The program consists of thirty semester hours (ten courses) of coursework, including:

• Fifteen semester hours of mathematics and pedagogical content;
• Nine semester hours of theory of pedagogy; and
• Six semester hours of research methods.

Courses

Mathematics and Pedagogical Content

You will take coursework geometry, algebra, advanced topics related to calculus, topics in discrete mathematics (graph theory, combinatorics), and topics in linear and abstract algebra.  Descriptions are given below.

GEOMETRY FOR TEACHERS:  Investigate traditional secondary school topics in Euclidian geometry, introduction to similar ideas in non-Euclidian spaces, examine the impact of mathematics education research on the teaching and learning of geometry, and explore real-world applications. Extensive use of the Geometer's Sketchpad will also be incorporated into every aspect of the course. Topics to be explored may include transformations, symmetry, spherical or hyperbolic geometry, centers of triangles (incenter, centroid, orthocenter, and circumcenter), similarity, and coordinate geometry.

ALGEBRA FOR TEACHERS:  Investigate traditional secondary school topics from introductory and advanced algebra courses, examine appropriate use of manipulatives (e.g. algebra tiles) to explore basic algebra concepts, introduction to the use of hand-held graphing technology and data collection devices in the study of algebra. Topics covered in the course may include basic properties and mechanics of both equations and functions, models for factoring polynomial expressions, integration of physical science and mathematics, and using functions to model real-world phenomena.

ADVANCED MATHEMATICS FOR TEACHERS:  A study of topics in advanced secondary mathematics for teachers, this course includes the exploration of concepts related to trigonometry and analytic geometry, precalculus, and calculus. Appropriate use of graphing technology and data collection devices to enhance student understanding in their investigation of real-world examples, and the implications of recent educational research on the teaching and learning of those advanced topics are also key concepts of this course, as well. A variety of topics could be covered and may include: trigonometric functions and applications; rate of change in business, physics, and society; limits, continuity, and differentiability; and applications of area and volume problems.

APPLICATIONS OF GRAPH THEORY AND COMBINATORICS IN MODERN MATHEMATICS:  An opportunity to study selected topics in graph theory and combinatorics in depth. Appropriate use of computing technology will be included. Topics may include an introduction to circuits and graph coloring theorems, traveling salesperson problems and sorting algorithms, problems and methods in counting, networks, and finding winning strategies for Nim-type games.

APPLICATIONS OF LINEAR AND ABSTRACT ALGEBRA IN MODERN MATHEMATICS:  Study of topics connected to real-world applications in both linear and abstract algebra, and incorporating and introduction to matrix operations with EXCEL and TI graphing technology. Topics covered may include: introductory coding theory and cryptography; symmetry groups in mathematics, science, engineering, architecture, and art; permutation groups; linear programming problems and the simplex method; and Markov chains.

Theory of Pedagogy

You will take coursework in models of teaching, philosophy of teaching, geometry, algebra, advanced topics related to calculus, topics in discrete mathematics (graph theory, combinatorics), and topics in linear and abstract algebra. Descriptions are given below.

MODELS OF TEACHING:  Analyze and experiment with various models of teaching that can be useful in studying classroom interaction and for evaluating teacher performance. The course is designed to enable a teacher to acquire knowledge of theory pertaining to the evaluation of teaching. The acquisition of such knowledge should enable the professional educator to work more effectively and reflectively in the classroom.

PHILOSOPHICAL STUDIES IN EDUCATION:  A study of the writings of major philosophers as they relate to education (including those of the Marianist tradition). Interpretations are made for the development of a critical, personal theory of teaching, counseling, educational administration, and psychological services. The goal of this course is to enable the students to acquire the interpretive, normative, and critical perspectives of education as called for by the Standards of the Council of Social Foundations of Education.

PROFESSIONAL DEVELOPMENT OF TEACHER LEADERS:  The study of existing and emerging models of professional development designed to provide classroom teachers with opportunities to assume new leadership roles and responsibilities in the school community. Goals for this course include providing veteran classroom teachers with professional development programming designed to impart the knowledge, skills, and dispositions fundamental to the role of master, mentor or lead teacher, and to create an informed cadre of local practitioners committing to building coalitions between school administrators, classroom teachers, and teacher educators necessary to support the change process necessary to the advancement of quality schools and enhanced student learning.

Research Methods

You will take one course in research methods and you will take a capstone course, called Mathematics Clinic, in which you will in a mathematics education research project. Descriptions are given below.

RESEARCH METHODS AND ISSUES IN MATHEMATICS:  Review of related literature and research in education and mathematics education, and a study of key concepts necessary to analyze, evaluate, and conduct educational research. Application of both qualitative and quantitative research methods specifically related to the development of a research proposal. The focus on quantitative research methods provides ample opportunities to review fundamental concepts and properties of both descriptive and inferential statistics. Introduction to SAS or SPSS, both statistical programming packages appropriate for use in educational research, will be included in the course.

MATHEMATICS CLINIC:  The capstone research experience of the program. Following the completion of MTH 548, students are prepared to address research questions in mathematics education. Degree candidates will design, conduct, and analyze research experiments. A Mathematics Clinic research project must be pre-approved by the candidate’s advisory committee. Candidates must present their work in an oral presentation, via a public briefing, and will submit a written report, suitable for submission to an appropriate scholarly publication in education or mathematics education, to his or her advisory committee.