544011 Mathematics
By fulfilling the Math major requirements students will meet most of the endorsement requirements for the State of Vermont. In addition the following courses are highly recommended.
MATH 0241 Elemental Number Theory 
A course on Statistics (see below) 
MATH 0247 Graph Theory 
A course in computer science (see below) 
MATH 0310 Probability 

These courses may coincide with the fulfillment of major or minor requirements
Specific course and endorsement alignments
Knowledge Standards
Attained through fulfillment of major or minor requirements and selected electives
Middlebury Course Offering 
Knowledge/skill required 
Algebra and Number Theory – Properties of natural numbers and integers, as well as complex number systems; ways that basic ideas of number theory and algebraic structures underlie rules for operations on expressions, equations, and inequalities; use of algebra to model and reason about realworld situations; use of algebraic reasoning for problem solving and proofs in number theory, geometry, discrete mathematics, and statistics 

Major requirements 
Geometry and Trigonometry – Core concepts and principles of geometry in the plane and in space using Euclidean geometry along with Cartesian coordinate and vector methods, and applications to transformations and problem solving; trigonometry from geometric and graphical perspectives, and applications to problem solving 
Major requirements 
Functions and Analysis – Equations and formulas associated with each important class of functions and the way that parameters in these representations determine particular cases; logarithmic functions; how to use functions to solve problems in calculus, linear algebra, geometry, statistics, and discrete mathematics 
Data Analysis, Statistics, and Probability – Use of surveys to estimate population characteristics, and design of experiments to test conjectured relationships among variables; use of both theory and simulations to study probability distributions, and applications of both theory and simulation in models of real phenomena; conditional probability and independence, and calculation of probabilities associated with these concepts; performance of formal hypothesis tests while applying appropriate statistical testing 

Discrete Mathematics and Computer Science – Graphs, trees, and networks; enumerative combinatorics; iteration and recursion; conceptual underpinnings of computer science 
Performance Standards
Attained through Senior work in major and presentations in all Math courses, Education Studies courses, including EDST 0410 Student Teaching Seminar, and understanding faculty modeling and use of best practice in Middlebury classes
Middlebury Course Offering 
Knowledge/skill required 
Major coursework 
Anticipates, elicits, and corrects typical errors and misconceptions in mathematical reasoning through the planning and execution of lessons 
Major coursework 
Models the habits of mind of flexibility and perseverance that support mathematical learning 
Designs and incorporates mathematical tasks/activities that enable students to investigate, explore, and discover structures and relationships; solidify basic mathematical skills; extend and generalize mathematical concepts; create and use mathematical models; apply concrete, formal, and informal strategies to solve mathematical problems; formulate and solve problems individually and collaboratively; and justify and communicate their conclusions orally and in writing 

Major coursework 
Conveys the real world applications of mathematical ideas, and the interconnections among mathematical ideas and between mathematics and other disciplines 
Communicates mathematical ideas using appropriate mathematical language and mathematical representations, and teaches students to use both to communicate about mathematical ideas 

Uses required mathematics scoring guides and benchmarks to evaluate student work and teaches students to use both to evaluate their own work 

Provides opportunities for students to use appropriate technological tools to explore algebraic ideas and representations of information, study individual functions and classes of related functions, conduct geometric investigations, and solve problems 

Major coursework 
Conveys to students how the development of mathematical theory and understanding is a historical process with continuous creation of new knowledge and refinement or rejection of “old” knowledge 
Conveys to students the roles and responsibilities of mathematicians with respect to social, economic, cultural, and political systems, and provides them with opportunities to actively explore the full scope of career choices available to people in mathematics 

Demonstrates sensitivity to inequities in mathematics teaching and careers by incorporating specific instructional strategies that promote equity 