Secondary Education Program Requirements

These requirements are from an excerpt from the University Academic Catalog, which outlines the requirements for a student to earn the distinction of being a Castleton University graduate. The complete catalog is available online.

This major is for students interested in teaching mathematics at the middle and high school level. Mathematics teachers play a critical role in our society, and students who complete this program are in great demand.

Students who complete the mathematics major are able to:

  1. Analyze and solve real-world problems using a variety of mathematical techniques,
  2. Convey mathematical information in effective ways,
  3. Choose and employ appropriate technology,
  4. Secure desired employment or gain admission to graduate or professional programs of study.

In addition, students who complete a program leading to teaching:

  1. Acquire a strong foundation in both mathematics content and teaching methods,
  2. Gain experience working with students through tutorships and internships.

To be accepted into the BA.MAT.SED program, students must obtain a positive letter of recommendation from a faculty member; receive approval from the Mathematics Department chair; and select an academic advisor in the Mathematics Department.

Complete the following courses (45 cr):

Code Course Credits

MAT 1531

Calculus I

Topics include limits, differentiation, applications of derivatives, and an introduction to integration. This course may utilize graphing calculators on a regular basis.

This course fulfills the Scientific and Mathematical Understanding Frame of Reference.

Prerequisite: MAT 1360 or equivalent.

Every semester

4

MAT 2532

Calculus II

Continuation of Calculus I, with topics to include techniques of integration, applications of integration, improper integrals, sequences, series, and Taylor polynomials. Students in this course may be required to utilize graphing calculators.

This course fulfills the Scientific and Mathematical Understanding Frame of Reference.

Prerequisite: MAT 1531

Every semester

4

MAT 3035

Teaching Mathematics

This course is a study of strategies, techniques, materials, technology, and current research used in the teaching of mathematical concepts to elementary and high school students. Students will review the traditional and contemporary standards involved in teaching mathematics at the elementary to secondary school level; develop an awareness of the professional resources, materials, technology and information available for teachers; prepare unit and lesson plans with related assessment procedures on a variety of topics; and acquire teaching experience by taking part in individual tutoring, observation at a school, and/or presenting lessons at the appropriate level. This course fulfills three pedagogy lab credits in secondary mathematics and may be taken as an elective for MDS majors.

Prerequisite: Math Ed or MDS major, junior or senior status.

Fall, odd years

3

MAT 3210

Linear Algebra

This course introduces students to linear algebra including a study of vector spaces, linear transformations, determinants, inner products, and characteristic equations. Topics to be studied include mathematical structures, algebraic properties, and applications of matrices, determinants, vectors, vector spaces, and linear transformations. Students develop and solve mathematical models involving systems of linear algebraic equations and systems of linear differential equations. Students utilize graphing calculators and a computer algebra system.

Prerequisite: MAT 2532

Fall

3

MAT 3220

Probability

This is a calculus-based course introducing probability theory including discrete and continuous random variables and their probability distributions, multivariate probability distributions, functions of random variables, and limit theorems.

Prerequisite: MAT 3533

Fall

3

MAT 3230

Mathematical Statistics

This calculus-based course is a continuation of MAT 3220 including estimation theory, hypothesis testing, analysis of enumerative data, regression, analysis of variance, and nonparametric statistics.

Prerequisite: MAT 3220.

Spring

3

MAT 3310

Differential Equations

This course is a study of first and higher order differential equations with many applications to science. Students explore analytical and numerical solution methods for ordinary and partial differential equations including series solutions and special functions for the solution of ODEs and the use of Fourier series to solve PDEs. Laplace transforms and numerical methods for solving ODEs and PDEs are introduced.

Prerequisite: MAT 2532 and MAT 3210.

Spring

3

MAT 3410

Introduction to Mathematical Proofs

This course is an introduction to mathematical proof and serves as a bridge from elementary courses to more advanced mathematics. Students explore fundamental ideas in logic, sets, the theory of numbers, relations and functions.

Prerequisite: MAT 1360

Fall

3

MAT 3533

Calculus III

Continuation of Calculus II, with topics including polar, spherical and cylindrical coordinates, partial derivatives, multiple integrals and vector calculus such as line integrals, surface integrals, and Gauss's, Green's, and Stoke's Theorems. Students in this course may be required to utilize graphing calculators.

Prerequisite: MAT 2532

Spring

4

MAT 3820

Mathematics Tutorship

(3 cr required)

A supervised experience in individual instruction. To include reading and discussion of individualized instructional systems as well as an actual tutorial experience in MAT 0190 or in a 1000’s or 2000’s level Mathematics course.

Prerequisite: Invitation of the Mathematics Department.

1-3

MAT 4110

Advanced Calculus

This course is devoted to rigorous presentation of the basics of mathematical analysis of real valued functions of one (real) variable from the standpoint of contemporary/modern mathematics. It is a natural continuation of the sequence of calculus courses and will give proofs of important theorems used in those courses. Emphasis will be on the concepts and theoretical approach to calculus. Topics to be covered include theory of the real number system, theory of sequences and series of real numbers, theory of continuity, differentiability of real-valued functions, and theory of the Riemann integral of real valued functions.

Prerequisite: MAT 3533 and MAT 3410

Periodically

3

MAT 4130

Abstract Algebra

This course is an introduction to the principles and concepts of modern abstract algebra. Topics will include groups, rings, and fields with applications to number theory, the theory of equations, and geometry.

Prerequisite: MAT 3210 and MAT 3410, or consent of instructor.

Periodically

3

MAT 4140

Geometry

This course includes a review of Euclidean geometry and an introduction to non-Euclidean geometries including finite geometries and systems of axioms, classical theorems and elementary transformations.

Prerequisite: MAT 3410 .

Spring

3

MAT 4720

Senior Seminar

An undergraduate research seminar. Students spend the first half of the semester studying and presenting undergraduate research in mathematics. In the second half, students investigate their own topic, prepare a written report, and present their research.

Prerequisite: Math major, senior standing, or consent of the instructor.

Fall

3

(Total of Math credits required: 45)

And complete all Education Department requirements for Secondary Education.