Elementary 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 elementary 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.EED program, students must obtain a positive letter of recommendation from a faculty member; receive approval from the Mathematics Department chair; select an academic advisor in the Mathematics Department.

Complete 1 of the following courses (3-4 cr):

Code Course Credits

MAT 1530

Applied Calculus

An introduction to calculus intended primarily for students in business, science, and the social sciences. Topics include functions, limits, continuity, differentiation, applications of derivatives, antiderivatives, definite integral and the Fundamental Theorem of Calculus.

This course fulfills the Scientific & Mathematical Understanding frame of reference.

Prerequisite: MAT 1360 or appropriate placement

Fall

3

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

And complete the following courses (24 cr):

Code Course Credits

MAT 2021

Statistics I

This course prepares students for quantitative methods in their respective fields. Descriptive and inferential statistics, including estimation, hypothesis testing, linear regression and correlation are covered. Basic tools of descriptive statistics, discrete probability, binomial distribution, normal distribution, t-distribution, estimates and sample sizes, hypothesis testing, elementary correlation and regression, contingency tables are explored. Students utilize graphing calculators and spreadsheet software on a regular basis.

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

Prerequisite: Students must take a math assessment (ACCUPLACER) for placement purposes prior to registration or MAT 1010.

Every semester

3

MAT 2022

Statistics II

This course is a continuation of MAT 2021 and includes estimation, hypothesis testing, single linear regression, and one-way analysis of variance using calculators and statistical software. This course addresses in-depth such topics as the Central Limit Theorem, Chebyshev's theorem, covariance, multiple regression, ANOVA, nonparametric methods, and applications of probability distributions. It includes problems dealing with multiple linear regression, multi-way analysis of variance, nonparametric statistics, enumerative data, and computer applications. Students utilize graphing calculators and spreadsheet software on a regular basis.

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

Prerequisite: MAT 2021

Every semester

3

MAT 3020

Mathematics for Elementary Teachers

This course will focus on achieving goals set forth in Vermont’s Framework of Standards and Learning Opportunities and the Standards of the National Council of Teachers of Mathematics (NCTM), while strengthening the mathematical knowledge of the prospective elementary school teacher. Students will be given numerous opportunities to discover and construct important mathematical concepts and techniques using a variety of student-centered learning strategies, including the use of manipulative devices, graphing calculators, computers, Internet, portfolio and journal assessment, and Video Vignettes.

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 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 3820

Mathematics Tutorship

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 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 4210

Teachers as Researchers

This course is intended for pre-service teachers who are seeking to increase their understanding of mathematics. The course uses data collection and analysis to guide improvement in K-6 mathematics programs. The student will build on the knowledge gained in MAT 3020 to obtain a deeper understanding of mathematics as related to NCTM and the Vermont Framework guidelines. In this course, students will function as researchers by gathering data and analyzing data, as means of improving the curriculum and instruction in K-6 mathematics programs. As researchers, students are encouraged to ask questions, pose problems, and identify means of solving problems by using different strategies. Emphasis will be on student-centered instructional approach, with ample use of manipulatives and technology.

Prerequisite: MAT 3020 or consent of instructor.

Every semester

2

And complete at least 2 of the following courses (at least 6 cr):

Code Course Credits

MAT 1230

College Algebra

This course is intended to prepare students for Precalculus by reviewing the fundamental concepts of algebra. Topics include equations and inequalities, exponents, radicals, functions, systems of equations, polynomials and applications.

This course satisfies the Scientific & Mathematical Understanding frame of reference.

Every semester

3

MAT 1360

Precalculus with Applications

In addition to preparing students for the study of calculus, this course presents a variety of functions that can be used for modeling and solving real-life problems. Functions are explored from numerical, graphical, and analytic perspectives and include the study of polynomial, rational, exponential, logarithmic and trignometric functions. Students utilize technology and practice applying concepts in weekly workshops.

This course satisfies the Scientific & Mathematical Understanding frame of reference.

Prerequisite: MAT 1230 with a grade of "C" or better, or appropriate placement.

Every semester

4

MAT 2015

History of Mathematics

This course studies the development of various branches of mathematics from ancient times to the present, and investigates historical and multicultural influences on the development of mathematics. Beginning with ancient number systems, we examine major discoveries in mathematics, development of mathematical methods and notation, and individuals having a prominent role in advancing the field of mathematics. Students conduct research and present their findings as written reports and oral presentations.

This course satisfies the World Views frame of reference.

Prerequisite: MAT 1230

Spring

3

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 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

(Subtotal of Math credits required: 33-34)

And complete all Education Department requirements for Elementary Education.