BA Mathematics Areas of Study

The WGU Bachelor of Arts in Mathematics program content is based on research of 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 Bachelor of Arts in Mathematics 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 hallmarks of our program include: (a) appropriate and rigorous subject-matter preparation, (b) research-based pedagogical course preparation, and (c) clinical field experiences in which teacher candidates are supervised by trained coaches.

General Education

Foundations of College Mathematics (For the 5-9 program)
Foundations of College Mathematics addresses the sequence of learning activities necessary to build competence in foundational concepts of College Mathematics, which include whole numbers, fractions, decimals, ratios, proportions and percents, geometry, statistics, the real number system, equations, inequalities, applications, and graphs of linear equations.

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.

College Algebra
College Algebra covers basic algebraic concepts and functions and their use in describing, interpreting, and modeling realworld situations. Topics include real and complex numbers; algebraic expressions; linear equations and inequalities; graphs; relations and functions; polynomial, rational, inverse, exponential, and logarithmic functions; function composition; and systems of linear equations.

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.

English Composition II
English Composition II introduces learners to research writing and thinking that are valued in college and beyond. The Composition II course at WGU should be seen as a foundational course designed to help undergraduate students build fundamental skills for ongoing development in writing and research. Students will complete an academic research paper.

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.

Critical Thinking and Logic (For the 5-9 program)
Reasoning and problem solving helps students internalize a systematic process for exploring issues that takes them beyond an unexamined point of view and encourages them to become more self-aware thinkers by applying principles of problem identification and clarification, planning and information gathering, identifying assumptions and values, analysis and interpretation of information and data, reaching well-founded conclusions, and identifying the role of critical thinking in the disciplines and professions.

Elements of Effective Communication
Elements of Effective Communication introduces learners to elements of communication that are valued in college and beyond. Materials are based on five principles: being aware of your communication with yourself and others; using and interpreting verbal messages effectively; using and interpreting nonverbal messages effectively; listening and responding thoughtfully to others, and adapting messages to others appropriately.

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 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.

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.

Integrated Natural Science
Integrated Natural Sciences explores the natural world through an integrated perspective and helps students begin to see and draw numerous connections among events in the natural world. Topics include the universe, the Earth, ecosystems and organisms.

Integrated Natural Science Applications
Integrated Natural Sciences Applications explores the natural world through an integrated perspective and helps students apply scientific concepts and methodologies to the examination of natural science fundamentals.

Middle School Mathematics Content

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. Candidates should have completed a course in College Algebra before engaging in this course.

Pre-Calculus 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. Candidates should have completed a course in College Algebra before engaging in 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. Candidates should have completed at least a course in College Algebra and preferably one in Pre-Calculus before engaging in 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.

Middle Schools Mathematics: Content Knowledge
This course is designed to help you refine and integrate the mathematics content knowledge and skills necessary to become a successful middle school mathematics teacher. A high level of mathematical reasoning skills and the ability to solve problems are necessary to complete this course. Candidates should have completed College Geometry, Probability and Statistics I, and Pre-Calculus before engaging in this course.

High School Mathematics Content


College Geometry
This course is designed for prospective secondary school mathematics teachers. It uses both synthetic and analytic approaches. In this course, you will be introduced to formal proofs using geometric properties, and have the opportunity to explore basic concepts of transformational geometry. You will also become familiar with the use of dynamic technologies and selected advanced topics in the study of geometry.

Probability and Statistics I
This course is designed to provide you with a broad overview of the field of probability and statistics, and a fundamental understanding of statistical reasoning.

Probability and Statistics II
This course is designed to provide students with a broad overview of the field of probability and statistics and a fundamental understanding of statistical reasoning. Topics include discrete and continuous random variables, point and interval estimation, and hypothesis testing.

Calculus I
Calculus I explores the key concepts, methods, and applications of differential calculus of one variable. It is the first course in the calculus sequence intended for secondary mathematics teachers. A solid background in precalculus is highly recommended. Topics include a review of functions, limits, derivatives, and applications of differential calculus. Upon completion, students will be able to apply the concepts and methods of differential calculus and appropriate technology to solve practical problems and communicate results.

Calculus II
In Calculus II you will study another important problem that led to the development of calculus: finding the area under a curve. You will study this problem and other applications of integration as you progress through this course. As you do, keep in mind that calculus is not only a theoretical branch of mathematics; calculus is used by scientists, engineers, and economists and has numerous applications to daily life.

Calculus III and Analysis

Linear Algebra

Mathematics: Content Knowledge
This course is designed to help you refine and integrate the mathematics content knowledge and skills necessary to become a successful secondary mathematics teacher. Successful completion of the course requires a high-level of mathematical reasoning skills and the ability to solve problems.

Abstract Algebra

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.

Fundamentals of Educational Psychology
Students will learn the major theories of typical and atypical physical, social, cognitive, and moral development of children and adolescents. Information processing, brain research, memory, and metacognition will also be covered.

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.

Teacher Education Diversity

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.

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.

Preclinical Experiences

Introduction to Preclinical Experiences
Introduction to Preclinical Experiences engages students in utilizing video observations to reflect on a wide range of educational considerations so that they can develop the tools necessary to be prepared in the classroom. Students will document and reflect on at least 40 hours of video observation.

Preclinical Experiences in Mathematics
Pre-Clinical Experiences in Mathematics provides students the opportunity to observe and participate in a wide range of inclassroom teaching experiences to develop the skills and confidence necessary to be an effective teacher. Students will reflect on and document at least 60 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, a completed resume, philosophy of teaching, and professional photo.

Over the course of your observations, you will:

  • examine the interaction between instruction and learning,
  • review the impact of culture on learning,
  • reflect on teaching strategies and assessment practices,
  • consider current classroom practices as they relate to the student experience,
  • address the needs of exceptional learners, and
  • analyze general and program-specific instructional methods based on student needs.

Once you have completed a majority of your coursework and your initial pre-clinical experiences, you will enter and observe a live classroom. This will be an excellent opportunity for you to see real-world examples of the principles you have learned. Theory often diverges from practice when it must be applied in a real-world, dynamic situation. In this course, you will reflect on your previous coursework, and look forward to the requirements still needed in preparation for Demonstration Teaching and graduation.

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.

Mathematics Education

Mathematics Learning and Teaching
In this course you will develop the knowledge and skills necessary for becoming a prospective and practicing educator. You will be able to use a variety of instructional strategies to effectively facilitate the learning of mathematics. The focus will be on selecting appropriate resources, using multiple strategies, and instructional planning. Methods will be 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.

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. Most importantly, you will learn to evaluate and apply technological tools and historical information to create an enriching student-centered mathematical learning environment.

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 Work Sample in Mathematics
The Teacher Work Sample 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
The 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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