Boarding and Day · Co-ed College Prep · Grades 6–12 & Postgraduate · Hebron, Maine

Mathematics & Computer Studies

The Department of Mathematics and Computer Studies aims to teach our students to think clearly, to use logical reasoning, and to manipulate quantitative relationships with accuracy. We hope that math students will come to appreciate the beauty of mathematics as a creation of human intelligence, that they may enjoy its intellectual challenge, and that they will use its logical training to approach real world problems. We teach problem-solving as a process and work with students to discredit the myth that either one can do math or one cannot.
 

By including in the curriculum questions and assignments that challenge students to reflect on and generalize from the skills they have acquired, we aim to complement these skills with an understanding of the concepts they demonstrate and the utility they offer. Because the worlds of education and work frequently require teamwork, our students practice communicating with mathematics, acquiring this skill by talking with each other about math, explaining their thinking to each other, and justifying their ideas. At Hebron, one doesn't merely know math, one does math!

 

ALGEBRA I

Algebra I is a standard first-year course in the fundamentals of algebra. Its content includes using mathematical symbols, solving equations in one and two variables, graphing linear equations, solving systems of linear equations, using ratio and proportion, and solving word problems. It provides the foundation for studying geometry and more advanced algebra.    

ALGEBRA II (HONORS)

Honors Algebra II covers all the topics of Algebra II as well as introductions to logarithms, trigonometry, and often sequences and series. The class emphasizes critical thinking and problem solving skills and encourages collaboration and communication. A TI-83,  TI-84, or TI-Nspire CX CAS calculator is required; for students intending to study AP-level Calculus, the TI-Nspire CX CAS calculator is recommended (as it will be required for AP Calculus students). Prerequisite: honors grades in Algebra I and departmental approval.

ALGEBRA II

Algebra II reviews the topics introduced in Algebra I and expands upon them. Additional topics covered are absolute value equations and inequalities, polynomial functions, rational expressions, roots and radicals, and quadratic equations and their graphs. The TI-83/84 is required for this course. Prerequisite: successful completion of Algebra I.                 

AP CALCULUS AB

Advanced Placement Calculus (AB Curriculum) is a rigorous course in differential and integral calculus open to upper-class students with departmental approval. Completion of the course normally prepares a student to take the Advanced Placement examination. A TI-Nspire CX CAS calculator is required. Prerequisite: honors grades in Honors Precalculus and departmental approval.                     

AP CALCULUS BC

Advanced Placement Calculus (BC Curriculum) reviews the AB Calculus curriculum and includes advanced calculus topics in preparation for taking the BC level advanced placement exam. The course is augmented with group projects and presentations. A TI-Nspire CX CAS calculator is required. Prerequisite: successful completion of the Calculus class or high honors grades in Honors Precalculus and departmental approval.       

AP STATISTICS

AP Statistics is a certified AP course that uses the guidelines set forth by the Colege Board to guide the curriculum. From the AP website:  "The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding."

CALCULUS

This course serves as a foundation for the basics of calculus in preparation for a college calculus course. It begins with a review of functions and their applications to develop numerical, graphical and analytical techniques of problem solving. The concepts of limits, derivatives and integrals are introduced with an emphasis on applications and practical problem solving. A TI-83,  TI-84, or TI-Nspire CX CAS calculator is required; for students intending to study AP-level Calculus, the TI-Nspire CX CAS calculator is recommended (as it will be required for AP Calculus students). Prerequisite: Precalculus

FINANCIAL MATH

In this class, seniors and post-graduate students explore the world of finance, with a focus on personal finance. The class investigates the details of saving, investing, budgeting, credit card debt, mortgages and other types of loans while using statistical analysis and representations as a tool to better understand finance. The class largely uses project- and inquiry-based learning to develop a deeper understanding of these topics and the mathematics behind them.

GEOMETRY

Our geometry course is designed so that students can be actively engaged as they learn geometry; students “learn by doing” using inductive techniques.  They learn to use the tools of geometry and perform investigations with them.  Many of the investigations are carried out in small cooperative groups in which students jointly plan and find solutions with other students.  Their investigations lead them to the discovery of geometric properties.  In addition, students gradually learn about deductive proof, which allows them to explain why their discoveries are true. The objective of this course is to promote an intuitive understanding of geometric concepts and objects.  After students come to understand a concept through experience they are introduced to the appropriate symbols and given opportunities to practice mechanics and problem solving.

GEOMETRY (HONORS)

Our Geometry course is designed so that students can be actively engaged as they learn geometry; students “learn by doing” using inductive techniques.  They learn to use the tools of geometry and perform investigations with them.  Many of the investigations are carried out in small cooperative groups in which students jointly plan and find solutions with other students.  Their investigations lead them to the discovery of geometric properties.  In addition, students gradually learn about deductive proof, which allows them to explain why their discoveries are true. The objective of this course is to promote an intuitive understanding of geometric concepts and objects.  After students come to understand a concept through experience they are introduced to the appropriate symbols and given opportunities to practice mechanics and problem solving.

In addition, the Honors Geometry class builds on the students’ skills with the graphing calculator and sometimes with the Geometer’s Sketchpad, a dynamic software program that allows for more investigation and manipulation.  Depth and breadth of topics are expanded, and more deliberate connections are made with Algebra.  Most students from this course move into our Honors Algebra II class.

PRECALCULUS

Precalculus provides the background for the mathematical concepts, problems, issues, and techniques in preparation for studying calculus. The fall term focuses on six basic functions – identity, squaring, cubing, reciprocal, square root, and absolute value.  In the winter term, the focus switches to exponential and logarithmic functions, and the spring concentration is on trigonometric functions. Each function is approached graphically through transformations and algebraically through equations. The TI-83 or TI-84 calculator is required. Prerequisite: Algebra II

PRECALCULUS (HONORS)

Honors Precalculus is an accelerated course intended to prepare students for success in single- and multivariable-calculus and beyond. Honors Precalculus begins by investigating include polynomials, exponents & logarithms, and analytic trigonometry. These fundamental topics are then used to explore vectors, parametric equations, polar and spherical coordinates, and introductory calculus topics including series, limits, and derivatives. Emphasis is placed on multi-step problem solving. A TI-83,  TI-84, or TI-Nspire calculator is required; for students intending to study AP-level Calculus, the TI-Nspire calculator is recommended (as it will be required for AP Calculus students). Prerequisite: Honors Algebra II and departmental approval.

PROGRAMMING, ROBOTICS, AND DESIGN

This class is an exploration of programming, game design, simple electrical circuits, robotics, computer-aided graphics, and 3D printing. The class is structured around nightly assignments as well as in-class projects. Previous programming experience or computer skills are not required. The year starts with simple programming exercises using the Python language and a Raspberry Pi while creating simple circuits to control LEDs and other electrical components. We then begin creating games using the Unity game engine and learning the C# language. We’ll mainly study classic video games, from aesthetics and functionality to what improvements can be made and how to create them from scratch. Along the way, we’ll learn how to create our own 2D graphics and 3D models, using Inkscape and Sketchup respectively, and how to use the 3D printer to bring our models to life and supplement our Raspberry Pi projects.

STATISTICS AND DATA ANALYSIS

Statistics and Data Analysis is a full-year course designed to acquaint students with the major concepts of statistics and give them the tools to properly collect, analyze, and draw conclusions from data. Students use real-world data in their explorations and are encouraged to keep up with recent news and come in with examples of statistics being used by newspapers, magazines, and other types of media. Students in this course learn how to be responsible consumers of information. Charts, graphs, data, and polls presented to us as media consumers on a daily basis and a deep understanding of what we are looking at is imperative for drawing the correct conclusions. Students in this course will never be wondering when they will have to use the knowledge they acquire in “real life.” Statistics has applications in almost every field of study, and this course provides students with a solid foundation for other statistics courses at the next level.