MA Program for Secondary Math Teachers

This class is for people who want to do the entire Masters degree, not just 18 hours. It might be okay to start with the seconds half of the course, but please talk to Jenya soprunova@math.kent.edu first.

This course is a follow-up to the Euclidean Geometry course. Euclidean geometry is not a prerequisite but it's important to have some previous experience with geometry. Fundamental Concepts of Geometry may suffice. We will first review some topics from Euclidean Geometry, such as Nine-point circle, Ceva's Theorem, and Menelaus Theorem. We will then talk about Mass Point Geometry; Conic Sections (including their reflection properties); Geometric Inequalities; Solid (3D) geometry; Analytic Geometry; Introduction to Spherical Geometry; Convex polytopes and Euler's Formula.

This course covers divisibility properties of the integers, prime numbers, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, and rational approximations.

This class meets every other week with homework assigned on-line every week. The emphasis is on problem-solving and connections between various topics in mathematics. We will cover many topics that involve deep ideas but do not require an extensive mathematical background, so at least some of them are accessible to high-school students and can be used by high-school teachers in the classroom. The topics covered may include: Parity, Invariants, Games, Chessboard Math, Sudoku, Magic Squares, Counterfeit Coins, Pick's formula, Lattice-Point Geometry, Pythagorean Triples, Liars and Knights problems, Painting 3D Polyhedra, Stable Marriages, Mathematics of Voting.

An in-depth exploration of the theoretical frameworks and methodologies used in current research in mathematics education will be conducted.

Fall 14 Classes

Summer 14 Classes

Courses offered in Spring 14

This course is aimed at in-service and pre-service high-school mathematics teachers. A goal is to give an idea of how applied mathematicians are trained and what they do.

A major part of the activity of "applied mathematics" is concerned with building and analyzing mathematical models of processes in a variety of areas, including the physical, engineering, biological, and social sciences.

We will illustrate by examples the iterative approach to developing simple models by successively adding features and complexity, distinguishing deterministic models from probabilistic ones. We will also show how computer environments (spreadsheets, in particular) can be used to explore and analyze mathematical models.

The course will be taught mostly on line.

Grading will be based upon written homework, a mid-term exam, and a final project.

Courses offered in Fall 13

This class is a gentle introduction into modern algebra with an emphasis on connections to high-school curriculum, problem-solving, examples, and applications.

The purpose is to develop knowledge of research and theories regarding teaching and learning mathematics via computing devices. Further to develop proficiency in the use of computing devices and software that would be used in the teaching and learning of mathematics.

Current research theory, methodology and results in mathematics education will be investigated. Implications for instructional practice and curriculum design will be examined.

Courses offered in Spring 13

Divisibility properties of the integers, prime numbers, congruences, quadratic reciprocity, Diophantine equations, number theoretic functions, simple continued fractions, rational approximations.

Geometry of Euclid extended to advanced topics of the triangle, quadrilaterals and circles: cross-ratio, groups, constructions, geometric generalizations; inversion.

An in-depth exploration of the theoretical frameworks and methodologies used in current research in mathmatics education will be conducted.

Courses offered in Fall 12

This course is aimed at in-service high-school mathematics teachers. The goal of the course is to introduce probability and statistics tools, and to discuss with the class how these ideas can be presented and used in the current and future high school curriculum.

We will start our discussion with the questions: what is an event? what is the probability of an event? We will then study discrete and continuous random variables, talk about normal distribution, and introduce ideas behind the limit laws and theorems. We will mix this up with applications to gambling and the Birthday paradox.

Next, we will move into the Statistics part of the course and chat about how to analyze large data sets and how to design an experiment. We will talk about sampling and linear regression as well as various other things. Along the way we will look at many practical examples.

There will be no exams. Grading will be based upon written homework and a final project.

The study of partisan and impartial combinatorial games; games as numbers; Grundy-Sprague theory.

This is the second half of a year-long sequence. The class meets every other week with homework assigned on-line every week. The emphasis is on connections between various topics in Algebra, Geometry, Analysis, and Probability. We will use Roots to Research by Judith D. Sally and Paul J. Sally, Jr. as well as some other sources. The topics covered may include: The Four Numbers Problem, Rational Right Triangles and the Congruent Number Problem, Lattice Point Geometry, Rational Approximation, Dissection, Voting Systems and Arrow's Theorem, Magic Squares.

Current research theory, methodology and results in mathematics education will be investigated. Implications for instructional practice and curriculum design will be examined.

The purpose is to develop knowledge of research and theories regarding teaching and learning mathematics via computing devices. Further to develop proficiency in the use of computing devices and software that would be used in the teaching and learning of mathematics.