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General Information |
Areas of Emphasis |
The faculty strives to consistently demonstrate outstanding teaching, with the hope that our graduates will be among the most talented and capable teachers in the schools. We want our students to experience learning mathematics in an interesting, growth-producing environment so that they will always be enthusiastic learners and teachers of mathematics.
All of our courses are designed specifically for the classroom mathematics teacher. In each course, students will develop a deeper understanding of central ideas in mathematics that are relevant to their own teaching. They will increase their own power to employ mathematical reasoning and problem-solving techniques, and they will learn techniques for teaching mathematics that will stimulate their own students' imagination and intelligence.
Mathematics students must meet the requirements for an emphasis in community college mathematics, secondary mathematics or middle school mathematics. An essay entitled "Why I Teach" must be completed at the time of application by the student and approved by the mathematics coordinator before acceptance into the mathematics MAT program.
Upon completing 9 credit hours Math MAT students are required to be advanced to candidacy. Refer to the section on Advancement to Candidacy in this catalog for specific guidelines.
During their penultimate semester, math MAT students need to register for MTHC 5900 Final Reflections. This is a no tuition, zero credit hour course in which students write an essay describing how they have changed as a result of participating in the math MAT program.
Students selecting either the middle school or secondary emphasis may transfer up to 6 credit hours of courses in mathematics or mathematics education provided that the courses are part of a graduate degree program at the host university; they may also apply toward their degree a maximum of 3 credit hours of Webster University in-service graduate credits.
Students selecting the Community College emphasis may transfer up to 6 credit hours of courses in mathematics provided that the courses are part of the host university's graduate degree program in mathematics. No in-service courses may be applied toward the degree.
Emphasis in Community College Mathematics
This emphasis is designed for community college teachers who wish to strengthen their ability to articulate mathematical arguments, increase their general problem solving abilities, and further develop their perspective and understanding of mathematics.
The requirements for the community college emphasis are 33 credit hours of mathematics courses numbered above MTHC 5200 with the following exceptions:
- Up to 6 credit hours of the 33 may be replaced by courses transferred from other universities, and,
- MTHC 5210 and MTHC 5410 do not apply.
Emphasis in Middle School Mathematics
This emphasis is designed for mathematics teachers of grades 5-8. Those choosing this emphasis will study a range of engaging mathematical ideas that require little mathematical background to comprehend and thus can be adapted for their own classroom use. Relevant courses include all those numbered below MTHC 5200, as well as an occasional course numbered above MTHC 5200.
The requirements for this emphasis are: (1) a minimum of 18 credit hours in courses numbered 5040 or above; and (2) a minimum of 3 credit hours in appropriate computer courses.
The following courses do not meet area-of-emphasis requirements: MTHC 5210, MTHC 5410.
Emphasis in Secondary Mathematics
This emphasis is designed for secondary mathematics teachers who wish to deepen their understanding and broaden their perspective of mathematics. Courses developed for this emphasis include most mathematics courses numbered above MTHC 5200.
Those choosing an emphasis in secondary mathematics must complete a minimum of 21 credit hours in mathematics courses numbered above MTHC 5200.
The content of the following courses may vary according to the interests of the faculty and the interest and mathematical background of the students. The course descriptions are meant only to be illustrative of the type of concepts that may be examined.
MTHC 5040 Number Theory (3)
Students examine the basic concepts of number theory with an emphasis on modular systems and their application to a variety of empirical problems.
MTHC 5080 Puzzles and Proofs (3)
This course examines a variety of materials useful in developing reasoning skills. Included are attribute block puzzles, Lewis Carroll puzzles, logic puzzles, and a variety of games which require deductive reasoning.
MTHC 5100 Functions and Structure (3)
This course investigates a variety of mathematical systems and functions.
MTHC 5110 Perspectives in Elementary Geometry (3)
This course focuses on geometry for grades 5-8. May be repeated for credit if content varies.
MTHC 5120 Topics for the Middle School Teacher (3)
This course covers areas of mathematics and/or mathematics education of particular interest to middle school teachers. Content varies according to the interests of faculty and students. May be repeated for credit if content varies.
MTHC 5130 Probability and Graphs (3)
Part of this course covers topics from probability and statistics with applications to gambling and game theory. The open part covers graphs, trees, Boolean algebra, and finite state automata.
MTHC 5150 Number Systems (3)
This course provides middle school teachers with a deeper understanding of the real number system. Topics covered include arithmetic algorithms in negative and whole number bases; rational and irrational numbers; arithmetic and geometric progressions; number properties; mental arithmetic; factorization and divisibility of integers and of Gaussian integers; and number puzzles and games.
MTHC 5200 Independent Study (1-6)
MAT students with special interests or needs that are not met by existing curricula may request that a member of the faculty supervise an independent study. Together the student and faculty member decide the content of the independent study and the criteria for evaluation. In no case can an independent study be set up when an existing course already covers the subject. May be repeated for credit if content differs.
MTHC 5210 In-Service Education (1-4)
Webster offers various graduate in-service courses that are not part of the existing MAT curricula but provide experiences important to the academic and professional development of educators. Consult the semester course listings for specific topics. Prerequisite: prior approval of the MAT advisor. May be repeated for credit if content differs.
MTHC 5230 Discrete Mathematics (3)
This course covers mathematical structures pertinent to an understanding of computers, including graphs, Boolean algebra, and finite state machines.
MTHC 5250 Vector Geometry (3)
Basic concepts pertaining to vectors in the plane are developed. Proofs of theorems of plane geometry, using a synthetic approach, an analytic approach, and a vector approach are compared. The class introduces vector spaces.
MTHC 5260 Algebra for Secondary Teachers (3)
Students examine and extend topics in secondary school algebra. Techniques and materials for teaching algebra are also discussed.
MTHC 5270 Elementary Functions (3)
This is a review of the elementary functions: polynomial and rational functions, the trigonometric functions, and the logarithmic and exponential functions, along with their algebraic structure and some applications. Computers and/or graphing calculators are used to help investigate ideas. Techniques for teaching elementary functions are discussed.
MTHC 5280 Calculus for Teachers (3)
The course reviews the basic concepts of differential and integral calculus, with special focus on central ideas, theory, and applications. Computers and/or graphing calculators are used to help investigate ideas.
MTHC 5300 History of Mathematics (3)
This course is based on selected readings that examine the history and philosophy of mathematics, along with the genesis of historical and current applications. An important goal is to provide students with a perspective on the relationship between mathematics and culture as well as an insight into how and why mathematical ideas have evolved.
MTHC 5310 Geometry for Secondary Teachers (3)
This course deals with areas of geometry relevant to high school teachers. Content varies according to the interests of the faculty and students. May be repeated for credit if content varies.
MTHC 5320 Topics in Mathematics (3)
Typically this course introduces areas of mathematics not covered in other courses. Content depends upon the interests of the faculty and students. May be repeated for credit.
MTHC 5330 Probability (3)
Participants study probability on finite sample spaces along with applications to gambling and game theory.
MTHC 5340 Topics in Mathematics Education (1-3)
The content of this course will include an analysis of curricular materials, teaching methods, and/or issues in mathematics education. This course may be repeated for credit if content varies.
MTHC 5350 Logic (3)
This course includes propositional and predicate logic, with the objective of increasing students' understanding of what constitutes valid reasoning, as well as increasing their ability to express formal mathematical arguments.
MTHC 5360 Algebraic Structures (3)
Students examine the algebra of various mathematical structures with the goal of gaining a broader and more sophisticated understanding of ordinary algebra. Relevant theory is developed.
MTHC 5370 Linear Algebra (3)
Concepts and techniques of linear algebra are developed.
MTHC 5390 Statistics (3)
This course covers the basic concepts (including applications) of the binomial and normal distributions, the chi-square test, analysis of variance, and nonparametric statistics. Emphasis is placed on educational applications as well as the abuses and misuses of statistical ideas. Computers and/or graphing calculators are used to investigate ideas.
MTHC 5410 In-Service Topics (1-3)
In-service courses are designed to provide MAT degree-seeking students with practical applications of contemporary research and methodology to improve classroom effectiveness. These courses have been approved for the MAT degree with prior approval of the student's advisor. May be repeated for credit if content differs.
MTHC 5430 The Real Number System (3)
The course covers the algebraic and topological properties of the real number system and several of its subfields and subrings.
MTHC 5450 Topics in Number Theory (3)
This course covers selected topics in number theory, such as modular systems, quadratic reciprocity, number-theoretic functions, Pythagorean Triples, and perfect numbers. Specific topics to be determined by instructor. Relevant theory will be developed.
MTHC 5480 Problem-Solving Strategies in Mathematics (3)
The primary objective of this course is to help students develop reasoning strategies that are powerful tools in solving problems. A secondary objective is to help students become more skillful at teaching problem-solving strategies.
MTHC 5500 Studies in Mathematics (1-6)
Courses in this category are offered on an irregular basis. May be repeated for credit if content varies.
MTHC 5900 Final Reflections (0)
All math MAT students are required to register for this zero-credit hour course during their penultimate semester. Students write an essay describing how they have changed as a result of their participation in the math program. For specific guidelines see the Math Coordinator. This course is graded on a credit/no credit basis only.
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