# Master of Arts in Mathematics, Teaching Emphasis

###### Questions?

If you have questions or would like more information about this program, please email Dr. Oscar Levin, or call him at (970) 351-2380.

This program is designed to prepare teachers to be experts in their own classroom. Upon finishing this program they should be able to teach the content of mathematics, assume leadership roles in mathematics curriculum within their schools, and read and understand the professional literature relating to the teaching and learning of their discipline. The emphasis is on preparing teachers for the 21st century with a dynamic and individualized program of study.

## Admission to the Master of Arts in Mathematics, Teaching Emphasis

Applications to this program must go through the Mathematics Teacher Leadership Center.

## Program Focus

The pedagogical focus of the program is on curricular, instructional, and assessment
reform in secondary mathematics education. Students will study the most recent literature
in these areas, including reports by the National Research Council and publications
of the National Council of Teachers of Mathematics such as the *Principle and Standards for School Mathematics*,* Curriculum and Evaluation Standards for School Mathematics* and *Professional Standards for Teaching Mathematics*.

The mathematical content of the program has been designed to supplement the pedagogical focus. Topics that have increased relevance due to the NCTM Standards for the secondary curriculum shall be emphasized: discrete mathematics, probability and statistics, geometry, mathematical modeling, and continuous mathematics. The course instruction will incorporate teaching strategies that are congruent with the constructivist viewpoint of learning: emphasize group-learning, the preparation of student projects, the development of skills in problem-solving, mathematical modeling, communicating mathematics, and direct involvement in using advanced technology accessible to the classroom. The program courses are specifically designed to empower students to be master teachers and change agents within their respective districts and geographical regions.

## Program Design

The program consists essentially of three components: two summers on campus enrolled in graduate level mathematics course work, four semesters online (during the academic years) enrolled in graduate level mathematics education courses, and the completion of an Action Research Project as the capstone requirement of the degree program and a substitute to Comprehensive Examinations. The courses and research provide advanced knowledge and abilities in mathematics content, mathematical content knowledge, and related research.

## Program Objectives

- Prepare a dedicated core group of secondary mathematics teachers to guide their peers in the curricular reforms of the next decade.
- Update secondary school mathematics teaching by encouraging a focus on problem-solving, cooperative learning groups, alternative means of assessment and the appropriate use of technology within the classroom.
- Increase the mathematical sophistication of secondary and community college mathematics teachers by providing a significant, while relevant education in mathematics at the master's degree level.
- Develop a regional network of educators committed to the improvement of mathematics education that builds lasting partnerships between secondary school teachers, administrators, community college faculty, university faculty, and state education administrators.

## Courses

This graduate program is designed especially for those teaching secondary school mathematics. Thirty semester hours of course work will be taken by graduate students consisting of 9 semester hours of required credit, and 21 semester hours of elective credits. In particular, MATH 534: Continuous Mathematics, MATH 543: Modern Geometry, and MED 600: Introduction to Research in Mathematics Education are required of all students. At least 12 semester hours of elective credits are to be selected from Group A (graduate level mathematics courses), and at least 9 semester hours of elective credits are to be selected from Group B (graduate level mathematics education courses). Alternative electives may be chosen from courses offered by the school or other schools with the approval of the student's adviser.

Group A Courses

MATH 520 - Functions and Equations

MATH 528 - Discrete Mathematics

MATH 529 - Mathematical Problem Solving

MATH 537 - Mathematical Modeling

MATH 550 - Applied Probability and Statistics

MATH 591 - Abstract Algebra and Number Theory

Group B Courses

MED 528 - Teaching of Discrete Mathematics

MED 534 - Teaching Algebra and Trigonometry

MED 543 - Teaching Geometry

MED 550 - Teaching Applied Probability and Statistics

MED 595 - Teaching Advanced Topics in Secondary School Mathematics

MED 599 - Action Research Project

#### Continuous Mathematics

MATH 534, 3 hrs: This course is designed to explore the notions that form the basis for calculus and the theory behind it. Topics include continuity and differentiability, generalizations to metric spaces and topological properties of subsets of the reals and of the plane. There will be a laboratory component for which we will use our Calculus Mathematica Lab. In this setting we will investigate many of the problems which form the basis of recent Calculus Reform efforts, including numerical solutions to differential equations, questions about Chaos, an interactive pictorial proof of the fundamental theorem of Calculus, and others.

Modern Geometry

MATH 543, 3 hrs: This course contains a broad overview of both Euclidean and Non-Euclidean geometries with an emphasis on coordinate and transformational approaches. This course will include such topics as hyperbolic geometry, fractal geometry, polyhedral surfaces, minimal surfaces (soap bubble geometry) and computer-based exploration of 2- and 3-dimensional figures, using current software accessible to high school classrooms and making connections with real world applications. The themes will basically include the different types of geometric structure, geometric transformations, distance, optimization, symmetry, regularity, visual reasoning and visualization, dimension, and coordinate systems. The Geometer's Sketchpad will also be used to discover numerous geometrical relationships and to solve applied problems.

Introduction to Research in Mathematics Education

MED 600, 3 hrs: Course objectives are to: (i) engage you in basic designs and analyses of educational research, (ii) study the basic research trends and issues in the teaching and learning of mathematics, (iii) identify and discuss problems associated with different research designs including statistical assumptions, (iv) synthesize and re-conceptualize research in mathematics education, (v) describe areas of research most useful to advancing the teaching and learning of mathematics, and (vi) incorporate areas of research most useful at advancing the teaching and learning of mathematics into classroom practices

Group A: Mathematics Electives

1. Functions and Equations (Math 5320, 3 hrs.): This course includes polynomial equations including DeMoivre's Theorem, the Fundamental Theorem of Algebra, methods of root extraction (e.g. Newton, Graffe) multiplicities, symmetric function, matrices, and determinants, also elementary computer applications.

2. Discrete Mathematics (MATH 528, 3 hrs): Introduction to combinatorics and graph theory emphasizing real-world applications and the development of skills in mathematical reasoning. The course will contain graduate experiences in discrete mathematics, addressing three broad categories of problems: existence problems, counting problems, and optimization problems. The following core topics will be the basis for the course: equivalence relations and posets, surjective and injective mappings, inductively defined sequences, recursions (solved using characteristic root technique, iteration, and generating functions), and applications involving graph theory. Content and ideas from NCTM's yearbook, Discrete Mathematics Across the Curriculum K-12 will be used. Also encountered in the course will be the use of the matrix features and cobweb routines for studying iterations using handheld technology, and linear programming routines of a computer spreadsheet.

3. Mathematical Problem Solving (MATH 529, 3 hrs.): This course includes techniques in problem solving applied to algebra, number theory, geometry, probability, discrete mathematics, logic and calculus, as well as a study of Poly's heuristic rules of mathematical discovery.

4. Mathematical Modeling (MATH 537, 3 hrs): This course will be based in large part on the NCTM publication Mathematical Modeling in the Secondary School Curriculum. The emphasis will be on constructing models and communicating results. Connections among fields in mathematics, applications in science and business and heavy use of technology (to include spreadsheets and graphics calculators) will all be part of this course. Evaluation will be based primary on written projects.

5. Applied Probability and Statistics (MATH 550, 3 hrs): Concepts addressed include history, counting techniques distributions and infernos (confidence intervals, point estimation, testing, ANOVA, regression, non-parametrics). As the course progresses, activities will be presented to supplement such concepts and topics as descriptive techniques, random variables, probability distributions, linear regression, sampling distributions, and such inferential statistics techniques as point estimation, confidence intervals and testing hypotheses. The statistical analysis and curve fitting features of hand held and computer technology will be an integral part of the course.

6. Abstract algebra and Number Theory (MATH 591, 3 hrs.): This course includes basic methods of problem solving in abstract algebra and number theory with applications in secondary school mathematics.

Group B: Mathematics Education Electives

1. Teaching Discrete Mathematics (MED 528, 2 hrs): This course (and all teaching courses) will be linked with it's MATH course by including some of the same content, but with emphasis in the learning and teaching of the content at the high school level. This will be associated with the cognition of how students learn and with discussion of difficulties frequently encountered by students in this area. NCTM's 1991 Yearbook, Discrete Mathematics Across the Curriculum K-12 , also provides numerous examples for this blend of content and pedagogy.

2. Teaching Algebra and Trigonometry (MED 534, 2 hrs): Curriculum materials such as the University of Chicago's School Mathematics Project and the Interactive Mathematics Project will be used in relating the content of high school algebra and geometry with appropriate instructional and assessment techniques. Concepts presented in the Standards will be integral to the course. Computers and graphics calculators will be essential for the analysis of functions.

3. Teaching Geometry (MED 543, 2 hrs): Knowledge of and ability to use appropriate technology (Logo, Sketchpad, etc.), manipulatives and other instructional materials to develop geometric understanding according to the van Hiele levels will be introduced. Participants will develop curricular activities/lessons that focus on making mathematical connections through multiple-representational forms, real-world applications and assessment of their understanding of mathematics using instructional and organizational strategies.

4. Teaching Probability and Statistics (MED 550, 2 hrs): Topics will include the Nature of Probability and Statistic; Frequency Distributions and Graphs; Data Description; Probability and Probability Distributions; the Normal Distribution; Confidence Intervals and Sample Size; Hypothesis Testing; Testing the Difference among Means, Variance, and Proportions; Correlations and Regressions; and Chi-Squared and Analysis of Variance.

5. Teaching Advanced Topics in Secondary Math (MED 595, 2 hrs): This course will consider some of the topics contained in the above mathematics courses and will have participants develop curriculum projects for students enrolled in their advanced mathematics classes. The projects will involve innovative instructional strategies that are consistent with the objectives of the Standards.

6. Action Research Project (MED 599, 1 hr.): Is designed to assist students in selecting a problem, creating a literature review, and devising a plan for their Action Research Project. The course is repeatable three times and offered each fall and spring semester, except the semester that MED 600 is offered.