MATH 1121 - Mathematics for Educational Arts

1. Know and apply concepts of mathematical patterns, relations, and functions, including the importance of number and geometric patterns in mathematics.
2. Know the importance of the educational link between primary school activities with patterns and the later conceptual development of important ideas related to functions and be able to identify and justify observed patterns.
3. Generate patterns to demonstrate a variety of relationships.
4. Relate patterns in one strand of mathematics to patterns across the discipline.
5. Know and apply concepts and techniques of discrete mathematics and how to use them to solve problems from areas including graph theory, combinatorics, and recursion, and apply these ideas to settings such as finance, population dynamics, and optimal planning.
6. Know how to help others investigate situations that involve counting finite sets, calculating probabilities, tracing paths in network graphs, and analyzing iterative procedures.
7. Know and apply concepts of numerical literacy, possess number sense, and be able to use numbers to quantify concepts in the student’s world.
8. Understand a variety of computational procedures and how to use them in examining the reasonableness of answers.
9. Understand the concepts of number theory including divisibility, factors, multiples, and prime numbers, and know how to provide a basis for exploring number relationships.
10. Understand the relationships of number sets and their properties.
11. Know and apply concepts of space and shape and the properties and relationships of geometric figures.
12. Know and apply concepts of space and shape by understanding geometry and measurement from both abstract and concrete perspectives and identify real world applications.
13. Know and apply mathematical processes to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality.
14. Understand the connections among mathematical concepts and procedures as well as their application to the real world.
15. Understand the relationship between mathematics and other fields.
16. Know and apply mathematical processes to problem solve, reason, communicate, and make connections both verbally and in written form.
17. Demonstrate an understating of set notation as well as the following concepts of set theory: universal set, union, intersection, complement, equal, equivalent, Cartesian product, and Venn diagram.
18. Demonstrate knowledge of a place value system.
19. Explain the four basic operations on whole numbers using set theory and/or number line models.
20. Explain the various algorithms for the basic operations on whole numbers.
21. Demonstrate mathematical literacy by presenting knowledge of field properties, law of exponents, mental math, and estimation techniques.
22. Provide an explanation, based on mathematical principles, why division by zero is undefined and why a non-zero number raised to the zero power is defined to be equal to 1.
23. Demonstrate an understanding of the following concepts in number theory: prime, composites, divisibility, factors, multiples, GCF, and LCD.
24. Construct a drawing to demonstrate basic fraction concepts and use standard algorithms for fraction computations.
25. Write a rational number in fraction, decimal, or percent form and use fractions to explain the standard algorithm for decimal.
26. Use proportions to solve real-world applications.
27. Solve linear equations by producing a concrete representation as well as by standard algebraic methods.
28. Demonstrate familiarity with current mathematical standards for curriculum in schools grade K-8 by means of written reaction papers.
29. Demonstrate the ability to understand a mathematical idea and, in collaboration with another person, present an organized explanation of it to a group.
30. Demonstrate thoughtful observation of mathematics being taught in an elementary school classroom by means of a written reaction paper.

1. Problem-solving strategies
2. Set theory
3. Numeration systems
4. Whole numbers: concepts and operations
5. Concepts in number theory
6. Fractions, decimals, percents: concepts and operations
7. Real numbers
8. Integers: concepts and operations