BA Mathematics Areas of Study

The WGU Bachelor of Arts in Mathematics program is a competency-based program that prepares students to be licensed as mathematics teachers in grades 5-9 or 5-12. All work in this degree program is online with the exception of the Demonstration Teaching and in-classroom field experience components.

General Education

Mathematics for Elementary Educators I (For the 5-9 program)
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 (For the 5-9 program)
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.

Finite Mathematics (For the 5-9 program)
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.

Introduction to Humanities
This introductory humanities course allows students to practice essential writing, communication, and critical thinking skills necessary to engage in civic and professional interactions as mature, informed adults. Whether through studying literature, visual and performing arts, or philosophy, all humanities courses stress the need to form reasoned, analytical, and articulate responses to cultural and creative works. Studying a wide variety of creative works allows students to more effectively enter the global community with a broad and enlightened perspective.

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.

Survey of United States History
This course presents a broad and thematic survey of U.S. history from European colonization to the mid-twentieth century. Students will explore how historical events and major themes in American history have affected a diverse population.

Introduction to Biology
This course is a foundational introduction to the biological sciences. The overarching theories of life from biological research are explored as well as the fundamental concepts and principles of the study of living organisms and their interaction with the environment. Key concepts include how living organisms use and produce energy; how life grows, develops, and reproduces; how life responds to the environment to maintain internal stability; and how life evolves and adapts to the environment.

Integrated Physical Sciences
This course provides students with an overview of the basic principles and unifying ideas of the physical sciences: physics, chemistry, and Earth sciences. Course materials focus on scientific reasoning and practical and everyday applications of physical science concepts to help students integrate conceptual knowledge with practical skills.

English Composition I
This course introduces learners to the types of writing and thinking that is valued in college and beyond. Students will practice writing in several genres and several media, with emphasis placed on writing and revising academic arguments. The course contains supporting media, articles, and excerpts to support a focus on one of five disciplinary threads (covering the topics of nursing, business, information technology, teaching, and literature, art, and culture) designed to engage students and welcome them into discussion about contemporary issues. The course supports peer review activities, though it may be completed asynchronously as well. Instruction and exercises in grammar, mechanics, research documentation, and style are paired with each module so that writers can practice these skills as necessary. This course includes full access to the MindEdge Writing Pad to support student writing and coaching sessions.

Natural Science Lab
This course gives you an introduction to using the scientific method and engaging in scientific research to reach conclusions about the natural world. You will design and carry out an experiment to investigate a hypothesis by gathering quantitative data.

English Composition II
English Composition II introduces undergraduate students to research writing. It is a foundational course designed to help students prepare for advanced writing within the discipline and to complete the capstone. Specifically, this course will help students develop or improve research, reference citation, document organization, and writing skills. English Composition I or equivalent is a prerequisite for this course.

Introduction to Communication
This introductory communication course allows students to become familiar with the fundamental communication theories and practices necessary to engage in healthy professional and personal relationships. Students will survey human communication on multiple levels and critically apply the theoretical grounding of the course to interpersonal, intercultural, small group, and public presentational contexts. The course also encourages students to consider the influence of language, perception, culture, and media on their daily communicative interactions. In addition to theory, students will engage in the application of effective communication skills through systematically preparing and delivering an oral presentation. By practicing these fundamental skills in human communication, students become more competent communicators as they develop more flexible, useful, and discriminatory communicative practices in a variety of contexts.

Survey of World History (For the 5-9 program)
Through a thematic approach, this course explores the history of human societies over 5,000 years. Students examine political and social structures, religious beliefs, economic systems, and patterns in trade, as well as many cultural attributes that came to distinguish different societies around the globe over time. Special attention is given to relationships between these societies and the way geographic and environmental factors influence human development.

Survey of United States Constitution and Government
In Survey of United States Constitution and Government, you will examine the structure, institutions and principles of the American political system. The foundation of the United States government is the U.S. Constitution, and this course will introduce the concepts of (a) separation of powers, (b) checks and balances, (c) civil liberties and civil rights, and (d) federalism and republicanism. By completing this course, you will have proven competency in the structures of government, your own role in the policy-making process, and the ways in which the Constitution and government has changed over time.

Teacher Education Foundations

Foundational Perspectives of Education
This course provides an introduction to the historical, legal, and philosophical foundations of education. Current educational trends, reform movements, major federal and state laws, legal and ethical responsibilities, and an overview of standards-based curriculum are the focus of the course. The course of study presents a discussion of changes and challenges in contemporary education. It covers the diversity found in American schools, introduces emerging educational technology trends, and provides an overview of contemporary topics in education.

Classroom Management, Engagement, and Motivation
Students will learn the foundations for effective classroom management as well as strategies for creating a safe, positive learning environment for all learners. Students will be introduced to systems that promote student self-awareness, self-management, self-efficacy, and self-esteem.

Educational Assessment
Educational Assessment assists students in making appropriate data-driven instructional decisions by exploring key concepts relevant to the administration, scoring, and interpretation of classroom assessments. Topics include ethical assessment practices, designing assessments, aligning assessments, and utilizing technology for assessment.

Middle School Mathematics Content

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. 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.

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 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

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.

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.

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 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.

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.

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.

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.

Educational Psychology

Psychology for Educators
This course prepares candidates to meet the expectations of society and prepares future educators to support classroom practice with research-validated concepts. The course helps future educators to create a framework for refining teaching skills that are focused on the learner, through engaged inquiry of integrating theory, critical issues in psychology, classroom applications with diverse populations, assessment, educational technology, and reflective teaching.

Teacher Education Diversity

Fundamentals of Diversity, Inclusion, and Exceptional Learners
Students will learn the history of inclusion and develop practical strategies for modifying instruction, in accordance with legal expectations, to meet the needs of a diverse population of learners. This population includes learners with disabilities, gifted and talented learners, culturally diverse learners, and English language learners.

Cultural Studies and Diversity (For the 5-9 program)
Cultural Studies and Diversity focuses on the development of cultural awareness. Students will analyze the role of culture in today’s world, develop culturally-responsive practices, and understand the barriers to and the benefits of diversity.

Mathematics Education

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 (for the 5-12 option)
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 (for the 5-12 option)
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.

Instructional Planning and Presentation

Introduction to Instructional Planning and Presentation
Students will develop a basic understanding of effective instructional principles and how to differentiate instruction in order to elicit powerful teaching in the classroom.

Instructional Planning and Presentation in Mathematics
Students will continue to build instructional planning skills with a focus on selecting appropriate materials for diverse learners, selecting age- and ability-appropriate strategies for the content areas, promoting critical thinking, and establishing both short- and long-term goals.

Preclinical Experiences

Preclinical Experiences in Mathematics
Preclinical Experiences in Mathematics provides students the opportunity to observe and participate in a wide range of in-classroom teaching experiences in order to develop the skills and confidence necessary to be an effective teacher. Students will reflect on and document at least 75 hours of in-classroom observations. Prior to entering the classroom for the observations, students will be required to meet several requirements including a cleared background check, passing scores on the state or WGU required basic skills exam and a completed resume.

Effective Teaching Practices

Secondary Reading Instruction and Interventions
Secondary Reading Instruction and Intervention explores the comprehensive, student-centered Response to Intervention (RTI) assessment and intervention model used to identify and address the needs of learners in grades 5–12 who struggle with reading comprehension and/or information retention. Course content provides educators with effective strategies designed to scaffold instruction and help learners develop increased skill in the following areas: reading, vocabulary, text structures and genres, and logical reasoning related to the academic disciplines. This course has no prerequisites.

Secondary Disciplinary Literacy
Secondary Disciplinary Literacy examines teaching strategies designed to help learners in grades 5-12 improve upon the literacy skills required to read, write, and think critically while engaging content in different academic disciplines. Themes include exploring how language structures, text features, vocabulary, and context influence reading comprehension across the curriculum. Course content highlights strategies and tools designed to help teachers assess the reading comprehension and writing proficiency of learners and provides strategies to support students' reading and writing success in all curriculum areas. This course has no prerequisites.

Demonstration Teaching

Supervised Demonstration Teaching in Mathematics
The Supervised Demonstration Teaching in Mathematics courses involve a series of classroom performance observations by the host teacher and clinical supervisor that develop comprehensive performance data about the teacher candidate’s skills.

Teacher Performance Assessment in Mathematics Education
The Teacher Performance Assessment is a culmination of the wide variety of skills learned during your time in the Teachers College at WGU. In order to be a competent and independent classroom teacher, you will showcase a collection of your content, planning, instructional, and reflective skills in this professional assessment.

Professional Portfolio
You will create an online teaching portfolio that includes professional artifacts (e.g. resume and Philosophy of Teaching Statement) that demonstrate the skills you have acquired throughout your Demonstration Teaching experience.

Cohort Seminar
Cohort Seminar provides mentoring and supports teacher candidates during their demonstration teaching period by providing weekly collaboration and instruction related to the demonstration teaching experience. It facilitates their demonstration of competence in becoming reflective practitioners, adhering to ethical standards, practicing inclusion in a diverse classroom, exploring community resources, building collegial and collaborative relationships with teachers, and considering leadership and supervisory skills.

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