Mathematics Education

Trigonometry and Precalculus covers the knowledge and skills necessary to apply trigonometry, complex numbers, systems of equations, vectors and matrices, and sequences 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 is the study of rates of change in 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. Precalculus is a prerequisite for this course.

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 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. College Algebra is a prerequisite to this course.

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 Statistics I are prerequisites for this course.

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, Pre-Calculus, Calculus I, and Calculus II. Linear Algebra, and Calculus III are recommended.

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 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 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 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 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.

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. College Algebra as well as Trigonometry and Precalculus are prerequisites.

Mathematics Learning and Teaching will help students develop the knowledge and skills necessary to become a prospective and practicing educator. This course will help students use a variety of instructional strategies to effectively facilitate the learning of mathematics. It 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 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 course focuses 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.

In Math History and Teaching, students will learn about a variety of technological tools for doing mathematics and develop a broad understanding of the historical development of mathematics. 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. This course will focus on the historical development of mathematics, including contributions of significant figures and diverse cultures. Students will learn to evaluate and apply technological tools and historical information to create an enriching student-centered mathematical learning environment.

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 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 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 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 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, and trees and networks. There are no prerequisites for this course.

This Secondary Mathematics course is designed to prepare future secondary math educators by focusing on the application of fundamental math concepts, the development of effective teaching strategies, and the alignment of instruction with state content standards. This course teaches key areas including application of number systems, algebraic structures, calculus, geometric reasoning, and probability and statistics in the secondary setting. Additionally, learners will learn to design and evaluate mathematical problems, integrate technology, and differentiate instruction to meet all students’ needs. Learners will also explore how to research and evaluate curricular resources to ensure they align with educational goals and standards. By the end of the course, participants will be equipped with the skills and knowledge necessary to deliver high-quality math instruction in secondary education.

Algebra for Secondary Mathematics Teaching offers an in-depth exploration of advanced algebraic concepts and instructional methodologies tailored for secondary education. The course emphasizes task-based learning, enabling participants to engage deeply with algebra as an extension of number theory, operations, and abstract reasoning. Students will explore key algebraic ideas, including equivalence, patterns of change through covariation, and the integration of multiple representations—such as tables, graphs, equations, and geometric models. The course also examines the historical evolution of algebra and incorporates diverse cultural perspectives. Core topics include variables, functions (including exponential, logarithmic, polynomial, rational, and quadratic functions), and their applications. This course is designed to enhance educators' ability to teach complex algebraic concepts effectively and adapt instructional strategies to meet diverse student needs.

Geometry for Secondary Mathematics Teaching is a comprehensive course designed to equip future educators with the expertise to teach secondary-level geometry. This course delves into core geometric concepts, including geometric reasoning, transformations, congruence, similarity, and coordinate geometry, while emphasizing the development of critical thinking and problem-solving skills. Students will engage in dynamic instructional strategies and hands-on learning experiences, using tools like GeoGebra and Desmos to create interactive lessons that address common misconceptions and support diverse learners. By the end of the course, students will have the confidence and skills to design, implement, and refine geometry lessons aligned with educational standards and tailored to the needs of a diverse student population, preparing them to inspire and engage the next generation of mathematicians.

Methods of Teaching Secondary Mathematics is an in-depth exploration of secondary mathematics content and pedagogy, distinguishing between subject mastery and effective teaching practices. This course will prepare students to teach and reflect on secondary mathematics lessons that emphasize the use of effective teaching practices, including differentiation, questioning techniques, and curriculum development. The course also covers strategies for presenting mathematical material at the appropriate level, utilizing humanizing approaches, co-teaching, Multi-Tiered Systems of Support (MTSS), accommodations, and inclusion. This course does not have any required prerequisites.

Statistics for Secondary Mathematics Teaching provides a comprehensive exploration of advanced concepts and methodologies in teaching statistics and probability. The course delves into key topics such as summarizing and representing data, study design, sampling, testing claims, drawing conclusions, and probability. Emphasizing a deep understanding of conceptual foundations, including their historical development and perspectives from diverse cultures, the course addresses common misconceptions and students' ways of thinking. The appropriate use of instructional practices is also highlighted. There are no prerequisites for this course.