M.A. Mathematics Education Areas of Study

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

The Master of Arts in Mathematics Education is a competency-based degree program that prepares already licensed teachers both to be licensed to teach mathematics and to develop significant skills in mathematics curriculum development, design, and evaluation. All work in this degree program is online and includes Mathematics Content, Mathematics Education and Research Fundamentals. All students complete a culminating Teacher Work Sample.

General Education (5-9 option only)

Mathematics for Elementary Educators I
Mathematics for Elementary Educators I engages pre-service elementary teachers in mathematical practices based on deep understanding of underlying concepts. The course covers important topics in problem solving, set theory, number theory, whole numbers and integers. This is the first course in a three-course sequence.

Mathematics for Elementary Educators II
This course engages pre-service elementary teachers in mathematical practices based on deep understanding of underlying concepts. This course takes the arithmetic of the first course and generalizes it into algebraic reasoning. The course also touches on important topics in probability. This is the second course in a three-course sequence.

College Algebra
This course provides further application and analysis of algebraic concepts and functions through mathematical modeling of real-world situations. Topics include: real numbers, algebraic expressions, equations and inequalities, graphs and functions, polynomial and rational functions, exponential and logarithmic functions, and systems of linear equations.

Elementary Mathematics Content (for the K-6 option)

Number Sense and Functions
Number Sense and Functions 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
Graphing, Proportional Reasoning and Equations/Inequalities 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 coordinate pairs and graphing, ratios and proportional reasoning, and equations and inequalities.

Geometry and Statistics
Geometry and Statistics 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 geometry and measurement, statistics and probability.

Mathematics (K-6) Portfolio Oral Defense
Mathematics (K-6) Portfolio Oral Defense: Mathematics (K-6) Portfolio Defense focuses on a formal presentation. The student will present an overview of their teacher work sample (TWS) portfolio discussing 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
Finite Mathematics covers the knowledge and skills necessary to apply discrete mathematics and properties of number systems to model and solve real-life problems. Topics include sets and operations; prime and composite numbers; GCD and LCM; order of operations; ordering numbers; mathematical systems including modular arithmetic, arithmetic and geometric sequences, ratio and proportion, subsets of real numbers, logic and truth tables, graphs, trees and networks, and permutation and combination. There are no prerequisites for this course.

Middle School Mathematics Content (for the 5-9 option)

Finite Mathematics
Finite Mathematics covers the knowledge and skills necessary to apply discrete mathematics and properties of number systems to model and solve real-life problems. Topics include sets and operations; prime and composite numbers; GCD and LCM; order of operations; ordering numbers; mathematical systems including modular arithmetic, arithmetic and geometric sequences, ratio and proportion, subsets of real numbers, logic and truth tables, graphs, trees and networks, and permutation and combination. There are no prerequisites for this course.

Trigonometry and Precalculus
Trigonometry and Precalculus 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. College Algebra is a prerequisite for this course.

Calculus I
Calculus I is the study of rates of change in relation to the slope of a curve and 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.

Probability and Statistics I
Probability and Statistics I covers the knowledge and skills necessary to apply basic probability, descriptive statistics, and statistical reasoning, and to use appropriate technology to model and solve real-life problems. It provides an introduction to the science of collecting, processing, analyzing, and interpreting data. Topics include creating and interpreting numerical summaries and visual displays of data; regression lines and correlation; evaluating sampling methods and their effect on possible conclusions; designing observational studies, controlled experiments, and surveys; and determining probabilities using simulations, diagrams, and probability rules. College Algebra is a prerequisite for 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. College Algebra and Pre-Calculus are prerequisites for this course.

Middle Schools Mathematics: Content Knowledge
Mathematics: Middle School Content Knowledge is designed to help candidates refine and integrate the mathematics content knowledge and skills necessary to become successful middle school mathematics teachers. A high level of mathematical reasoning skills and the ability to solve problems are necessary to complete this course. Prerequisites for this course are College Geometry, Probability and Statistics I, and Pre-Calculus.

High School Mathematics Content (for the 5-12 option)

Trigonometry and Precalculus
Trigonometry and Precalculus 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. College Algebra is a prerequisite for 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. College Algebra and Pre-Calculus are prerequisites for this course.

Calculus I
Calculus I is the study of rates of change in relation to the slope of a curve and covers the knowledge and skills necessary to apply differential calculus of one variable and to use appropriate technology to model and solve real-life problems. Topics include functions, limits, continuity, differentiability, visual, analytical, and conceptual approaches to the definition of the derivative, the power, chain, sum, product, and quotient rules applied to polynomial, trigonometric, exponential, and logarithmic functions, implicit differentiation, position, velocity, and acceleration, optimization, related rates, curve sketching, and L'Hopital's Rule. Pre-Calculus is a pre-requisite for this course.

Calculus II
Calculus II is the study of the accumulation of change in relation to the area under a curve. It covers the knowledge and skills necessary to apply integral calculus of one variable and to use appropriate technology to model and solve real-life problems. Topics include antiderivatives; indefinite integrals; the substitution rule; Riemann sums; the Fundamental Theorem of Calculus; definite integrals; acceleration, velocity, position, and initial values; integration by parts; integration by trigonometric substitution; integration by partial fractions; numerical integration; improper integration; area between curves; volumes and surface areas of revolution; arc length; work; center of mass; separable differential equations; direction fields; growth and decay problems; and sequences. Calculus I is a prerequisite for this course.

Probability and Statistics I
Probability and Statistics I covers the knowledge and skills necessary to apply basic probability, descriptive statistics, and statistical reasoning, and to use appropriate technology to model and solve real-life problems. It provides an introduction to the science of collecting, processing, analyzing, and interpreting data. Topics include creating and interpreting numerical summaries and visual displays of data; regression lines and correlation; evaluating sampling methods and their effect on possible conclusions; designing observational studies, controlled experiments, and surveys; and determining probabilities using simulations, diagrams, and probability rules. College Algebra is a prerequisite for this course.

Probability and Statistics II
Probability and Statistics II covers the knowledge and skills necessary to apply random variables, sampling distributions, estimation, and hypothesis testing, and to use appropriate technology to model and solve real-life problems. It provides tools for the science of analyzing and interpreting data. Topics include discrete and continuous random variables, expected values, the Central Limit Theorem, the identification of unusual samples, population parameters, point estimates, confidence intervals, influences on accuracy and precision, hypothesis testing and statistical tests (z mean, z proportion, one sample t, paired t, independent t, ANOVA, chi-squared, and significance of correlation). Probability and Statistics I is a prerequisite for this course.

Mathematics: Content Knowledge
Mathematics: Content Knowledge is designed to help candidates refine and integrate the mathematics content knowledge and skills necessary to become successful secondary mathematics teachers. A high level of mathematical reasoning skills and the ability to solve problems are necessary to complete this course. Prerequisites for this course are College Geometry, Probability and Statistics I, and Pre-Calculus.

Mathematical Modeling and Applications
Mathematical Modeling and Applications applies mathematics, such as differential equations, discrete structures, and statistics to formulate models and solve real-world problems. This course emphasizes improving students’ critical thinking to help them understand the process and application of mathematical modeling. Probability and Statistics II and Calculus II are prerequisites.

Calculus III
Calculus III is the study of calculus conducted in three-or-higher-dimensional space. It covers the knowledge and skills necessary to apply calculus of multiple variables while using the appropriate technology to model and solve real-life problems. Topics include: infinite series and convergence tests (integral, comparison, ratio, root, and alternating), power series,taylor polynomials, vectors, lines and planes in three dimensions, dot and cross products, multivariable functions, limits, and continuity, partial derivatives, directional derivatives, gradients, tangent planes, normal lines, and extreme values. Calculus II is a prerequisite for this course.

Linear Algebra
Linear Algebra is the study of the algebra of curve-free functions extended into three-or-higher-dimensional space. It covers the knowledge and skills necessary to apply vectors, matrices, matrix theorems, and linear transformations and to use appropriate technology to model and solve real-life problems. It also covers properties of and proofs about vector spaces. Topics include linear equations and their matrix-vector representation Ax=b, row reduction, linear transformations and their matrix representations (shear, dilation, rotation, reflection), matrix operations, matrix inverses and invertible matrix characterizations, computing determinants, relating determinants to area and volume, and axiomatic and intuitive definitions of vector spaces and subspaces and how to prove theorems about them. College Geometry and Calculus III are prerequisites for this course.

Abstract Algebra
Abstract Algebra is the axiomatic and rigorous study of the underlying structure of algebra and arithmetic. It covers the knowledge and skills necessary to understand, apply, and prove theorems about numbers, groups, rings, and fields. Topics include the well-ordering principle, equivalence classes, the division algorithm, Euclid's algorithm, prime factorization, greatest common divisor, least common multiple, congruence, the Chinese remainder theorem, modular arithmetic, rings, integral domains, fields, groups, roots of unity, and homomorphisms. Linear Algebra is a prerequisite for this course.

Advanced Calculus
Advanced Calculus examines rigorous reconsideration and proofs involving calculus. Topics include real-number systems, sequences, limits, continuity, differentiation, and integration. This course emphasizes students’ ability to apply critical thinking to concepts to analyze the connections between definitions and properties. Calculus III and Linear Algebra are prerequisites.

Mathematics Education (5-9 and 5-12 options only)

Mathematics Learning and Teaching
Mathematics Learning and Teaching will help you develop the knowledge and skills necessary to become a prospective and practicing educator. You will be able to use a variety of instructional strategies to effectively facilitate the learning of mathematics. This course focuses on selecting appropriate resources, using multiple strategies, and instructional planning, with methods 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. There are no prerequisites for this course.

Algebra for Secondary Mathematics Teaching
Algebra for Secondary Mathematics Teaching explores important conceptual underpinnings, common misconceptions and students’ ways of thinking, appropriate use of technology, and instructional practices to support and assess the learning of algebra. Secondary teachers should have an understanding of the following: algebra as an extension of number, operation, and quantity; various ideas of equivalence as it pertains to algebraic structures; patterns of change as covariation between quantities; connections between representations (tables, graphs, equations, geometric models, context); and the historical development of content and perspectives from diverse cultures. In particular, the focus should be on deeper understanding of rational numbers, ratios and proportions, meaning and use of variables, functions (e.g., exponential, logarithmic, polynomials, rational, quadratic), and inverses. Calculus I is a prerequisite for this course.

Geometry for Secondary Mathematics Teaching (5-12 option only)
Geometry for Secondary Mathematics Teaching explores important conceptual underpinnings, common misconceptions and students’ ways of thinking, appropriate use of technology, and instructional practices to support and assess the learning of geometry. Secondary teachers in this course will develop a deep understanding of constructions and transformations, congruence and similarity, analytic geometry, solid geometry, conics, trigonometry, and the historical development of content. Calculus I is a prerequisite for this course.

Statistics and Probability for Secondary Mathematics Teaching (5-12 option only)
Statistics and Probability for Secondary Mathematics Teaching explores important conceptual underpinnings, common misconceptions and students’ ways of thinking, appropriate use of technology, and instructional practices to support and assess the learning of statistics and probability. Secondary teachers should have a deep understanding of summarizing and representing data, study design and sampling, probability, testing claims and drawing conclusions, and the historical development of content and perspectives from diverse cultures. Calculus I is a prerequisite for this course.

Mathematics History and Technology
Mathematics History and Technology introduces a variety of technological tools for doing mathematics, and you will develop a broad understanding of the historical development of mathematics. You will come to understand that mathematics is a very human subject that comes from the macro-level sweep of cultural and societal change, as well as the micro-level actions of individuals with personal, professional, and philosophical motivations. Most importantly, you will learn to evaluate and apply technological tools and historical information to create an enriching student-centered mathematical learning environment. There are no prerequisites for this course.

Research Fundamentals (K-6 and 5-9 options only)

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 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.

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