Curriculum Detail

SPL: Picker

Mathematics

In the universe of numbers, there are truths and falsehoods. Fundamentally, mathematics is the business of figuring out which is which. The goals for our students are to experience the beauty of the discipline, master its essential content, and most of all, develop resilient, flexible and efficient problem-solving skills. Real problems are those to which one doesn’t already know the answer, so solving them requires persistence and ingenuity. Our students learn to experiment, notice patterns, make conjectures, generalize, test with counterexamples, construct convincing arguments, present ideas orally and in writing, use precise structures and language, gauge the reasonableness of answers and critique the arguments of others. Fluency of skills is critical for progress, and skills are learned in meaningful contexts so that each new idea contributes to a coherent big-picture understanding.
 
In Grades 9 through 11, students follow a sequence of integrated, problem-centered courses, using as primary texts Math 1 through Math 4 published by Phillips Exeter Academy. Courses are integrated because the study of geometry, transformations, vectors, matrices, combinatorics and data analysis are woven throughout the curriculum so that meaningful connections are developed to a core strand of algebraic techniques. Courses are problem-centered because they are designed around carefully constructed sequences
of problems where all needed information is embedded in the questions themselves. Class is structured as a seminar where students present problems and discuss their approaches. The teacher helps students evaluate the effectiveness of different strategies and identify key ideas that emerge. In this way, students develop a deep conceptual understanding and gain genuine authority as mathematical thinkers.
 
In Grades 11 and 12, a broad range of elective courses is offered, reflecting the variety of engaging problems and styles of thinking across different fields of higher mathematics.

Upper School Mathematics Sequence
Grade 9 Integrated Math 9 
Grade 10 Integrated Math 10
Grade 11 Integrated Math 11, Semester Electives (Optional)
Grade 12 Semester and Yearlong Electives (Optional)

  • Integrated Math II

    In addition to developing a mastery of the core topics in plane Euclidean geometry, students in this course also learn how to develop, extend and defend their mathematical thinking. This is very much a “habits of mind” course. Students learn to formulate mathematical arguments and to justify their claims about the geometric objects they study. A variety of tools are employed to reach these objectives, from traditional straight-edge and compass constructions to more recent reflection constructions and computer software to simulate geometric properties dynamically. Numerous practice and extension problems serve to reinforce students’ understanding. In many cases this study takes place in small group sessions where students are encouraged to support one another and take responsibility for each other’s mastery.

  • Integrated Math II (Accel)

    In addition to developing a mastery of the core topics in plane Euclidean geometry, students in this course also learn how to develop, extend and defend their mathematical thinking. This is very much a “habits of mind” course. Students learn to formulate mathematical arguments and to justify their claims about the geometric objects they study. A variety of tools are employed to reach these objectives, from traditional straight-edge and compass constructions to more recent reflection constructions and computer software to simulate geometric properties dynamically. Numerous practice and extension problems serve to reinforce students’ understanding. In many cases this study takes place in small group sessions where students are encouraged to support one another and take responsibility for each other’s mastery.

  • Integrated Math III

    Through a mix of numerical, graphical and algebraic approaches, students investigate the properties of mathematical functions in general and develop a beginning understanding of polynomial, rational, radical, exponential, logarithmic and the six trigonometric functions in particular. Students use a variety of approaches including learning how to use graphing calculators and understanding their limitations. The variety of approaches is designed to help students formulate and understand a basic library of functions, as well as the logical development of their definitions and appropriate applications in developing mathematical models.

  • Integrated Math III (Accel)

    Through a mix of numerical, graphical and algebraic approaches, students investigate the properties of mathematical functions in general and develop a beginning understanding of polynomial, rational, radical, exponential, logarithmic and the six trigonometric functions in particular. Students use a variety of approaches including learning how to use graphing calculators and understanding their limitations. The variety of approaches is designed to help students formulate and understand a basic library of functions, as well as the logical development of their definitions and appropriate applications in developing mathematical models.

  • Integrated Math 11

    This course is an in-depth study of functions, their graphs and their use in modeling real-world phenomena. Polynomial, rational, exponential, logarithmic and trigonometric functions are studied from numerical, graphical and analytical perspectives. Graphing is done by hand and with the aid of graphing calculators. Conic sections may be covered. Series and sequences are discussed and the notion of limit is introduced.

  • Integrated Math 11 (Accel)

    This course is an in-depth study of functions, their graphs and their use in modeling real-world phenomena. Polynomial, rational, exponential, logarithmic and trigonometric functions are studied from numerical, graphical and analytical perspectives. Graphing is done by hand and with the aid of graphing calculators. Conic sections may be covered. Series and sequences are discussed and the notion of limit is introduced.

  • Statistics

    Statistics is the science of data, and data are numbers with a context. In contemporary society, collecting, summarizing, representing, and analyzing data are activities of major importance. Statistics serves to enhance social and scientific awareness and help us evaluate the numerous statistical claims we encounter. The study of statistics makes us better consumers of information. In this course, students will explore four big questions in statistics: What do we do with data? How do we get data? What do the data tell us and how do we interpret it? How do we communicate the results?

  • Calculus

    This course covers single-variable differential and integral Calculus. Topics include: the definition of the derivative, the definition of the definite integral, the Fundamental Theorem of Calculus, techniques of differentiation, antiderivative and accumulation functions, techniques of antidifferentiation and applications of integration. The ability to make connections between analytic, graphical, numerical, and verbal approaches is developed. This course covers a full semester of college Calculus.

  • Calculus (Accel)

    This course covers all of the topics listed for Calculus (271) as well as the following: accumulation functions, additional techniques of antidifferentiation, Taylor series and series of constants, vector-valued functions, curvature, parametric and polar equations. This course makes a significant time demand on students.

  • Multivariable Calculus

    The derivative, the integral, and their applications are revisited and reimagined in higher dimensions. Using Exeter's Math 6 problem set, functions in several variables are analyzed using tools including partial derivatives, multiple integrals, line intervals, vector calculus and Lagrange multipliers. Graphing in three dimensions will be done with the use of computers. Prerequisite: Calculus (Accelerated) and permission of the department.

  • Economics

    Economics is the study of how a society organizes its production, distribution, and consumption. In this yearlong course, students are introduced to an economist's way of thinking as they explore the history of economic thought and its evolution toward modern economic theory. Students investigate the principles of a college-level introduction to micro- and macroeconomics through engaging lab simulations and generalized models. Historical and current events serve as case studies for the masteries of economic principles. Students develop a practical and theoretical framework that enables them to reflect on and engage in meaningful debate about current economic issues in the world around us.
     

  • Collaborative Problem Solving

    In Collaborative Problem Solving students work together, in an informal atmosphere, to solve challenging math problems. Problems are taken from a variety of topics, including algebra, geometry, combinatorics, probability, and number theory. Problems are chosen for their interest, they are sometimes discussed for fairly long periods of time, and they are tackled collaboratively. The class should be of interest to students who love math and want to learn more, and to students who want to become better problem solvers. Offered through Interschool. Meeting time and location: One evening per week TBA, 6-8 pm at the Dalton School.

    Prerequisite: Students must have completed Integrated Math III Accelerated.

  • Game Theory

    Game Theory is the mathematical analysis of conflict and cooperation, where "players" can include individuals, corporations, governments, or even nature. The theory attempts to predict, explain, or recommend courses of action in situations where one player's success depends on the decisions of all players. The theoretical analysis of such situations is taught through applications in economics, politics, business, evolutionary biology, religion, philosophy, computer science, and sports, as well as through games like poker and chess. We develop quantitative models for strategic situations, and analysis includes optimization and graphical analysis. Offered through Interschool. Meeting time and location: One evening per week TBA, 6-8 p.m. at the Dalton School.

Middle & Upper School

22 East 91st Street
New York, NY 10128

Lower School

56 East 93rd Street
New York, NY 10128

Athletic & Educational Facility

412 East 90th Street
New York, NY 10128
A K-12 independent school in New York City, The Spence School prepares a diverse community of girls and young women for the demands of academic excellence and responsible citizenship.

212-289-5940


© 2025 Spence School