MA in Mathematics for Teachers

York University has an active part-time MA program especially designed for teachers. We welcome in particular students who have been away from formal schooling for some years. We recognize that teachers interested in this program may have completed their university studies some time ago, and our courses have been designed to take this into account. This program has been in existence since 1975. Peter Gibson, Jane Heffernan, Stan Kochman, Martin Muldoon, Margaret Sinclair, Juris Steprans, Paul Szeptycki, Byron Wall, Walter Whiteley, Augustine Wong, Mike Zabrocki and Hongmei Zhu are among its recent teaching staff.

This Program is designed to upgrade the breadth of knowledge of high school mathematics teachers, thus making them more effective in their classrooms. As such, it is more course-intensive than our Regular Program. The courses in this Program are clearly distinguished from those in the Regular Program. They aim at developing mathematical insight in general by, among other things, examining the significance of various areas of mathematics relative to one another. Another important component of the instruction in the Teachers Program is the development in the student of a historical perspective on the growth of mathematical ideas. This program does not prepare students for study at the PhD level in mathematics nor does it lead to teacher certification in Ontario. Students will enroll in it on a part-time basis.

The program focuses on giving students an exposure to a variety of mathematical subjects providing to those that are teachers a broader experience that they can bring to their own classrooms. The range of this program gives students an historic perspective as well as chances to practice techniques of problem solving, writing and presenting mathematics. These elements are relevant for teachers of mathematics at any level. Courses in the program will be scheduled in the evenings, usually with a three-hour session once a week for a course in the Fall-Winter term, and two three-hour sessions per course in the Summer term. Ordinarily, two courses are offered in the Fall-Winter session and one course in the Summer session.

Admission Requirements
Graduates with a four-year degree in mathematics (or equivalent background) may be admitted as "Candidates" for the MA degree--that is, they will undertake a normal program of studies. Teachers with a three-year degree in mathematics and additional qualifications (e.g., a B.Ed.) or a four-year degree in a related discipline (science, engineering, . . .) are also encouraged to enquire. An interview with the Coordinator of the Teachers' Program may be required.

Students can be admitted for either the Fall/Winter or Summer terms and the application deadline is normally March 1 for the Summer and Fall/Winter terms.

The Graduate Admissions on-application website is: http://www.yorku.ca/web/futurestudents/graduate/

Course Requirements
The normal program of studies requires satisfactory completion of six courses, which must include Mathematics 5020 6.0: Fundamentals of Mathematics for Teachers, and Mathematics 5400 6.0: History of Mathematics. The remaining four corses will be chosen from among Mathematics 5100 6.0, 5200 6.0, 5300 6.0, 5410 6.0, 5420 6.0, 5430 6.0, 5450 6.0, and 5500 6.0, 5900 3.0. (See below for calendar descriptions.)

The MA Program in Mathematics for Teachers, like all graduate programs at York, permits you to take some courses outside the program, including the Graduate Program in Education. These courses can be either additional courses or substitutes and can involve no extra fees. Contact the program director for more information.
Students may complete their MA degree in two years, although study at a slower pace is also possible. For details on fees for this program, contact the Graduate Program in Mathematics & Statistics.

Further Information
Each year, about late February, we offer an information session for prospective applicants to the Teachers' Program. For details or further information, please call the Assistant of the Graduate Program in Mathematics and Statistics at 736-5250, ext. 33974, e-mail: gradir@mathstat.yorku.ca.

General Course Descriptions

MATH 5020 6.0 Fundamentals of Mathematics for Teachers
Number theory and combinatorics are branches of mathematics in which theorems and problems are usually easy to state but often difficult to prove or resolve. This course deals with topics in these two fundamental mathematical fields, including modular arithmetic, linear and quadratic diophantine equations, continued fractions, permutations and combinations, distributions and partitions, recurrence relations, generating functions, formal power series. Stress is placed on solving challenging problems.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5830 6.0

MATH 5100 6.0 Mathematical Literature Seminar for Teachers
The course deals with a variety of mathematical issues, and is intended to convince the students that mathematics is meaningful, that some of its problems are profound, and that the evolution of some of its ideas is an exciting chapter of intellectual history. Students are encouraged to present material in class, and one of the key objectives of the course is to develop in students the ability to read independently and critically in the relevant mathematical literature.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5831 6.0

MATH 5200 6.0 Problem Solving
This course aims to develop the student's problem solving ability by examining a variety of challenging problems from famous collections. Emphasis will be placed on problem- solving techniques of wide applicability, such as recursion and iteration methods, generating functions and power series, transformation methods, vector methods (both geometric and algebraic), and congruences.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5835 6.0

MATH 5300 6.0 Computation in Mathematics for Teachers*
This course will concentrate on the role of computation in mathematics relying on popular software designed for this purpose. The examples to be discussed will be chosen from applied mathematics using high school calculus, elementary number theory, probability, numerical approximation of familiar constants and discrete mathematics. The intention will be that any one of the topics could serve as the basis for supplementary material or a project for highly motivated students in the final years of high school. Students taking this course will be evaluated on the basis of reports written on each of the topics discussed.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5839 6.0

Math 5350 3.0 An introduction to Mathematical Modeling - Discrete-Time and Probability
This course provides an introduction to discrete-time and probabilistic mathematical models. The course focuses on the mathematical methods underlying scientific inquiry and discovery. Through hands-on exploration and reflection, students will examine topics such as historical connections between mathematics and science, empirical modeling, model validation, proportionality, and simulation. The course starts with an overview of the modeling process and a review of relevant technology - Texas Instrument TI-92, the Internet and the World Wide Web, Java applets and computer algebra systems. Strategies to initiate modeling in the secondary classroom and classroom assessment of modeling activities are introduced and discussed. Topics include difference equations, Markov chains, and leslie matrices, applied to problems in biology, the environment, and finance i.e. modeling infectious disease spread, species extinction, power delivery. Particular attention is given to topics in the intermediate and senior Ontario curriculum.

Math 5360 3.0 An introduction to Mathematical Modeling – Continuous Time and Probability
This course provides an introduction to continuous-time and probabilistic mathematical models. The course focuses on the mathematical methods underlying scientific inquiry and discovery. Through hands-on exploration and reflection, students will examine topics such as historical connections between mathematics and science, empirical modeling, model validation, proportionality, and simulation. The course starts with an overview of the modeling process and a review of relevant technology - Texas Instrument TI-92, the Internet and the World Wide Web, Java applets and computer algebra systems. Strategies to initiate modeling in the secondary classroom and classroom assessment of modeling activities are introduced and discussed. Topics include differential equations, Markov processes, and leslie matrices, applied to problems in biology, the environment, and finance i.e. modeling infectious disease spread, predator prey, heat flow. Particular attention is given to topics in the intermediate and senior Ontario curriculum.

MATH 5400 6.0 History of Mathematics
The course deals with the historical development of the main currents of mathematical thought from ancient to modern times, with emphasis on ideas of particular relevance to high school teachers. It is intended that this course give students an overview of mathematics and its relation to other disciplines. Presentation of various topics by students with ensuing discussions is an integral part of the course.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5833 6.0

MATH 5410 6.0 Analysis for Teachers
Some of the basic concepts and methods of analysis are discussed. Among these are: axiomatic development of the real and complex number systems, classical inequalities, sequences, series, power series, uniform convergence, Taylor's theorem, elementary functions of a real and of a complex variable, entire functions, transcendental numbers and functions, fundamental theorem of algebra and Picard's theorem, transcendentality of e and pi, elementary differential equations, applications.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5834 6.0

MATH 5420 6.0 Algebra for Teachers
The intent of this course is to give the student an appreciation of mathematical structure through the study of fields, rings and groups, with examples from, and applications to, number theory and geometry. Emphasis is placed on how modern algebra unifies diverse results, and how it sheds light on classical algebraic problems. For example, field extensions will be applied to problems of construction with ruler and compass; factorization theory in integral domains will be applied to solutions of diophantine equations.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5836 6.0

MATH 5430 6.0 Statistics and Probability for Teachers*
Review of the concepts underlying the Ontario high school course: MDM4U: Mathematics of Data Management. Use of public data to address social issues. Data analysis and visualization using the Fathom statistical package. Fundamental issues, controversies and paradoxes in probability and in statistical inference. Association and causation, Simpson’s Paradox, ecological correlation, conditional association and stratification.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5838 6.0

MATH 5450 6.0 Geometry for Teachers
This course will expose students to the richness and variety of geometrical methods. Various geometries including euclidean, affine, projective, inversive, noneuclidean, and finite geometries, and the transformations associated with these geometries, will be studies from the unifying point of view of affine and metric affine geometry. Many applications to euclidean geometry will be given.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with EDUC 5837 6.0

MATH 5500 6.0 Topics in Mathematics for Teachers
Topics are chosen according to the interests of students. Typical subject material includes mathematical modelling, applications of mathematics in the physical and social sciences, and recent developments in mathematics.
Prerequisite: Permission of the instructor is required for students who are not in the Graduate Program in Mathematics and Statistics.
Crosslisted with Education 5832 6.0

MATH 5840 3.0 Mathematics Learning Environments
This course explores issues in mathematics education in light of new developments in cognitive theory, in order to characterize environments for learning mathematics that are both learner centered and knowledge centered. Topics include mathematics learning as a social/cultural experience, mathematics as sense making, the impact of technology on mathematics learning environments.
Crosslisted with EDUC 5840 3.0

MATH 5900 3.0 Thinking about Teaching Mathematics
This course invites participants to reflect on the practice of teaching mathematics in light of research and their own experiences. It examines how teachers draw on mathematical and pedagogical knowledge in their work. A specialized mathematics background is not a prerequisite.
Crosslisted with EDUC 5841 3.0

Mathematics 5910 3.0 Quantitative Research Methods
This course deals with the principles of scientific reasoning and how they inform the research process. The theoretical and practical problems involved in data collection are examined (questionnaire construction, interview procedures, sample design). The second part of the course concentrates on the logic of analysis used in assessing and interpreting data. No formal knowledge of statistics is required.
Crosslisted with EDUC 5210 3.0

* this is a revised course description and cross listing is subject to approval by the faculty of graduate studies

The Graduate Diploma in Mathematics Education
Focuses on mathematics education as an area of study grounded in critical examination of teaching practice, learning theories, and curriculum, and supported by analyses of socio-cultural, equity, and gender issues in the teaching and learning of mathematics. It is designed to provide opportunities for graduate level study of theories and research in Mathematics Education, as well as enriched mathematical experiences and reflection on the practice of mathematics, to practising teachers and administrators and to people in the community whose work involves developing mathematical literacies.

The Graduate Diploma in Mathematics Education is jointly offered by the Graduate Program in Education and the Graduate Program in Mathematics and Statistics. For students in the MA in Mathematics for Teachers, the diploma will provide a recommended pathway towards future PhD studies in Mathematics Education.
If you have questions about any aspect of the Program please call or write to:
 
Mike Zabrocki
Coordinator of the MA for Teachers Program
Web page: http://garsia.math.yorku.ca/~zabrocki/
Blog: http://maformathteachers.blogspot.com/
(416) 736-2100, Ext. 33980
e-mail: zabrocki@mathstat.yorku.ca
Dept. Of Mathematics & Statistics
York University
Toronto, Ontario M3J 1P3

or

Graduate Program Office
(416) 736-5250, Ext. 33974
e-mail: gradir@mathstat.yorku.ca