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.

### General Education (Middle grades option only)

**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 middle grades 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.

**College Geometry**

College Geometry covers the knowledge and skills necessary to use dynamic technology to explore geometry, to use
axiomatic reasoning to prove statements about geometry, and to apply geometric models to solve real-life problems.
Topics include axiomatic systems, analytic proofs, coordinate geometry, plane and solid Euclidean geometry, non-
Euclidean geometries, constructions, transformations, deductive reasoning, and dynamic technology. For candidates
enrolled in the MAMEMG program, College Algebra as well as Trigonometry and Precalculus are prerequisites.

**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, including representations, constructions and
interpretation of graphical displays (e.g., box plots, histograms, cumulative frequency plots, scatter plots). 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. Candidates should have
completed a course in College Algebra before engaging in 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.

**Middle School 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 secondary 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 use dynamic technology to explore geometry, to use
axiomatic reasoning to prove statements about geometry, and to apply geometric models to solve real-life problems.
Topics include axiomatic systems, analytic proofs, coordinate geometry, plane and solid Euclidean geometry, non-
Euclidean geometries, constructions, transformations, deductive reasoning, and dynamic technology. For
candidates enrolled in the MAMES program, Trigonometry and Precalculus is a prerequisite.

**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, including representations, constructions and
interpretation of graphical displays (e.g., box plots, histograms, cumulative frequency plots, scatter plots). 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. Candidates should have
completed a course in College Algebra before engaging in 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 and includes statistical variability and its sources and the role of
randomness in statistical inference. 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). Calculus II and Probability and Stats I are
prerequisites to 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 II 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 (Middle grades and secondary 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** (secondary 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** (secondary 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**

In this course, you will learn about a variety of technological tools for doing mathematics, and 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. You will focus on the historical development of
mathematics including contributions of significant figures and diverse cultures. Most importantly, you will learn to evaluate
and apply technological tools and historical information to create an enriching student-centered mathematical learning
environment.

### Education

**Teaching in the Middle School**

Teaching in the Middle School examines the guiding principles and best teaching practices for educating middle school
students. The course explores the history of the middle school, the philosophy, theory, and rationale behind middle school
organization; and the differences between elementary, middle, and secondary schools. The course also examines the
unique needs of middle school students and teaching methods used to meet the needs of these learners. This course has
no prerequisites.

### Research and Research Fundamentals (K-6 and middle grades 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.