## WGU Master of Arts in Mathematics Education (K-6, 5-9 or 5-12)

The WGU Master of Arts in Mathematics Education (K-6, 5-9 or 5-12) program content is based on research on effective instruction as well as national and state standards. It provides the knowledge and skills that enable teachers to teach effectively in diverse classrooms. The M.A. in Mathematics Education program content and training processes are consistent with the accountability intent of the No Child Left Behind Act of 2001. The degree program is focused on the preparation of highly qualified teachers. As described in the federal legislation, a highly qualified teacher is one who not only possesses full state certification, but also has solid content knowledge of the subject(s) he or she teaches.

### Elementary Mathematics Content

**Number Sense and Functions**

This is a performance-based assessment that evaluates a student's portfolio of work. This portfolio includes the student's responses to various prompts and an original lesson plan for each of the mathematics modules such as number sense, patterns and functions, integers and order of operations, fractions, decimals, and percentages.

**Graphing, Proportional Reasoning and Equations/Inequalities**

This is a performance-based course that evaluates a student's portfolio of work. This portfolio includes the student's responses to various prompts and an original lesson plan for each of the mathematics modules such as coordinate pairs and graphing, ratios and proportional reasoning, and equations and inequalities.

**Geometry and Statistics**

This is a performance-based course that evaluates a student's portfolio of work. This portfolio includes the student's responses to various prompts and an original lesson plan for each of the mathematics modules such as geometry and measurement, statistics and probability.

**Mathematics (K-6) Portfolio Oral Defense**

Mathematics (K-6) Portfolio Oral Defense focuses on a formal presentation and the student answering questions during their Capstone Oral Defense. The student will present an overview of their teacher work sample (TWS) portfolio. They will talk about the challenges they faced and how they determined whether their goals were accomplished. They will explain the process they went through to develop the TWS portfolio and reflect on the methodologies and outcomes of the strategies discussed in the TWS portfolio. Additionally, they will discuss the strengths and weaknesses of those strategies and how they can apply what they learned from the TWS portfolio in their professional work environment.

**Finite Mathematics**

Included in this course are the following main topics: proofs, set theory, logic, number theory, mathematical systems, modular arithmetic, and graph theory.

### Middle School Mathematics Content

**Finite Mathematics**

Included in this course are the following main topics: proofs, set theory, logic, number theory, mathematical systems, modular arithmetic, and graph theory.

**Pre-calculus**

Pre-Calculus covers the knowledge and skills necessary to apply trigonometry, complex numbers, systems of equations,
vectors and matrices, sequence and series, and to use appropriate technology to model and solve real-life problems.
Topics include degrees; radians and arcs; reference angles and right triangle trigonometry; applying, graphing and
transforming trigonometric functions and their inverses; solving trigonometric equations; using and proving trigonometric
identities; geometric, rectangular, and polar approaches to complex numbers; DeMoivre's Theorem; systems of linear
equations and matrix-vector equations; systems of nonlinear equations; systems of inequalities; and arithmetic and
geometric sequences and series. Candidates should have completed a course in College Algebra before engaging in this
course.

**Probability and Statistics I**

This course is designed to provide you with a broad overview of the field of probability and statistics, and a fundamental understanding of statistical reasoning.

**College Geometry**

College Geometry covers the knowledge and skills necessary to apply geometry to model and solve real-life problems, to
do formal axiomatic proofs in geometry, and to use dynamic technology to explore geometry. Topics include axiomatic
systems and analytic proof; non-Euclidean geometries; construction, analytic, and synthetic methods for investigating and
proving properties and relationships of two- and three-dimensional objects; geometric transformations, tessellations, and
using inductive reasoning; concrete models; and dynamic technology to conduct geometric investigations. Candidates
should have completed at least one course in College Algebra and preferably one in Pre-Calculus before engaging in this
course.

**Calculus I**

Calculus I is the study of rates of change in relation to the slope of a curve. It covers the knowledge and skills necessary to
use differential calculus of one variable and appropriate technology to solve basic problems. Topics include graphing
functions and finding their domains and ranges; limits, continuity, differentiability, visual, analytical, and conceptual
approaches to the definition of the derivative; the power, chain, and sum rules applied to polynomial and exponential
functions, position and velocity; and L'Hopital's Rule. Candidates should have completed a course in Pre-Calculus before
engaging in this course.

**Middle Schools Mathematics: Content Knowledge**

This course is designed to help you refine and integrate the mathematics content knowledge and skills necessary to become a successful middle school mathematics teacher. Successful completion of the course requires a high-level of mathematical reasoning skills and the ability to solve problems.

### High School Mathematics Content

**Pre-Calculus**

Pre-Calculus covers the knowledge and skills necessary to apply trigonometry, complex numbers, systems of equations,
vectors and matrices, sequence and series, and to use appropriate technology to model and solve real-life problems.
Topics include degrees; radians and arcs; reference angles and right triangle trigonometry; applying, graphing and
transforming trigonometric functions and their inverses; solving trigonometric equations; using and proving trigonometric
identities; geometric, rectangular, and polar approaches to complex numbers; DeMoivre's Theorem; systems of linear
equations and matrix-vector equations; systems of nonlinear equations; systems of inequalities; and arithmetic and
geometric sequences and series. Candidates should have completed a course in College Algebra before engaging in this
course.

**College Geometry**

College Geometry covers the knowledge and skills necessary to apply geometry to model and solve real-life problems, to
do formal axiomatic proofs in geometry, and to use dynamic technology to explore geometry. Topics include axiomatic
systems and analytic proof; non-Euclidean geometries; construction, analytic, and synthetic methods for investigating and
proving properties and relationships of two- and three-dimensional objects; geometric transformations, tessellations, and
using inductive reasoning; concrete models; and dynamic technology to conduct geometric investigations. Candidates
should have completed at least one course in College Algebra and preferably one in Pre-Calculus before engaging in this
course.

**Calculus I**

Calculus I explores the key concepts, methods, and applications of differential calculus of one variable. It is the first course in the calculus sequence intended for secondary mathematics teachers. A solid background in precalculus is highly recommended. Topics include a review of functions, limits, derivatives, and applications of differential calculus. Upon completion, students will be able to apply the concepts and methods of differential calculus and appropriate technology to solve practical problems and communicate results.

**Calculus II**

Calculus II addresses important principles, techniques, and applications of integration and introduces the concept and
application of sequences.

**Probability and Statistics I**

This course is designed to provide you with a broad overview of the field of probability and statistics, and a fundamental understanding of statistical reasoning.

**Probability and Statistics II**

This course is designed to provide students with a broad overview of the field of probability and statistics and a fundamental understanding of statistical reasoning. Topics include discrete and continuous random variables, point and interval estimation, and hypothesis testing.

**Mathematics: Content Knowledge**

This course is designed to help you refine and integrate the mathematics content knowledge and skills necessary to become a successful secondary mathematics teacher. Successful completion of the course requires a high-level of mathematical reasoning skills and the ability to solve problems.

**Calculus III and Analysis**

Calculus III extends your calculus knowledge and ability to solve problems into three dimensions. This branch of
mathematics was developed as a way to describe, analyze, and predict the paths, velocity, and acceleration of bodies in 3-
D space. Ultimately, these tools allowed Kepler to devise his laws of planetary motion based on Newton's laws of gravity
and motion. In this course you, too, will learn the skills needed to comprehend such real-world phenomena. You will also
learn to analyze surfaces and solids and tackle infinite sequences and series.

**Linear Algebra**

Logical reasoning and proofs underlie the main concepts of higher mathematics in subjects such as Linear Algebra and
Abstract Algebra. In the Logic portion of this course, you will consider the relationship between the truth of one statement
and the truth of other related statements. To avoid the ambiguities of natural languages such as English, logic uses formal
languages with precisely defined symbols. In this course, you will learn about both Propositional Logic and Predicate
Logic.

The Linear Algebra portion of the course addresses systems of equations, matrix operations and characteristics, vector spaces, and linear transformations. While this course has some similarity to the basic algebra of real numbers that you learned in the past, it is a bit different because it moves up into problem solving in higher dimensions. Learning linear algebra will reinforce the importance of the principles and concepts of the algebra you already know.

**Abstract Algebra**

Abstract algebra introduces you to new structures: groups, rings, and fields that are the foundation of the arithmetic you
use every day. This course will give you a deeper understanding of the concepts that you will teach to your students, thus
making you a better teacher.

### Mathematics Education

**Mathematics Learning and Teaching**

In this course you will develop the knowledge and skills necessary for becoming a prospective and practicing educator. You will be able to use a variety of instructional strategies to effectively facilitate the learning of mathematics. The focus will be on selecting appropriate resources, using multiple strategies, and instructional planning. Methods will be based on research and problem solving. A deep understanding of the knowledge, skills, and disposition of mathematics pedagogy is necessary to become an effective secondary mathematics educator.

**Mathematics History and Technology**

In this course, you will learn about a variety of technological tools for doing mathematics, and you will develop a broad understanding of the historical development of mathematics. More importantly, you will learn to evaluate and apply technology and history in order to create a student-centered mathematical learning environment.

### Research Fundamentals

**Research Foundations**

The Research Foundations course focuses on the essential concepts in educational research, including quantitative,
qualitative, mixed, and action research; measurement and assessment; and strategies for obtaining warranted research
results.

**Research Questions and Literature Review**

The Research Questions and Literature Reviews for Educational Research course focuses on how to conduct a thorough literature review that addresses and identifies important educational research topics, problems, and questions, and helps determine the appropriate kind of research and data needed to answer one's research questions and hypotheses.

**Research Design and Analysis**

The Research Design and Analysis course focuses on applying strategies for effective design of empirical research studies. Particular emphasis is placed on selecting or constructing the design that will provide the most valid results, analyzing the kind of data that would be obtained, and making defensible interpretations and drawing appropriate conclusions based on the data.