Mathematics is as old as civilization itself, for only the most primitive form of civilization can exist without it. History and mathematics are deeply wedded, and where mathematics has flourished so has the human condition; where mathematics has remained sterile, so too has any form of progress, be it art, literature, science or thought. It is no accident that the technological revolution of today is the product of the mathematics of 60 years ago. The great irony in all this is that, although mathematics has been essential to man’s ascent and knowledge, the reverse is not necessarily true.
The goal of the VES Math Department is to bring as much of this form to our students as possible. We seek to teach students the mechanics of how all this works, why all this works and, to a certain degree, to prove that all this works. A close but constant secondary goal is to demonstrate at all levels the applications of mathematics in the world around us. Regardless of the particular class, students will be engrossed in problem solving, investigating, predicting, calculating, analyzing and verifying, followed by a well-reasoned presentation of results. Our math classes focus on discovery, taking chances, critical thinking and following where mathematics leads.
Algebra I, the introduction to mathematics at VES, is a vast world of functions, graphs and the fascinating exploration of numbers and their invaluable uses and qualities. The course seeks to develop a facility in working with numbers, variables, graphs, inequalities, tables, and various equations. Particular emphasis is placed on solving word problems and reading questions carefully. This process helps build algebraic skills and strengthens the understanding of needing to solve problems in a context, rather than from drill and practice alone. Students learn to use graphing calculators as a problem-solving tool. Topics include the study of equations and graphs (linear and quadratic), linear data versus nonlinear data, exponents, inequalities, radicals, solving fractional equations, special products, and factoring.
Prerequisite: Algebra I or permission of the Department Chair
This course is designed to integrate algebra with the foundations of geometry. Topics include, but are not limited to angles, triangle congruences, parallel lines, polygons and polyhedrons, area, volume, circles and spheres, similarity, right triangle trigonometry and transformations. Independent thinking and discovery are encouraged throughout the course, as well as the study of and defending geometric proofs. This course seeks to demonstrate math’s usefulness and encourages students to see connections to real-world problems. Problem solving, logical reasoning and critical thinking skills will be emphasized through the use of cooperative learning, manipulatives and technology.
Prerequisite: Algebra I or permission of the Department Chair
The study of Honors Geometry encompasses far more than its definitions, postulates and theorems. Students will consistently be challenged to reason analytically. The process of formal proof is emphasized early in the course, and direct and indirect proofs are investigated extensively. Proofs include parallel and perpendicular lines, congruent triangles, parallelograms and geometric inequalities. The emphasis then shifts to applications. Topics include circles, right triangle trigonometry, coordinate geometry, areas and volumes. Late in the year, a computer software-assisted project is assigned, focused on the ideas of construction and locus. Graphing calculators and Geometer’s Sketchpad software are used to demonstrate and model much of the geometry presented within the course.
Prerequisite:Algebra I or permission of the Department Chair
This course provides a continuation and extension of the basic algebraic concepts from Algebra I and Geometry. Students discuss, represent and solve increasingly sophisticated real-world problems using more advanced algebraic techniques, bringing opportunities for doing mathematics into focus. Incorporating appropriate technology, they study the properties and the algebra of quadratic, exponential, logarithmic and rational functions, systems of equations and inequalities, as well as conic sections and applied trigonometry. This course provides a sound understanding of all elementary functions, including linear, trigonometric and circular.
Prerequisite: Honors Geometry or permission of the Department Chair
The main topics of Honors Algebra II / Trigonometry are basic number theory, algebraic properties and proofs, formal notation, word problems and the algorithms to solve them. As the course advances, students solve higher order equations, formal functions, logarithms, exponentials and more extensive word problem applications. The spring term introduces trigonometry and vectors, including Laws of Sines and Cosines, radian and degree trigonometry, graphs of trig functions and trigonometric word problem applications.
Math Analysis helps students understand the fundamental concepts of algebra, trigonometry and analytic geometry. Topics covered in this course are the study of functions (polynomial, rational, trigonometric, exponential and logarithmic), systems of equations and inequalities, matrices, solving triangles and conic sections, along with the introductory concepts of calculus (determinants and limits). A balance is maintained among the algebraic, numerical, graphical and verbal methods of representing problems. Students use the graphing calculator daily to visualize topics from a numerical and graphical representation.
Prerequisite: Honors Algebra II/Trigonometry or permission of the Department Chair
The mathematical spectrum heightens as students enter the world of Honors Analysis. This course is aimed at those who have demonstrated excellent mathematical ability in their previous coursework, with the expectation being toward preparing them for Advanced Placement Calculus in the following year. The first term begins with an emphasis on mathematical reasoning and proof, with a specific focus on general functions and their properties. After a guided tour of the functions, student begin to explore the concepts of series and sequence, complex numbers, exponential and logarithmic functions, polynomial and trigonometric functions, conic sections, matrices and vectors. The students finish the year delving into topics essential to calculus such as polar coordinates, complex numbers, analytical geometry and an introduction to limits and continuity.
Prerequisite:Algebra II / Trigonometry or permission of the Department Chair
The course concentrates on application rather than formal theory. Students learn to formulate questions that can be addressed with data, and to collect, organize and display relevant data to answer them. They learn to select and use appropriate statistical methods. Students develop and evaluate inferences and predictions, and apply basic concepts of probability.
Prerequisites: Algebra II-Trigonometry Students must have: 1. An interest in pursuing higher level mathematics 2. The support of the department and the recommendation of their current teacher 3. Completed a second year course in Algebra with an average of 85 or better 4. A PSAT Critical Reading score of 500 or better (or an equivalent score on the SAT, Pre-ACT, or ACT)
Statistics is the most widely applicable branch of mathematics, used by more people than any other kind of math both in the workplace and by consumers. Students study lists of raw data, graphical displays and charts, rates, probabilities, percentages, averages, forecasts and trend lines. Advanced Placement Statistics provides the opportunity for students to acquire statistical literacy. This course is designed to be the equivalent of an introductory college level Statistics course. The syllabus has been constructed under the guidelines of the College Board and will prepare the student to take the Advanced Placement Examination in the spring.
Prerequisite:Math Analysis or permission of the Department Chair
Students learn the mechanics behind solving derivatives and integrals both by hand and using a graphing calculator. Interspersed among the lessons throughout the year are applications of the course material in the form of physical motion, product package design, architecture, finance, flowing water, medication, populations, swings, springs, see-saws, police radars, wrecking balls, balloons, ballistics, bacteria and rocket science – to name a few. This is not a class about theorems or mathematical rigor as is the AP Calculus class, but is an excellent basis for college calculus.
Prerequisite: Honors Analysis Students must have: 1. The support of the department and the recommendation of their current teacher 2. A grade of 90 or better in Honors Analysis (a grade of 90 or higher) 3. PSAT Math score of 550 or better (or an equivalent score on the SAT, Pre-ACT, or ACT)
This is a rigorous course aimed at building a strong foundation in differential and integral calculus along with its various applications. The course begins with a study of limits, continuity and parametric equations. Topics include differentiation and integration of polynomial, exponential and trigonometric functions. Specific applications studied include velocity, acceleration, position, optimization, slope fields, exponential growth and decay, area and volume. Various techniques of integration are studied with particular emphasis placed upon the Fundamental Theorem of Calculus and its applications. The course prepares students for the College Board Advanced Placement Examination, with the potential for students to begin their college mathematics at a more advanced level of calculus.
Prerequisite: AP Calculus AB Students must have: 1. The support of the department and the recommendation of their current teacher 2. Successfully completed the AP Calculus AB course by scoring > 3 or greater on that exam
This course is highly rigorous and aimed at building a strong foundation in differential and integral calculus, along with its various applications. The AP BC curriculum includes all of the material covered in the AP AB course, with more emphasis on the underlying proofs. Additional topics include the study of Euler’s method, logistical growth models, integration by parts, partial fractions, volumes by cylindrical shells, arc length and indeterminate forms. Focus is put upon polynomial approximations and series (Taylor and Maclaurin), as well as polar, parametric and vector functions and the analysis of planar curves. Students prepare for the College Board Advanced Placement Examination, and have the potential to begin their college mathematics at a significantly more advanced level of calculus.
Prerequisite: AP BC Calculus (with a score of 3 or higher on the AP Calculus exam) and permission of the Department Chair.
The course begins with a thorough review of analytic geometry, polar coordinates and parametric equations, then proceeds to vectors in both 2-space and 3-space. The topics include tangent and normal vectors, curvature, dot product, cross product, curves and planes in 3-space, and quadric surfaces. Further topics include the analysis of cylindrical and spherical coordinates, partial derivatives, gradients, directional derivatives and double and triple integrals. Stokes’ and Green's theorems, as well as the related underpinnings of vector theory will be discussed and studied as time permits.
Prerequisite: Open to a limited number of seniors who have completed and excelled in at least one AP Science and/or AP Mathematics course. Tests scores (Standardized and AP), grades, interview, essay, teacher recommendations, and transcript rigor are all factors in the application process.
A year-long academic offering for students as a core academic class in either Mathematics or Science that seeks to provide rigorous interdisciplinary study in a collaborative and project-based setting. This class quickly grows into a student-driven format with significant critical thinking applied throughout the course.
First semester topics include Team Building, Effective Collaboration, Learning Styles, Analysis, Methodology, Innovation, and Design Thinking as well as day-long mini projects and three team based collaborative projects with presentations. Second semester is designed around a thesis project that is significant in scale, interdisciplinary in nature, and collaborative in format. Teams will work toward creating a significant document and large scale presentation that will be delivered in front of both small and large panels. Teams will build a website to track and display their project and a physical design model or equivalent display (ex., a piece of music, a computer program, etc.) depending on each individual project’s aim and components. Clearly defined individual roles will be identified in all facets of the project while ensuring a collaborative approach among the team throughout the venture.
The 9th Grade ARC Collaborative provides an interdisciplinary introduction to three different subject areas that students can apply to the rest of their VES experience and future studies. ‘A’ stands for the Arts, which students will engage with through a trimester-long Intro to the Arts course; ‘R’ stands for Reasoning, which will be the focus of their trimester in the Critical Thinking course; ‘C’ is for Computer Science and the work they will complete through the trimester in Computer Science I.
These three academic experiences and the skills our ninth graders will acquire from them will be applicable across academic disciplines. The ARC Collaborative will enrich students’ learning in core subject areas while exposing them to other aspects of our curriculum that may spark a new interest, talent, or passion to pursue further over the course of their VES career. In short, the ARC courses will be a meaningful segment in the path of our ninth graders’ high school experience.
Chair of Math Department & Math Teacher/Head Coach, Golf
Steve comes to VES with a wealth of experience including boarding schools in New York, Connecticut, Maine and Colorado. At VES, he primarily teaches AP Statistics but enjoys dabbling in many other Math and Science classes. Steve is a coach with VES’ boys and girls varsity tennis teams and has coached a number of other sports over the years, including a New England Champion Ski Team. Steve had the pleasure of teaching both his son and his daughter who are now both Navy Captains. In his spare time he writes vocal arrangements, and travels to coach singing groups and adjudicate A Cappella competitions all over the world.