The goal of the Winsor mathematics program is to teach for understanding and mastery, and these goals are best reached through regular practice, feedback, and ongoing collaborative problem-solving with peers. 

The Upper School offers the following courses: Algebra 2, Geometry, Precalculus, Calculus, Statistics, and Post-Calculus Mathematics. Algebra 2, Geometry, and Precalculus are also offered at the advanced and honors levels. AP Calculus is also available at the AB and BC levels. AP Statistics is also offered. Students who have successfully completed either AB or BC calculus can choose between Topics in Post Calculus Mathematics and AP Statistics. Any student enrolled in an AP course is strongly encouraged to take the AP exam, which is administered by the College Board in May. All mathematics courses are major courses.  

Three years of mathematics are required; the Mathematics Department strongly recommends that students take math through Class VIII. The department places students into sections that are based on the pace and depth of topics that are studied, while trying to balance the best interests of each individual student with the needs of the grade as a whole. The department uses input from a student’s current and past teachers, including both grades and the teacher’s sense of a student’s comfort with a particular pace to make these decisions. TI-84 graphing calculators are used regularly in US math courses. All mathematics courses available to seniors meet the requirement for a quantitative course during the fall semester of senior year.

The advanced level courses study the topics in more depth and investigate problems of greater complexity and challenge, with limited review of prerequisite courses’ material. The honors level requires mastery of prerequisite courses’ material. In addition to studying the topics in more depth and with greater complexity and challenge, the fast pace of this level may allow for additional topics to be explored.

The program’s design enables all students to study calculus while at Winsor. Some Upper School students who have developed advanced skills might feel that they have already mastered the material in a course in the traditional math sequence; these students should speak with their teacher or the head of the Mathematics Department. In the rare instance that acceleration is considered a possibility, the student will need to demonstrate on a Winsor assessment a mastery of the material of the course they will skip. A student may skip a course in this manner only once during their time at Winsor.

Algebra 2 (1 credit)

All students will study the core topics of Algebra 2: quadratic equations and functions, and polynomial equations and functions. Complex numbers, systems of equations, inverse functions, transformations and rational expressions will also be studied. The algebraic and graphical aspects of each topic will be emphasized. The applications of the TI-84 graphing calculator will be introduced. This course is open to students who have completed a full year of Algebra 1 at Winsor or by department permission.

Geometry (1 credit)

This yearlong course introduces and reinforces the principles of mathematical logic by emphasizing rigorous geometric proofs at all levels; proof work is extensive at the advanced and honors level. Students will study the formal definitions, postulates, and theorems concerning parallel and perpendicular lines, congruent triangles, quadrilaterals, polygons, and circles. In addition to using these theorems in their proof-work, students will apply them to problems concerning right triangle trigonometry, similar figures, areas, and volumes. Additional topics such as symmetry, coordinate geometry, probability, constructions, and transformations will be included as time permits. This course is open to students who have completed a full year of Algebra 2 at Winsor or by department permission.

Precalculus (1 credit)

In this course, students continue to study functions, including polynomial, rational, exponential, logarithmic, and trigonometric, in addition to their applications. Graphing calculators are used throughout the course to build understanding and help solve problems. Analytic and algebraic problem-solving methods are also emphasized so that students will understand multiple approaches and techniques. Other topics covered include transformations of graphs, inverses of functions, solving equations and inequalities, trigonometric identities, and the laws of sines and cosines. In addition, polar coordinates, sequences and series, limits, and introductory calculus concepts are introduced, if time permits. This course is open to students who have completed Geometry at Winsor or by department permission.

AP Calculus (1 credit)

AB and BC Calculus are both AP courses open to students by permission of the department. Beginning with the concepts of limits and continuity, students go on to learn about derivatives and their applications and then progress to the theory, techniques, and applications of integration. Throughout the course, graphing calculators are used as a tool to enhance understanding of the concepts and facilitate problem-solving. BC Calculus covers additional topics including logistic growth, improper integrals, polar and vector calculus, and convergent infinite series. Students are strongly encouraged to take the AP exam, which is administered by the College Board in May. Enrollment is by permission of the department.

Calculus (1 credit)

Calculus is a yearlong course where students study the concepts of both derivatives and integrals. Emphasis will be placed on graphical interpretation of limits, slopes, and area in addition to computational accuracy. Applications of calculus (e.g., optimization, related rates, areas, and volumes) will be presented and examined. The course will begin studying these topics with polynomial functions although other functions may be included should time allow. Throughout the course, a graphing calculator is used as a tool to enhance understanding of the concepts and facilitate problem-solving. This course is open to students who have completed Precalculus at Winsor or by department permission.

AP Statistics (1 credit)

This yearlong course introduces students to the field of data analysis and statistics. Topics fall into four themes: Exploring data, Collecting data, Distributions of data, and Statistical inference. The focus of this course is analysis with an emphasis on understanding and communicating with statistical concepts and language. Understanding formulas is prioritized over memorization. Significant written work is required. The TI-84 calculator is a primary, required tool. Students are strongly encouraged to take the AP Statistics exam, which is administered by the College Board in May. This course is open to Class VII and VIII students. Prerequisite or corequisite: Precalculus. This course meets at the same time as Statistics & Data Analysis.

Statistics & Data Analysis (0.5 credits, fall)

Students in this one-semester course will have class with the AP Statistics course. First semester topics include exploring data, collecting data, and distributions of data. The focus of this course is analysis, with an emphasis on understanding and communicating with statistical concepts and language. Understanding formulas is prioritized over memorization. Significant written work is required. The TI-84 calculator is a primary, required tool. This course is open to Class VII and VIII students. Prerequisite or corequisite: Precalculus. This course meets at the same time as AP Statistics.

Topics in Post-Calculus Mathematics (1 credit)

This yearlong course is for students who have completed an AP calculus class. Students will be introduced both to the rigors of higher mathematics beyond calculus and to some of the more intriguing mathematical concepts that have been developed over the past 2500 years. Particular attention will be paid to the formality of mathematical notation and writing. Topics to be investigated may include—but are not limited to—proof techniques, formal logic, set theory, formal limit proofs, number theory, non-Euclidean geometry, group theory, and dynamics. Enrollment is by permission of the department.