MA Mathematics Domains of Study

Areas of Study Within the
M.A. in Mathematics Education Degree

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.

The following section includes the larger domains of knowledge, which are then followed by the subject-specific subdomains of knowledge.

Elementary Mathematics Education Domain (for the K-6 program)

This domain focuses on the following mathematics content, as well as central issues related to the teaching of these topics in grades K–6:

Mathematics (K-6) Content
This subdomain focuses on the following mathematics content with integrated mathematics pedagogy: Introduction to Number Sense; Patterns and Functions; Integers and Order of Operations; Fractions, Decimals, and Percentages; Coordinate Pairs and Graphing; Ratios and Proportional Reasoning; Equations and Inequalities; Geometry and Measurement; and Statistics, Data Analysis, and Probability.

Finite Mathematics
This subdomain focuses on the real number system, symbolic logic, number theory, set theory, graph theory and their applications.

Middle School Mathematics Content Domain (for the 5-9 program)

This domain focuses on the following areas of mathematics: Finite Mathematics, College Algebra, Pre-calculus, Probability and Statistics I, College Geometry and Calculus I.

Finite Mathematics
This sub-domain focuses on the real number system, symbolic logic, number theory, set theory, graph theory and their applications.

College Algebra
This sub-domain focuses on equations, inequalities, polynomials, conic sections, and functional analysis including logarithmic, exponential, and inverse functions in problem solving.

Pre-calculus
This sub-domain focuses on the complex number system and trigonometry.

Probability and Statistics I
This sub-domain focuses on applications of probability and statistics to solve problems, make predictions, data collection and analysis, and probability distributions.

College Geometry
This sub-domain focuses on synthetic, analytic, and transformational geometry and modeling, measurement, spatial visualization and proofs of theorems in both Euclidean and non-Euclidean Geometries.

Calculus I
This sub-domain focuses on limits, derivatives, continuity, and applications of differential calculus to mathematics and the sciences.

Comprehensive Exam
The CYV1 is a comprehensive exam assessing the student’s knowledge of the subdomains listed above.

Specific Teaching Practices
Content focuses on the effective teaching of mathematics in grades 5–9.

High School Mathematics Content Domain (for the 5-12 program)

This domain focuses on the following areas of mathematics: This domain focuses on the following areas of mathematics: Pre-Calculus, Probability and Statistics, College Geometry, Calculus and Analysis, Linear Algebra, Abstract Algebra, and Mathematical Modeling and Connections.

Pre-calculus
This sub-domain focuses on the complex number system and trigonometry.

Probability and Statistics I
This sub-domain focuses on applications of probability and statistics to solve problems, make predictions, data collection and analysis, and probability distributions.

Probability and Statistics II
This sub-domain focuses on problem solving, descriptive statistics, statistical inference, sampling, confidence intervals, and hypothesis testing.

College Geometry
This sub-domain focuses on synthetic, analytic, and transformational geometry and modeling, measurement, spatial visualization and proofs of theorems in both Euclidean and non-Euclidean Geometries.

Calculus I
This sub-domain focuses on limits, derivatives, continuity, and applications of differential calculus to mathematics and the sciences.

Calculus II
This sub-domain focuses on integration techniques and applications, the solution of differential equations, and the analysis of sequences.

Calculus III and Analysis
This sub-domain focuses on real analysis, vectors, multivariable functional analysis, and infinite series.

Linear Algebra
This sub-domain focuses on matrices, vector spaces, linear transformations and their applications.

Comprehensive Exam
The CXV1 is a comprehensive exam assessing the student’s knowledge of the subdomains listed above.

Abstract Algebra
This sub-domain focuses on number theory, groups, rings, fields, and proofs of theorems involving these algebraic structures.

Mathematical Modeling and Connections
This sub-domain focuses on connections among mathematical disciplines and to the sciences.

Specific Teaching Practices
Content focuses on the effective teaching of mathematics in grades 5–9.

Research Fundamentals Domain (for the K-6 and 5-9 programs)

The research fundamentals domain prepares students to conduct research and also to become informed consumers of research. Your studies in this domain will include the following:

Foundations of Research
Focuses on differentiating between different research paradigms, including qualitative, quantitative, and action research.

Literature Reviews for Educational Research
Focuses on selecting an appropriate research topic, evaluating the reliability of primary and secondary source information, and conducting a literature review.

Research Proposal
Focuses on developing a research proposal that includes the literature review, research questions, methodology, and data analysis.

Issues in Research Fundamentals
Focuses on developing a research strategy that clarifies what data to collect and how to analyze it using descriptive and inferential statistics.

Capstone Project (for the K-6 program)

The Capstone Project is the culmination of the student’s WGU degree program. It requires the demonstration of competencies through a deliverable of significant scope that includes both a written capstone project and an oral defense.

Students will be able to choose from two areas of emphasis, depending on personal and professional interests. These two areas include instructional design and research. If carefully planned in advance, the individual domain projects may serve as components of the capstone. For capstones with the instructional design emphasis, students will design, manage, and develop an instructional product for which there is an identified need. The product can be delivered via the medium of choice (e.g., print-based, computer-based, video-based, web-based, or a combination of these), but you must provide a rationale for the medium selected. The instructional product you develop for your capstone should be an exportable form of instruction designed to bring your target audience to a mastery of predetermined knowledge and skills.

For capstones with the research emphasis, students will design and conduct a data-based investigation of a conclusion-oriented question (decision-oriented investigations are most generally considered to be evaluation projects). The project report should be of publishable quality and may be submitted to an appropriate professional journal at the completion of the project. At the minimum you should plan to share your results with your school or organization.

The final master's exam will be a comprehensive oral defense. This exam may be face-to-face when possible but will most likely be held by telephone conference. Questions related to your work in the program will test your preparation and ability to synthesize and practically apply information obtained from your courses, self-directed study, and project experiences. The oral exam will include questions covering the mathematics content domain. The purpose of the exam is a checkpoint to ensure that you have acquired the critically required skills and knowledge specified in the program competencies.

Teacher Work Sample Written Project (for the 5-9 and 5-12 programs)

The Teacher Work Sample Written Project is the culmination of the student’s WGU degree program. It requires the demonstration of competencies through a deliverable of significant scope that includes both a written project and an oral defense.

The Teacher Work Sample is a written project containing a comprehensive, original, research based curriculum unit designed to meet an identified educational need. It provides direct evidence of the candidate’s ability to design and implement a multi-week, standards-based unit of instruction, assess student learning, and then reflect on the learning process. The WGU Teacher Work Sample requires students to plan and teach a multi-week standards-based instructional unit consisting of seven components: 1) Contextual factors, 2) learning goals, 3) assessment, 4) design for instruction, 5) instructional decision making, 6) analysis of student learning, and 7) self-evaluation and reflection.

The final master's exam will be a comprehensive oral defense. This exam may be face-to-face when possible but will most likely be held by telephone conference. Questions related to your work in the program will test your preparation and ability to synthesize and practically apply information obtained from your courses, self-directed study, and project experiences. The oral exam will include a presentation (typically PowerPoint) and defense of the Teacher Work Sample (TWS). Candidates will be asked to reflect upon the TWS, note its strengths and weaknesses, discuss its impact on student learning, and suggest future improvements. The purpose of the exam is a checkpoint to ensure that you have acquired the critically required skills and knowledge specified in the program competencies.