097 with a grade of "C" or better or an acceptable score on the current college assessment instrument. Includes numeration systems, sets and their properties, classification of number systems (whole numbers through real number), operations and their properties, arithmetical algorithms, and problem solving. Uses a variety of learning styles, manipulatives, and calculator and computer applications. The National Council of Teachers of Mathematics Standards are incorporated. Students may use either MTH 115W or MTH 110, not both, to fulfill graduation requirements. (45-0)

Outcomes and Objectives

Students will develop their problem-solving skills.

Objectives:

• Give a general definition of problem solving in mathematics and distinguish between exercises and problems.
• Explain, illustrate and use Polya’s 4-step problem solving process:
• Explain, illustrate, and apply strategies that include but are not limited to:

Use technology appropriately to do mathematics.

Objectives:

• Use and review software packages established for use in the elementary classroom for mathematics.

Students will develop their understanding, vocabulary, and nomenclature of sets to enable them to formalize the meaning of whole numbers.

Objectives:

• Define a set by using:
• Use the concept of matching sets to formalize the meaning of whole numbers.
• Describe and compare the concepts of cardinal, ordinal, and identification numbers.
• Describe the difference between a whole number, the name of a whole number, and the numeral of the whole number.
• Describe the relations of less than and greater than for whole numbers using sets.

Students will enhance their computational skills with and without a calculator.

Objectives:

• Add, subtract, multiply and divide whole numbers.
• Add, subtract, multiply, and divide fractions.
• Add, subtract, multiply, and divide decimals.
• Add, subtract, multiply, and divide with percents.
• Add, subtract, multiply, and divide real numbers.
• Set-up and simplify ratios and rates.
• Solve proportions.
• Carry out fraction, decimal, and percent conversions.
• Solve percent equations.
• Simplify numerical expressions using the order of operations.
• Add, subtract, multiply, and divide integers.
• Add, subtract, multiply, and divide real numbers.

Students will demonstrate their understanding of mathematical ideas and operations with concrete models.

Objectives:

• Represent addition, subtraction, multiplication, and division of whole numbers (fractions, and decimals) using a set model and a measurement model.
• Give examples of real world addition, subtraction, multiplication and division problems involving set and measurement models.
• Explain and illustrate the comparison model of subtraction.
• Represent fractions, decimals, and percents using area models, measurements models, set models, and towers of bars.
• Represent integers with the chip (or charged ion) model.
• Use manipulative to illustrate basic arithmetic operations.

Students will develop an arsenal of computational algorithms.

Objectives:

• Explain, illustrate and use a)intermediate algorithm, b) standard algorithm, c) the lattice method for addition and multiplication.
• Explain, illustrate and use long division algorithms that lead to the standard division algorithm (scaffolding, intermediate).
• Find the GCF and LCM of a given pair of numbers using a) the set intersection method, (factor list method), b) the prime factorization method and c) the Euclidean Algorithm.

Students will develop their estimation and thinking skills.

Objectives:

• Use, identify, and apply various mental computation and estimation strategies including:
• Explain, illustrate, and use the following thinking strategies for learning basic addition facts:
• Explain, illustrate, and use the following thinking strategies for learning basic multiplication facts:

Students will develop their skills with number theory.

Objectives:

• Define, compare, and contrast the following terms: prime, composite, divides, factor (divisor), factor trees, multiple, is divisible by, common factor (divisor), common multiple, greatest common factor (GCF), least common multiple (LCM)
• Use the sieve of Eratosthenes to find prime numbers.
• State and apply the fundamental theorem of arithmetic.
• State and apply tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 12.
• Find the prime factorization of a given composite number.
• Use the exponents in the prime factorization of a number to count its factors.
• Relate the GCF and LCM of any two numbers to the product of the numbers.
• State and use the Prime Number Test.