MAT-180 Mathematics/Elementary School Teachers I
This is the first of a two-course sequence designed for prospective elementary school teachers. The course presentation is informed by the National Council of Teachers of Mathematics (NCTM) Process Standards, emphasizing problem solving, communication, reasoning and proof, representation, and mathematical connections. Students will explore mathematical concepts and theories underlying the topics which include: set theory; the history of numeration and different number systems, including other base numeration systems; operations on whole numbers, integers, rational numbers, and irrational numbers; and elementary number theory. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.
For more detailed course information view the
Course Outline
Course Description
This is the first of a two-course sequence designed for prospective elementary school teachers. The course presentation is informed by the National Council of Teachers of Mathematics (NCTM) Process Standards, emphasizing problem solving, communication, reasoning and proof, representation, and mathematical connections. Students will explore mathematical concepts and theories underlying the topics which include: set theory; the history of numeration and different number systems, including other base numeration systems; operations on whole numbers, integers, rational numbers, and irrational numbers; and elementary number theory. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.
Credit Hours
3Semester(s) Course Will Be Offered
Fall, Spring, Summer
SUNY General Education Course
- Mathematics and Quantitative Reasoning
Course Learning Outcomes
- Interpret information and apply arithmetic procedures to solve problems.
- Communicate representations of mathematical ideas visually, numerically, and symbolically.
- Explain the reasoning behind mathematical ideas and their connection to the foundational concepts that underlie the elementary school mathematics curriculum.
Topic Outline
- 1. Problem solving (Note: the strategies outlined below are threaded throughout this course.)
- a. Pólya's problem-solving principles
- b. Problem-solving strategies
- i. Brute force methods, including guess, test, and revise, and use of kinesthetic materials
- ii. Visual representations
- iii. Creating a table
- iv. Using patterns and generalizing
- c. Assessing the reasonableness of a solution
- 2. Set theory
- a. Basic terminology and notation
- b. Set representations
- i. List form
- ii. Verbal form
- iii. Set-builder notation
- iv. Venn diagrams
- c. Set relationships and special sets
- i. One-to-one correspondence
- ii. Subsets: general vs. proper
- iii. Set equivalence
- iv. Empty set
- v. Universal set
- d. Operations
- i. Intersection
- ii. Union
- iii. Complement
- 3. The number system
- a. History of numeration and early numeration systems
- i. Egyptian numerals
- ii. Roman numerals
- iii. Babylonian numerals
- b. Place value systems
- i. Hindu-Arabic or base 10 system (whole numbers)
- ii. Other base numeration systems
- (1) Binary (base 2), base 5, base 6, and hexadecimal (base 16)
- (2) Counting
- (3) Understanding place value
- iii. Using base blocks to represent numerals
- iv. Operations: addition, subtraction, multiplication, and division
- c. Fractions
- i. Definition of rational number
- ii. Understanding the part-versus-whole relationship
- iii. Visual representations
- (1) Pattern blocks
- (2) Cuisenaire rods
- (3) Other visual representations (rectangles, circles, geoboard figures, number lines, etc.)
- iv. Simplifying and ordering fractions
- d. Decimals
- i. Place values
- ii. Representations with base blocks
- iii. Connections to fractions
- iv. Equivalent numerals and ordering decimals
- e. Integers and real numbers
- 4. Addition and subtraction
- a. Connections to part-versus-whole relationships
- b. Whole numbers
- i. Addition and subtraction models
- ii. Using base block visualizations to compute sums and differences
- iii. Traditional and alternative algorithms
- iv. Understanding why algorithms work
- v. Addition and subtraction in base 2, base 5, base 6, and base 16
- vi. Properties
- c. Fractions
- i. Using visual models to compute sums and differences of fractions
- ii. Applying algorithms to compute sums and differences of fractions
- iii. Understanding why algorithms work
- d. Decimals
- i. Using base block visualizations to compute sums and differences of decimals
- ii. Applying algorithms to compute sums and differences of decimals
- iii. Understanding why algorithms work
- e. Integers
- i. Using color chip visualizations to compute sums and differences of integers
- ii. Applying algorithms to compute sums and differences of integers
- (1) Addition by position
- iii. Understanding why algorithms work
- 5. Multiplication and division
- a. Meaning of and contexts for multiplication and division
- b. Properties
- c. Using visualizations to motivate computations of products and quotients
- d. Traditional and alternative algorithms
- e. Understanding why algorithms work
- f. Dimensional analysis
- 6. Number theory
- a. Prime and composite numbers
- b. The fundamental theorem of arithmetic
- c. Divisibility
- i. Understanding the definition
- ii. Selected divisibility tests
- d. Greatest common factor and least common multiple