Mathematics Education Degree
(Secondary)

Welcome to Composition: Successful Self-Expression! In this course, you will focus on four main topics: professional writing for a cross-cultural audience, narrowing research topics and questions, researching for content to support a topic, and referencing research sources. Each section includes learning opportunities through readings, videos, audio, and other relevant resources. Assessment activities with feedback also provide opportunities to check your learning, practice, and show how well you understand course content. Because the course is self-paced, you may move through the material as quickly or as slowly as you need to gain proficiency in the seven competencies that will be covered in the final assessment. If you have no prior knowledge or experience, you can expect to spend 30-40 hours on the course content. You will demonstrate competency through a performance assessment. There is no prerequisite for this course and there is no specific technical knowledge needed.

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, everyday applications of physical science concepts to help students integrate conceptual knowledge with practical skills.

Introduction to Systems Thinking and Applications provides learners with the skills required to engage in a holistic systems-based approach to analyzing complex problems and solutions. This course introduces the foundational concepts and principles of systems thinking and provides opportunities to use a systems thinking approach to analyze and evaluate real-world case studies. The course will culminate with using systems thinking to develop a solution to an authentic complex problem. This course has no prerequisites, but general education math (C955 or C957) is preferred. Because the course is self-paced, learners may move through the material as quickly or as slowly as needed, with the goal of demonstrating proficiency in the five competencies covered in the final assessment. If learners have no prior knowledge of this material, they can expect to spend 30 to 40 hours on the course content.

Technology and Ethics: Emerging Trends and Society explores the intersection of ethical thinking and technological innovations. A foundational introduction to ethical frameworks is applied to emerging trends in technology, including artificial intelligence, social media, and other forms of digital media. This course examines the impact of technology on our understanding of self, as well as the individual’s role in interacting with others in a globalized society. The course helps students gain the ability to recognize ethical actions within the context of current and newly evolving technological landscapes. This course has no prerequisites.

Welcome to Introduction to Communication: Connecting with Others! It may seem like common knowledge that communication skills are important, and that communicating with others is inescapable in our everyday lives. While this may appear simplistic, the study of communication is actually complex, dynamic, and multifaceted. Strong communication skills are invaluable to strengthening a multitude of aspects of life. Specifically, this course will focus on communication in the professional setting, and present material from multiple vantage points, including communicating with others in a variety of contexts, across situations, and with diverse populations. Upon completion, you will have a deeper understanding of both your own and others’ communication behaviors, and a toolbox of effective behaviors to enhance your experience in the workplace.

American Politics and the U.S. Constitution examines the evolution of representative government in the United States and the changing interpretations of the civil rights and civil liberties protected by the Constitution. This course will give candidates an understanding of the powers of the branches of the federal government, the continual tensions inherent in a federal system, the shifting relationship between state and federal governments, and the interactions between elected officials and the ever-changing electorate. This course will focus on such topics as the role of a free press in a democracy, the impact of changing demographics on American politics, and the debates over and expansion of civil rights. Upon completion of the course, candidates should be able to explain the basic functions of the federal government, describe the forces that shape American policy and politics, and be better prepared to participate in America’s civic institutions. This course has no prerequisite.

Quantitative Literacy views real-world problems through the lens of quantitative reasoning. The application of quantitative concepts to topics such as financial decisions is explored. Algebraic models and functions, as well as principles of geometry, are reviewed as fundamental ways to explore real-life scenarios. The use of mathematical concepts as a tool for modeling and understanding everyday problems is leveraged to promote students' thinking of math as a useful and relevant tool for many situations and scenarios. Numeracy and quantitative thinking skills are developed through these applications.

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.

Welcome to Composition: Writing with a Strategy! In this course, you will focus on three main topics: understanding purpose, context, and audience, writing strategies and techniques, and editing and revising. In addition, the first section, will offer review on core elements of the writing process, cross-cultural communication, as well as working with words and common standards and practices. Each section includes learning opportunities through readings, videos, audio, and other relevant resources. Assessment activities with feedback also provide opportunities to check your learning, practice, and show how well you understand course content. Because the course is self-paced, you may move through the material as quickly or as slowly as you need to gain proficiency in the seven competencies that will be covered in the final assessment. If you have no prior knowledge or experience, you can expect to spend 30-40 hours on the course content.

Precalculus builds on previous math courses to provide a deeper understanding of fundamental mathematical concepts and problem-solving skills to prepare students for calculus and professional success. The course will lead students to engage with functions, trigonometry, systems of equations, analytic geometry, and sequences and series. Through interactive learning experiences and real-world applications, precalculus will help students develop a deeper understanding of mathematical principles and their practical significance across diverse fields. Successful completion of a college level algebra course is a prerequisite for this course.

Planning Instructional Strategies for Meaningful Learning is a dynamic course designed for educators seeking to deepen their understanding of instructional planning and the execution of educational strategies that foster meaningful learning experiences. This course provides candidates with the knowledge and skills necessary to create engaging and standards-aligned lessons that meet the needs of all students. This course also covers a range of high-leverage instructional practices to increase student learning, engagement, and achievement. Participants will learn to utilize assessments to inform instruction, adapt teaching to accommodate all students, and incorporate technology to enhance learning.

Creating Positive Learning Environments delves into the key elements that contribute to creating and maintaining a positive learning atmosphere for educators focused on fostering supportive and productive classroom climates. The course teaches effective communication, classroom norms and routines, and positive behavior supports. Emphasizing the importance of a safe and inclusive environment, the course also explores methods to promote student engagement, collaboration, and mutual respect among all learners. It also addresses the role of mental well-being in learning, exploring trauma-informed and restorative practices, which are addressed in relation to online and hybrid learning environments. Through a blend of theoretical frameworks and practical applications including case studies, Creating Positive Learning Environments teaches learners how to develop and sustain environments that not only enhance academic performance but also support the holistic development of students.

Instructional Technology and Online Pedagogy is an innovative course designed to equip students with the skills to effectively integrate technology in their teaching practices. The course also covers best practices for online pedagogy, assessment and feedback, collaborative learning, and the use of multimedia and interactive elements to enhance learning experiences. With a focus on practical application, students will leave the course ready to create and facilitate compelling, high-quality online learning experiences that meet the needs of today's diverse learners. This course also provides a foundation for supporting digital literacy in K–12 education. In addition, this course prepares students to use technology to improve professional productivity and effectiveness in areas like data analysis and data representations.

The Professional Educator prepares WGU students to excel in the exciting and impactful profession of being an educator. Additionally, the course addresses the importance of continuous professional development and ethical considerations in teaching through the School of Education (SOE) Professional Dispositions and Ethics. Upon completion of the course, WGU students will be equipped with the tools and insights needed to continue their professional journey of becoming effective, inspiring, and adaptive educators, capable of making a significant impact in the lives of their students and the broader educational community. (This is not a transferable course.)

Personalized Learning for Inclusive Classrooms empowers educators to create more inclusive and effective learning environments. This course focuses on the principles and strategies of personalized learning, emphasizing the need to value and support the unique needs, interests, and abilities of each learner. The course provides a foundation for learner characteristics of learners with exceptionalities and other unique learning needs. This course helps candidates develop skills for partnering with parents and families to advocate for all students with exceptionalities, including those impacted by provisions of the Individuals with Disabilities Education Act (IDEA) and Section 504 of the Rehabilitation Act. Multitiered systems of support are addressed to prepare candidates for their future classrooms as they seek to select appropriate instructional practices and interventions to best serve their learners. These factors are also addressed in relation to online and hybrid learning environments.

Learners and Learning Science provides WGU students with a deep understanding of the science behind learning processes. This course covers a broad spectrum of topics pertaining to the science of learning, including cognitive development, learning theories, neuroscience in education, and the impact of developmental milestones on learning. Students will explore how these concepts apply to learning environments and educational levels, from early childhood through adolescence. The course emphasizes evidence-based practices and the practical application of learning science principles, equipping students with strategies to enhance learning outcomes and student engagement. This course aims to empower educators to create more effective, inclusive, and engaging learning experiences for all learners.

Assessing and Monitoring Student Learning is a targeted course crafted for candidates who aim to enhance their skills in evaluating student progress and educational outcomes. This course provides an in-depth exploration of various assessment techniques, including formative and summative assessments, standardized tests, benchmark assessments, progress monitoring, and alternative assessment strategies. Participants will learn how to design effective assessment tools, interpret data to inform instruction, and provide meaningful feedback to students. This course also provides a foundation of data analysis that supports educators’ need to understand data and present data to stakeholders. Candidates will also explore online and digital assessment tools. Assessing and Monitoring Student Learning will prepare learners to align assessments to standards to monitor student learning, assess data, and provide on time and quality feedback.

Calculus I offers a foundational exploration of the essential concepts and applications of calculus, crucial for higher-level mathematics and various scientific fields. This course begins with an overview of calculating limits and continuity of functions, setting the stage for the study of derivatives. Then, students will explore applications of derivatives, including applications to objects in motion, optimization, and related rates. Finally, the course focuses on both definite and indefinite integrals, leading to the mastery of the Fundamental Theorem of Calculus. This course prepares students for advanced mathematical studies and provides the groundwork for advanced calculus topics addressed in Calculus II and Multivariable Calculus. 

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.

Probability and Statistics offers candidates a comprehensive introduction to the fundamental principles of probability theory and statistical analysis, specifically designed for educators and aspiring statisticians. Beginning with the basics, students will explore essential concepts such as probability rules, conditional probability, and counting techniques, learning how to apply these in real-world contexts and effectively communicate them to K-12 students. Students will then learn sampling methods and estimation techniques, equipping them with the knowledge to gather, analyze, and interpret representative data for statistical analysis. Finally, students will focus on hypothesis testing and statistical inference, where they will learn to conduct and interpret various tests, including confidence intervals, using statistical software. Through a blend of interactive simulations, scenario-based challenges, and reflective activities, this course prepares students to apply these statistical tools in educational settings and beyond, fostering data-driven decision-making and effective teaching practices.

Linear Algebra delves into the study of linear systems, matrices, and vector spaces, forming a critical foundation for advanced mathematics. Students will begin by mastering matrix operations, including solving linear systems and finding determinants and inverses. As they progress, they will explore vector spaces, linear transformations, and inner product spaces, gaining the skills to work with higher-dimensional systems. The course also covers advanced topics such as eigenvalues, eigenvectors, diagonalization, and sophisticated techniques like the least squares method, linear programming, and singular value decomposition. This course is essential for those preparing for Multivariable Calculus and other advanced mathematical studies.

Multivariable Calculus provides an advanced exploration of calculus in multiple dimensions. The course begins with vector operations in both two and three dimensions, with emphasis on mastering computations and interpretations of magnitudes, directions, and vector products. Then, it presents partial differentiation and the integration of functions of multiple variables. Finally, the course teaches learners how to analyze applications of vector fields using line, surface, and volume integrals. This course integrates and extends previous calculus concepts, providing students with the opportunity to gain a deep understanding of key mathematical theorems while preparing students for specialized courses and professional applications. Calculus II is a prerequisite for this course.

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.

Advanced Calculus builds on prior calculus concepts to provide a rigorous and comprehensive exploration of advanced topics in calculus and analysis. The course begins with an introduction to writing proofs, using definitions and theorems, to analyze the real number system. The course progresses to using definitions and theorems to analyze the properties of functions, focusing on continuity, differentiability, integrability, and convergence. Then, it examines the rigorous treatment of advanced vector calculus operations, including the differentiation and integration of vector functions, and applies these skills to solve real-world problems in physics and engineering. Finally, students will synthesize and apply advanced integration and topological techniques to solve complex problems. This course solidifies the mathematical foundation needed for specialized and research-focused applications in mathematics and related fields.

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.

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.

Trigonometry delves into the core concepts and applications of trigonometric functions and identities, critical for advanced mathematics and practical problem-solving. The course starts with foundational topics, including the definition and calculation of sine, cosine, and tangent ratios, and progresses to solving right triangles and applying trigonometric functions to model real-world periodic phenomena. Students will explore the unit circle, derive fundamental identities, and solve complex trigonometric equations, including applications of vectors, parametric, and polar forms. Emphasizing both theoretical understanding and practical application, this course equips students with the skills necessary for higher-level mathematics courses and various professional fields. No prerequisites are required for this course.

Calculus II builds upon foundational calculus concepts to deepen learners' understanding of integration techniques, sequences, series, and differential equations. The course begins with advanced integration methods, including improper integrals and numerical approximation techniques, crucial for solving complex real-world problems in fields such as physics and engineering. Students will explore sequences and series, applying convergence tests and power series expansions to analyze and represent functions accurately. Additionally, the course covers differential equations, parametric equations, and polar coordinates, providing essential tools for modeling dynamic systems and solving higher-level mathematical problems. Throughout the course, practical applications in various scientific and engineering disciplines are emphasized, ensuring students develop strong analytical and problem-solving skills. This course prepares learners for advanced studies in mathematics and related fields and prepares students for the more complex applications found in Multivariable Calculus.

Differential Equations examines the methods and theory of ordinary differential equations (ODEs), focusing on the classification and solution of initial- and boundary-value problems. The course advances to the analysis and solution of linear and nonlinear differential equations, including systems of equations and higher-order differential equations with both constant and variable coefficients. Emphasis is placed on real-world applications and stability analysis. Students will explore advanced techniques such as matrix exponential, fundamental solution matrices, phase-space analysis, Laplace transforms, and an introduction to partial differential equations (PDEs). This course builds on matrix and vector concepts and prepares students for more advanced mathematics courses.

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. This methods course will count towards 5 hours of the 50 total clinical hours that learners will gain from their SCED methods courses.

Advanced Probability and Statistics provides students with advanced knowledge and skills in probability theory and statistical analysis. Students will learn to conduct an analysis of variance (ANOVA), regression analysis, and correlation analysis. Additionally, they will learn to apply R programming language, generate functions, and use modes of stochastic convergence. The course will focus on applying these concepts to real-world scenarios, decision-making processes, and predictive modeling.