Master of Arts in MathematicsEmphasis in Teaching
[View the UNC Catalog for this program.]
Admission to the Master of Arts in Mathematics - Teaching EmphasisYou must apply to the UNC Graduate School before the department reviews your request. To access an on-line application form or download an application form, please see www.unco.edu/grad/admissions/home.htm. You will need to submit the following materials before your application will be screened:
Program FocusThe pedagogical focus of the program is on curricular, instructional, and assessment reform in secondary and community college 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 DesignThe 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 Objectives1) Prepare a dedicated core group of secondary mathematics teachers to guide their peers in the curricular reforms of the next decade. 2) Update secondary school and community college 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. 3) 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. 4) 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. This graduate program is designed especially for those teaching secondary school
or community college 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 543: Continuous
Mathematics, MATH 534: 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 advisor. 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. 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. 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. 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. 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.): Designed to assist students
in selecting a problem, creating a literature review, and devising a plan for
their Action Research Project. See the Action Research Project Guide
(PDF file), Project Evaluation Rubric, and the Project Planning (PDF file).
The course is repeatable three times and offered each
fall and spring semester, except the semester that MED 600 is offered. |
School of Mathematical Sciences
Ross Hall 2239, Box #122
University of Northern Colorado
Greeley, CO 80639
Phone: (970) 351-2820
Fax: (970) 351-1225