MAED - Mathematics Education

Introduction to middle and secondary mathematics education, its principles and practices. Organization of schools, planning, teaching styles, classroom management, and instructional materials in mathematics education are among the topics considered. Direct experiences with middle and secondary school students are an integral part of the course.

Provides participants an opportunity to observe classroom operations, observe and describe the role of the teacher, conduct focused observations and interviews, work with individual and small groups of candidates on a teaching project.

The course is designed for students working as Math and Science Partnership mathematics tutors in the local community. Students eligible for the work-study program or working as volunteers, tutor in area schools or after-school programs. The course examines issues such as getting children interested in mathematics, how to explain various topics, working with groups vs. individuals, and cultural differences. Problems encountered in the tutoring experience will be discussed. Students must apply through the Mathematical Sciences department.

Selected readings, discussions, and problem solutions on a topic in mathematics education at an introductory level. Permission of department required.

This course will include data collection, random sampling, numerical and graphical summaries, statistical variability, the logic behind tests of significance and confidence intervals, simulation, regression and chance. Activities for learning statistics and resources available for teaching and learning statistics at a middle school level will be used.

The course provides an overview of the processes involved in literacy acquisition and instructional technologies available to enhance teaching in science and mathematics. The relationship of reading and writing, and aspects of writing development and writing process appropriate to each stage of reading development will be presented. Topics: conceptual and methodological issues related to instruction and acquisition of reading, the role and use of technology in literacy instruction, assessment of candidate's reading and writing, diversity in reading acquisition, use of computers, graphing calculators and other multimedia applications.

Meaning, development, and communication of number ideas and logical structure of base 10 number systems (as well as other bases); the concepts and procedures related to the basic algorithms of arithmetic; problem solving and mathematical modeling within the whole number system and positive rational number system. Course open only to students seeking certification to teach at the early childhood, childhood, or middle childhood level. Sophomore standing required.

Meaning, development and communication in the real number system; problem solving and mathematical modeling within this system; including proportional reasoning; algebra, statistics, probability, properties of geometric shapes and measurement in 2 and 3-dimensions. Course open only to students who are seeking certification to teach at the early childhood, childhood or middle childhood level.

Further development of geometry concepts; including triangle congruence and similarity; coordinate geometry and transformations; advanced problem solving using algebraic models, geometric models and other modeling techniques; emphasis on the framework provided by the National Council of Teachers of Mathematics for elementary/middle school mathematics; investigation of concepts teachers must know in order to build and refine mathematical ideas and connections in K-8.

The course provides a theoretical framework for exploring and developing a culturally responsive approach to the teaching of mathematics and science. In exploring different instructional formats, the course allows candidates to develop approaches that prepare them for an ever-increasing population of students that reflect diverse backgrounds and abilities. The field experience is a co-requisite that allows the candidates the opportunity to apply their knowledge of the issues presented in the course work to a diverse population.

The course will use the vehicle of problem solving to help students develop their abilities in reading and writing mathematics. It will also focus on how reading and writing exercises can be used to enhance the teaching and learning of mathematics, and how reading and writing mathematics can be used to enhance the teaching of literacy. The course will include discussions of reading mathematics, writing mathematics, oral presentation of mathematics, and problem solving techniques. "Communication" is one of the standards from Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics. Students will read and discuss material from the NCTM and other sources related to the standard.

The course is the field component to MAED 305. Candidates will use different instructional formats to develop effective approaches for teaching mathematics and science to students with different backgrounds and abilities in diverse educational learning environments.

Introduction to software packages appropriate for use by mathematics educators. Topics selected from, but not limited to: applets, geometry software, calculators, web page design, programming, scientific word processors, spreadsheet applications, computer algebra systems, electronic whiteboards and other specialized software.

Independent study of a selected list of readings approved by a faculty advisor. Permission of department required.

The course is intended for future teachers of high school mathematics to help them develop a deeper knowledge of some key topics in the high school curriculum. Topics will be chosen from the following: Complex numbers, functions including logarithmic, exponential and trigonometric functions, curve-fitting, transformations, equations, inequalities and algebraic expressions. Students must have senior standing in the Mathematics Adolescence Education major.

The course complements the student teaching practicum in either Adolescence Mathematics Education or Middle Childhood Mathematics Education. Candidates receive detailed instruction in the completion of the applied teaching and learning projects associated with their student teaching placements.

Principles, materials, and methods for teaching middle school (grades 5-9) mathematics. The course serves as the primary methods course for students pursuing initial certification in Middle Childhood Education - Mathematics Specialist. Departmental approval required.

Principles, materials, and methods for teaching secondary school (grades 7-12) mathematics. The course serves as the primary methods course for students pursuing initial certification in Adolescence Education - Mathematics. Note: must be successfully completed before student teaching. Departmental approval required.

A field assignment to teach middle school mathematics. Assignments provided in grades 5 through 6 during this placement. Arrangements made by the Office of Field Experiences.

A field assignment to teach middle school mathematics. Assignments provided in grades 7 through 9 during this placement. Arrangements made by the Office of Field Experiences.

A field assignment to teach mathematics at the adolescence level. Assignments provided in grades 7 through 9 during this placement. Arrangements made by the Office of Field Experiences.

A field assignment to teach mathematics at the secondary level. Assignments provided in grades 10 through 12 during this placement. Arrangements made by the Office of Field Experiences.

Independent study of a set of related topics agreed to by the student and the instructor.

A survey of software or technology used in teaching mathematics and of current issues in the use of technology in the teaching and learning of mathematics.

Study of the design and evaluation of various models of mathematics curricula including the latest National Council Teachers of Mathematics (NCTM) materials.

A critical study of the literature on current methods of teaching mathematics.

Overview of the development of mathematics education as a discipline, the major influence from other fields and society, trends in recent decades, and the impact on school mathematics.

Graduate level mathematics education course emphasizing connections between mathematics and other STEM disciplines. Mathematical topics include: Vector calculus; Jacobian matrices and their determinants; differentiation and integration of differential forms and applications to physics; generalizations of the fundamental theorem of calculus, including Green's theorem, the divergence theorem, Gauss's theorem, and Stokes' theorem; potential theory. Successful undergraduate completion of Linear Algebra and Calculus III recommended.

Introductory course with emphasis on applications of calculus. Topics include: first order equations, higher order linear equations, undetermined coefficients, variation of parameters, linear systems, bifurcation analysis, series solutions, Laplace transforms, numeric and qualitative techniques, mathematical modeling and applications, and computational technology. Additional topics selected from linear and nonlinear systems as time permits. Prerequisites: MATH 122, 123, 223, 231 or permission from the instructor.

Topology of the real line, measure and integration on the real line, function spaces and their topologies.

Geometric interpretation of the complex plane, analytic functions and power series representations, introduction to Riemann Surfaces, the Cauchy Integral Theorem and Intergral Formula, calculation of integrals by residues, application to potential theory.

An introduction to rings and fields: rings; integral domains; fields; charactersistic of a ring; subrings; ideals; factor rings; ring homomorphisms; polynomial rings; introduction to Galois theory as time permits.

Study of selected applications of abstract algebra. Topics selected from: identification numbers, symmetry, applications to combinatorics, coding theory, cryptography.

This course focuses on a problem with a rich mathematical history, that of solving polynomial equations. Topics selected from: review of rings and fields; construction of the real numbers from the rationals; algebraic and complex numbers; fundamental theorem of algebra; finite fields and integral domains; polynomial rings, including the division algorithm and Euclidean algorithm for polynomials; counting and locating real roots; cubic and quartic equations; introduction to Galois theory.

Topics selected from: congruence relations; arithmetic functions; primitive roots; quadratic reciprocity; sums of squares; continued fractions; Farey sequences; factoring and primality testing; analytic and additive number theory. The course relates directly to the following N.Y.S. Learning Standards for Mathematics, Science, and Technology: mathematical reasoning, numbers and numeration, and patterns/functions.

The addition, multiplication and pigeonhole principles. Permutations and combinations, partitions and distributions; the binomial and multinomial theorems. Generating functions; recurrence relations; principle of inclusion-exclusion; combinatorial algorithms or designs as time permits. The course relates directly to the following N.Y.S. Learning Standards for Mathematics, Science, and Technology: mathematical reasoning, modeling/multiple representation, and pattern/functions.

Graph models; graph structure and representation; trees; connectivity; graph traversals; graph colorings; other topics as time permits. The course relates directly to the N.Y.S. Learning Standards for Mathematics, Science, and Technology: mathematical reasoning, modeling/multiple representation, and pattern/functions.

Neutral geometry; Euclidean geometry; comparison of various models of Euclidean geometry, such as that of Hilbert and the SMSG; comparison of Euclidean geometryto various finite geometries and non-Euclidean geometries; geometry of circles and triangles; other topics such as analytic and transformational geometry as time permits.

Neutral geometry; hyperbolic geometry; elliptic geometry; various models of hyperbolic and elliptic geometry; comparison of results to those of Euclidean geometry.

A study of varieties and morphisms between them; foundational material from commutative ring theory; the Zariski topology; dimension and degree of varieties; select problems in enumerative geometry.

Detailed study of topological spaces and their invariants. The emphasis will be on the geometric aspects of topology. Topics may include Sperner's lemma and Brouwer Fixed Point Theorem, classification of compact surfaces, application to systems of differential equations.

Given the emphasis on statistics in the mathematics 5 - 12 grades curriculum, and the increased need for teachers competent to teach AP Statistics, mathematics educators need to understand statistical concepts and methods to a greater depth than what is acquired in an undergraduate level statistics course or sequence. In this course, students will learn to understand and explain why certain statistical techniques are used in certain situations and why they work, why certain methods don’t work well sometimes, and also common conceptual errors that users and consumers of statistics often make. Students in the course will investigate some current resources that exist to help their students understand statistics, as well as teaching methods and activities that increase student understanding. Prerequisite: a university-level statistics course.

Regression, hypothesis testing and confidence intervals in regression, nonparametric statistics, chi-square tests, sampling, use of activities in probability and statistics.

This course concerns the conic sections: the parabola, ellipse, and hyperbola. It covers their basic definitions and equations, from both a synthetic and analytic perspective, including their equations in polar coordinates. It then moves on to consider the conic sections in light of Bezout’s theorem, which concerns the number of points of intersection of two algebraic curves.

Formulation and solution of linear programming problems using graphical and algebraic methods and computer software, sensitivity analysis, and the dual problem; additional topics chosen from network analysis, game theory, and integer programming.

A study of selected topics in the history of mathematics and their applications to teaching. Permission of instructor required.

The week-long academy is dedicated to the development of instructional and curricular materials in K-12 mathematics. Special topics include proof and communication, the use of current technology and manipulatives, and preparation strategies for N.Y.S. Math Assessments.

Selected readings, discussions, reports and problem solutions on a topic of interest in mathematics, mathematics education or statistics.

Selected reading, discussions, and reports on current issues in mathematics education.

Students will be required to research a topic pertaining to mathematics education and apply it to their own classroom experiences if possible. The project will require a written proposal, a final report and an oral defense.