The mathematics curriculum aims to teach students the skills necessary for academic and personal success while examining some core philosophical questions: what mathematics is, how it has evolved, and what reasons we have for wanting to study it. Following our principles of progressive education our math courses not only cover fundamental materials necessary for college preparation but also encourages our students to explore the beauty of mathematics and its connection with other subjects. Students at The Putney School are expected to take three years of high school mathematics and finish Algebra 2 before they graduate. Students who have finished Algebra 2 are encouraged to take advantage of our more advanced courses such as Statistics, Precalculus, Calculus and Survey of Computer Science. All courses are two-trimester (full-credit) courses unless otherwise specified.
Mathematics Courses
Algebra (full credit)
Algebra begins with a review of fundamental mathematical skills in working with numbers, variables and ratios. Students are encouraged to become active learners and develop strategies that will aid their development in mathematical thinking throughout their school careers. As students progress they develop core algebraic skills and an understanding of the connection between algebra and geometry by working with functions, linear equations, linear inequalities, systems of linear equations, and quadratic functions. Algebra also contains a statistics and data analysis component as well as an introduction to mathematical concepts that students will find essential in their science courses.
Geometry (full credit)
Geometry introduces students to the properties of plane geometric figures. Students study the general properties of polygons, parallel lines, and circles, and develop a basic understanding of trigonometry. The elements of formal proof and logic are also major components of this course. Students study areas and volumes of shapes and investigate practical geometric problems drawn from many domains. There is significant use of geometric and modeling software in this course as well. The overall goals of Geometry are to develop students’ reasoning and visual thinking skills and to prepare students to study more complex mathematical problems in future courses.
Algebra 2 (full credit)
The main theme of Algebra 2 is the understanding of functions. Students begin by furthering their study of linear functions and systems from Algebra and then moving on to studying quadratic functions/equations and then more general polynomial and radical functions/ equations. Major algebraic concepts students will also study include operations on functions, exponential and logarithmic functions, trigonometry, probability and combinatorics. Emphasis will be placed on word problems and algebraic skills necessary for both college mathematics and practical applications.
Problem Solving with Algebra (half credit)
This course is a bridge course between Algebra 2 and Precalculus or Calculus. It is intended for new incoming students who need to strengthen their algebraic skills in preparation for Precalculus, Calculus, an elective course or college mathematics requirements. It is also intended for new students who have taken a second high school algebra course but feel that they may benefit from a trimester of review. This course reviews material from Algebra 2 including linear, quadratic, exponential and logarithmic functions with a focus on practical problems and applications. Techniques for solving any unfamiliar problems are also introduced, and students will examine problems from fields such as graph theory, statistics and probability.
Precalculus (full credit)
The main goal of Precalculus is for students to further their understanding of the fundamental concepts and relationships of functions. Students will expand their knowledge of quadratic and polynomial functions and move on to study exponential, logarithmic, rational, piece-wise, and trigonometric functions. Students will investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use mathematical software to build understanding, make connections between representations, and provide support in solving problems. A major focus of this course will be having students apply mathematical skills and make meaningful connections to life’s experiences. Students who passed Algebra 2 (or an equivalent in another school) but do not have the department’s confidence that they will succeed in Precalculus, will be asked to complete Problem Solving with Algebra first before taking Precalculus.
Statistics (half credit)
This one-trimester elective course examines statistics both as a rigorous study of data analysis and as a bridge to numeracy. Students will review elementary descriptive statistics and explore deceptively simple concepts, such as mean and median, in depth. From then on students will study topics such as measures of dispersion, data gathering and probability distributions and confidence intervals. This course will use computer software (spreadsheets, presentations, simulations and statistical packages) extensively. Data will be drawn from relevant sources including current political trends, environmental issues, the college application process and The Putney School’s new Field House. Prerequisite: Algebra 2 or Problem Solving with Algebra.
Survey of Computer Science (half credit)
In this one trimester introduction to the study of computer science, students will explore how computers work from low level architecture to high level application scripting and data analysis. Although basic programming is a major component of the course, other topics including circuitry, Boolean logic, cryptography, computer graphics and algorithms will be studied as well. This is a project based course; students who already have basic programming experience will be expected to devise and complete more challenging projects suitable to their level of expertise. A laptop computer is required for this course; students without laptops are encouraged to speak to the department or the technology office to arrange a loaner. Prerequisite: Algebra 2 or Problem Solving With Algebra.
Calculus 1 (full credit)
Calculus 1 is a course based around the concepts of limits, derivatives, and integrals. We approach calculus by following a traditional curriculum (the course covers the first three-fifths of a traditional college calculus course) through progressive means. Through a mixture of computer and graphing calculator activities and labs, investigative lecture-discussions and problem-based instruction, students will gain a conceptual understanding of calculus and learn creative methods of problem solving. Please note that The Putney School does not teach to the AP curriculum and that this course is not intended to prepare students for the AP exam.
Calculus 2 (full credit)
The continuation course of Calculus 1, Calculus 2 picks up where its predecessor left off by reviewing the basic concepts of calculus and then moving on to integration techniques and more applications of the integral, ultimately leading to power series expansions of functions. Particular attention is paid to differential equations and how calculus can be used to model scientific problems. This course also covers other traditional calculus topics such as parametric equations and polar coordinates. If time allows, students will study the beginnings of multivariable calculus at the end of the year. Please note that The Putney School does not teach to the AP curriculum and that this course is not intended to prepare students for the AP exam.
Advanced Topics in Mathematics (full credit)
This course is a full-credit small seminar designed for students who have finished Calculus 1 and have had some success in their mathematical lives. The purpose of this course is three-fold: it aims to present a broad survey of college and graduate-level mathematics to the students, it provides an opportunity for the students to learn to write rigorous mathematics, and it provides a window into beautiful mathematical topics that exist outside of the traditional sequence embraced by secondary school curricula. Students can elect to take this course concurrently with Calculus 2. Topics covered vary depending on the interests of the students and the expertise of the instructor; in 2009-2010, Advanced Topics in Mathematics covered vector calculus, selected topics from physics, abstract algebra and real analysis.
