Math Education Course Descriptions

This is an introductory, 3-credit course designed for students with no prior knowledge. It provides a foundational understanding of key computer science principles, algorithms, and basic programming concepts. Three hours.

MAT 1230 Calculus I This course is a traditional introductory calculus course. We will study functions, limits, derivatives, and integrals. Applications of the derivative and the fundamental theorem of calculus will be particular highlights of this class as well as integrals and derivatives of logarithms and exponential functions. Students must enroll concurrently in MAT 1240. Four hours.

This course is a continuation of the topics covered in Calculus 1. We will study integration techniques, as well as integrals and derivatives of a variety of functions: logarithms, exponential functions, inverse trigonometric functions, and hyperbolic trigonometric functions. We will also study applications of integration, improper Riemann integrals, and L’Hopital’s rule for taking limits. Investigating infinite sequences and infinite series will be a highlight of this course. Prerequisites: MAT 1230 or permission of the mathematics program director. Three hours.

This course is an introductory course on proofs and emphasizes logic, set theory and proof techniques. Theorems will be taken from topics including set theory, number theory and real analysis. Three hours.

This course is an introduction to discrete mathematics, including combinatorics and graph theory. Topics covered include graph coloring, trees and searching, network flows, network algorithms and complexity analysis, recurrence relations, functions and relations, generating functions, set theory, and probability. An emphasis will be on proof by induction. Prerequisite: MAT 2100. Three hours.

This course is an investigation of limits, derivatives, and integrals of functions of more than one variable. We will study various applications of calculus, further topics of multivariable calculus, and ways in which calculus interplays with the other mathematical disciplines such as linear algebra, probability theory, and complex analysis. Prerequisites: MAT 1250 or permission of the mathematics program director. Three hours.

This course builds on the geometric interpretation of vectors and linear equations from Calculus 3 to consider a more abstract view of linear algebra using vector spaces and linear transformations. The history of linear algebra is interspersed throughout the course. Emphasis is placed on real life applications, and technology is used when necessary. Prerequisite: MAT 2250. Three hours.

This course is a thorough investigation of the axioms and theorems of Euclidean geometry. Throughout this course we will also cover several topics in non-Euclidean geometry, symbolic logic, and axiomatic systems in general. This course is designed to thoroughly equip a future high school teacher with the content knowledge needed to successfully teach geometry. Prerequisite: MAT 2100 or permission of the mathematics program director. Three hours.

This is a capstone course for mathematics and mathematics education majors. This course will cover several topics that draw together the various mathematical disciplines, and will portray the global perspective of mainstream mathematics. This course may meet in conjunction with other capstone courses within the science division for a portion of the semester. Prerequisites: declared mathematics or mathematics education major; and MAT 2250. Three hours.

Standard algebra is a study of the arithmetic structure of numbers, and of functions of numbers. There are other objects that we study in mathematics besides numbers, and consequently other arithmetic structures; for example, matrices, functions, and permutations. Abstract algebra is the study of general arithmetic structures, and of functions of these general structures. In this course we study the axioms of group theory and develop the body of theorems associated with these axioms. If time permits, we will also investigate the axioms and theorems of ring theory and field theory. Prerequisite: MAT 2100 or permission of the mathematics program director. Three hours.

Introduction to the fundamental concepts of real analysis. A study of the real number system, limits, sequences, series, convergence, functions, continuity, differentiability, and Riemann integration can all be touched on. Prerequisite: MAT 2100 or permission of the mathematics program director. Three hours.

This course in statistics provides a rigorous introduction to applied statistics. Topics include sampling principles, elementary probability, the normal distribution, hypothesis testing, confidence intervals, inference on numerical and categorical variables, chi-squared, ANOVA, and linear regression. Multiple linear regression and logistic regression will be covered if time permits. Three hours.

A study of differential equations using analytical, numerical and graphical techniques. Emphasis is placed on solving first and second order, and systems of differential equations. Various types of differential equations, their solutions and their applications in physical sciences will be studied. Prerequisite: MAT 2250. Three credit hours.

An independent study in mathematics is designed for students who have excelled in several post-calculus classes and desire to study a topic that is not currently available in the curriculum. A student wishing to take an independent study will establish a topic to study and seek out a faculty member to whom he or she will be responsible. Once a topic and a faculty member are determined, permission for the independent study must be obtained from the mathematics program director. Independent study in mathematics is a non-repeatable class. Prerequisites: MAT 2250, availability of professor, and permission of the mathematics program director. Three hours.

In this course we study the axioms and theorems of probability theory. We study probability distributions of discrete and continuous random variables, and many of their applications. Throughout this course we will use a significant amount of calculus to develop the theory of probability. Material covered in this course is included on Exam P/1 of the SOA/CAS. Prerequisites: MAT 2250 and MAT 2100, or permission of the mathematics program director. Three hours.

This course is the study of multivariable statistics on real data sets. Correlation, hypothesis testing and ANOVA are highlights of this class, which require a significant use of calculus. Prerequisites: MAT 2250 and MAT 3200.

Research in mathematics is designed for students who have excelled in several post-calculus classes and have a desire to investigate the fine details of a topic in an attempt to advance the theory with new theorems, new proofs, or new applications. A student wishing to undertake such a research project must do so under the strict supervision of a faculty member and with the permission of the mathematics program director. The supervising faculty member must be willing to invest significant time into helping the student find appropriate resources, ask appropriate research questions, and seek out coherent answers to the questions asked. This course is intended to give students precursory experience into what a graduate thesis experience would be like. Research in mathematics is a non-repeatable class. Prerequisites: MAT 2200, and permission of mathematics program director. Three hours.

An introduction to the profession of teaching. Learning experiences are structured both in and out of the classroom with the purpose of assisting the college student in making career decisions relative to the profession, e.g., to teach or not, at which level, and in which subject area. Both content and field experiences are aligned with the missions of Grace College and the School of Education. A grade of B- or better is required to continue on toward candidacy status. Three hours.

A study of the learner at all grade levels and the many factors affecting learning, including but not limited to, theories of learning, environment, heredity, cultural impact, discipline, classroom management, exceptionalities, and development. The measurement of academic aptitude and achievement is also covered. Practical application is stressed. Prerequisite: SED 1000. Three hours.

This course is designed for prospective teachers, elementary or secondary, and any interested persons working with children at home or in social agencies. The intent is to develop an introduction to children with exceptionalities and practical strategies to assist these children, especially in an educational setting. This course will examine the types of exceptionalities, the laws that apply to them, as well as adaptations and special services that are provided to them in a regular classroom setting and in alternative educational settings. Prerequisite: SED 1000. Three hours

The course consists of cooperative teaching and learning. The instructor’s role is that of a facilitator, rather than a “giver” of knowledge. There are lectures, small and large group discussions of readings and related information, writing, and research focusing on issues of diversity in schools. To better appreciate the influence of culture on behavior and values, students explore their own diversity through written and/or group discussions and inquire into the cultural diversity of school populations in Indiana and surrounding regions. Among the topics included in this study are multicultural education, social classes and socioeconomic status, ethnicity and race, gender, religion, language, community involvement, curriculum, justice, privilege, and other relevant topics that relate to multicultural concerns. Prerequisite: SED 1000. Three hours.

This course provides you with a theoretical, research-based background for classroom instructional and assessment strategies you will be implementing in your teaching. Key issues discussed will include how people learn, instructional planning, how we successfully assess student learning, and how our instruction and assessment strategies can lead to improved student learning and increased motivation to learn. Prerequisite: SED 1000 & SED 2200. Three hours

The purpose of this course is to develop a working knowledge of responsive instruction by applying differentiation strategies and Universal Design for Learning (UDL) principles. Students will learn to promote all students’ development, learning, and success through ongoing assessment that informs instruction. Multi-tiered systems within the general education setting will be explored. Students will learn technology skills and culturally responsive teaching to enhance student learning. Prerequisites: SED 2600, and candidacy status. Three hours.

This course presents best practices in classroom assessment, environment, and behavior management. Topics include relationship development, organization of the classroom learning environment, classroom procedure development, and approaches for managing individual and large group student behaviors. Various strategies to instruction and assessment will be explored. Candidates will develop lessons utilizing formative and summative assessment tools. Candidates will understand how these assessments inform the teaching and learning process. Prerequisites: candidacy status. Three hours.

This course is an introduction to critical thinking 1 as a fundamental process instrumental in applying philosophy to the craft of teaching. Various topics that deal with classroom concerns, student teaching experiences are discussed each week. Topics include: school law, interviewing, résumé construction, best practices, and classroom management. Candidates will complete the TWS designed to help the teacher education candidates continue their development as reflective practitioners by systematically documenting and analyzing student learning. This course is an introduction to critical thinking2 as a fundamental process instrumental in applying philosophy to the craft of teaching. The course is a systematic study of the philosophy of education and the ethics that undergird the profession. Both secular and Christian philosophical views are examined. Candidates also integrate elements of a chosen set of philosophical beliefs to sharpen their competence as a professional. Candidates interact with key stakeholders associated with the craft of teaching. Describing the work of moral practice is part of the activities of the course. Prerequisite: All SED course work completed, additional school requirements me. Three hours.

Includes full-time teaching experience for an entire semester as well as a seminar for majors during the experience. This course deals with a variety of topics and issues especially germane to candidates who are about to enter the teaching profession. Each candidate enrolled in this course will be required to complete a Teacher Work Sample and earn a passing score of C or higher. Prerequisites: All SED course work completed, additional school requirements met. Nine hours.

This course is offered to help the preservice teacher understand the special characteristics of early adolescents and adolescents and their school settings (middle and high school). Prerequisites SED 2200, SED 2600, candidacy status. Three hours.

This course is designed to address the needs and concerns of students preparing to teach mathematics in grades 5-12. The structure of this methods course is organized around Standards for IDOE Developmental Secondary Educators and NCATE/NCTM Standards for Initial Preparation for Mathematics Teachers. Though the course does not promote a particular methodology, it presents principles of learning from which teachers can draw as they make decisions about instruction. Students will discover practical ideas for teaching mathematics, as well as background information to help formulate their own hypotheses about student learning and retention, in an effort to stimulate a desire to further research the field and contribute to the theory building process. In today’s classroom with diverse learners and varied curricular options, teachers must have a repertoire of teaching practices grounded in their research and knowledge base. Mathematics teachers serve as facilitators to develop students’ problem-solving skills and can create classroom environments of collaboration, cooperation and inquiry through social interactions, technology usage, multiple representations, and a variety of appropriate instructional strategies. Prerequisites: SED 2200, SED 2600, SED 3600, candidacy status. Three hours.