Upper School Curriculum

Mathematics

The mission of the Rivers mathematics department is to inspire curiosity and foster enthusiasm for learning and applying mathematics. Through meaningful work and student-centered classrooms, we create an environment that encourages students to collaborate with their peers and teachers while also taking ownership of their own learning process. We aim for students to feel both challenged and successful by pushing them outside their comfort zones, but always instilling in them a confidence that they have the tools to tackle complex and unfamiliar problems. They learn to think creatively and develop critical thinking skills that allow them to approach any problem like a mathematician. We believe this way of teaching and learning leads to self-assured students who will graduate with an appreciation for and excitement of the study of mathematics.
  • Geometry with Algebra

    This course is designed for students in ninth grade who would benefit from review of skills typically covered in Algebra I. The course focuses on strengthening essential algebra skills and providing enough coverage of geometry for students to proceed with Algebra II in tenth grade. It differs from our Geometry course by providing more coverage of algebra skills with a reduced amount of geometry. Algebra topics include solving multi-step equations, exponent rules, radicals, graphing basic polynomials, and factoring. Geometry topics include congruent triangles, trigonometric ratios, and surface area and volume of solids. Study skills specific to math are scaffolded into the structure of the course so that students are able to navigate their transition to high school math with the most opportunity for success.
  • Geometry

    This course covers properties and relationships of two- and three-dimensional objects. Deductive and inductive reasoning techniques are stressed as methods of investigating properties and relationships between figures and means of drawing conclusions. Students learn in a collaborative environment and concepts are reinforced through a variety of hands-on activities.  Students are introduced to constructing formal proofs, and algebra skills are reinforced consistently throughout the curriculum.  Students will be taught effective strategies for taking notes, studying for assessments, and completing group work. Emphasis on recall, mindset, and learning will be used so that they will be able to navigate their transition to high school math with the most opportunity for success.
  • Honors Geometry

    This challenging course is for students of demonstrated ability who have a strong desire and capability to learn and work independently and to think creatively. The entire content of the Geometry course is completed in more depth and with greater rigor. Constructing logical arguments, especially through formal proof, and using the coordinate plane to reinforce geometric concepts are central features of the course. Additionally, algebra skills are reviewed and developed, with particular emphasis on setting up and solving linear equations, quadratic equations, and systems of equations.
  • Algebra II

    This course reinforces and extends the concepts and methods covered in Algebra I, including mathematical properties, solving linear equations and inequalities, absolute value equations and inequalities, quadratic equations and factoring techniques, and systems of equations. The primary focus is learning the concept of a function and using parent functions to model real world situations. Families of functions studied include linear, quadratic, absolute value, exponential, logarithmic, polynomial, radical, and rational functions. Students are instructed in the use of graphing technology to explore and investigate concepts and learn about the behavior of the different families of functions.
  • Advanced Algebra II

    This course covers concepts of algebra and prepares students to be successful in precalculus and higher-level math courses. Students will study linear, absolute value, piecewise, quadratic, polynomial, radical, exponential and logarithmic functions, and rational expressions. Students will create and draw connections between graphical, algebraic, and analytical models, in order to identify critical information and transfer understanding between modes of representation. By completing projects that apply functions to real-life situations, students gain an understanding of how mathematics can be employed to solve complex real-world problems.
  • Honors Algebra II

    This rigorous course is intended for students of demonstrated ability who have the desire and capability to learn independently and think creatively. Combining the Algebra II curriculum with advanced graphing techniques and topics from Precalculus, this course introduces the concept of a function and examines properties and applications of linear, absolute value, piecewise, radical, exponential, logarithmic, quadratic, polynomial, and rational functions. Additionally, the course may include topics such as sequences and series, conic sections, and systems of nonlinear equations. The frequent use of real-world applications illustrates and reinforces mathematical ideas, and students are instructed in the use of graphing technology.
  • Precalculus

    This course will review and build upon concepts from Algebra II that are a vital foundation for higher level math courses. Students will analyze linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions by sketching graphs, exploring their transformations, and making interpretations in a real world context. This course challenges students to effectively employ problem solving skills while also sharpening their critical thinking skills.
  • Advanced Precalculus

    This course introduces students to new concepts needed for the study of calculus and strengthens understanding of topics in algebra and geometry. Students study functions with particular attention to graphing and manipulating polynomial, rational, exponential, logarithmic, and trigonometric functions. Students learn to work with functions numerically, visually, algebraically, and verbally. Graphing technology is utilized throughout the course to enhance student understanding of mathematical concepts. The frequent use of real-world applications illustrates and reinforces mathematical ideas.
  • Honors Precalculus

    This course is for students of demonstrated ability and includes all of the topics covered in Advanced Precalculus in addition to polar coordinates, vectors, parametric equations and plane curves, and other advanced topics. The material in this course provides a strong preparation for Advanced Placement Calculus, with the study of formal calculus topics beginning in the second half of the year. The course covers all of differential calculus by the end of the year.  Students are exposed to the power of mathematical modeling through examination of real-world applications and interdisciplinary connections. Through this course, students develop the intellectual disposition to continue studying mathematics and related fields at a high level.
  • Statistics

    The goal of this interdisciplinary course is for students to conduct and assess statistical analyses by utilizing statistical tools and technology in order to tell a clear story with data that informs decision making. It serves as an introduction to the fundamental concepts of statistics involved in displaying, summarizing, and drawing inferences from data. Topics include generating statistical questions, sampling methods, exploratory data analysis, design of surveys and experiments, probability, sampling distributions, estimation, significance testing, and regression. Students frequently engage in hands-on activities and explorations to learn the concepts and how they are applied across a variety of industries. The statistical programming language R is used to wrangle and analyze real datasets. Through the work done in this class, students also practice the iterative nature of statistical analysis that includes asking questions, collecting data, exploring ethical considerations around data privacy, conducting statistical analyses, and generating conclusions.  Overall, this course prepares students to positively impact a world that is increasingly generating and utilizing vast amounts of data.
  • AP Statistics

    This course follows the College Board AP Statistics syllabus. The four main units of study are: data analysis, data collection and experimental design, probability, and statistical inference. This course differs from the non-AP statistics course in the rigor and type of content to be examined and in the quantity of work asked of the student. Topics are taught through extensive investigations of real-world examples. Students are required to take the AP Statistics exam in May.
  • AP Microeconomics

    The purpose of this interdisciplinary course is to give students a thorough understanding of the principles of economics that apply to the functions of individual decision makers, both consumers and producers, within the economic system. This course focuses on introducing students to the principles of microeconomics, placing primary emphasis on the nature and functions of product markets. Additionally, the course includes the study of factor markets and the role of government in promoting greater efficiency and equity in the economy. Relevant principles from game theory and psychology are also introduced. Concepts are taught and brought to life through a variety of means including readings, class simulations, visiting visual art faculty, projects, and debates. At the conclusion of the course, students are required to take the AP Microeconomics exam.
  • Calculus

    This course is designed for those who plan to continue the study of calculus in college and/or who may need this background for courses in applied sciences. The curriculum introduces the fundamental concepts of calculus, including the ideas of limits, continuity, and standard differentiation formulas and their applications. Through applications of derivatives to problems in maxima and minima, students gain experience in the power of calculus. In addition, basic methods of integration are discussed. This course does not prepare students for either of the Calculus AP exams.
  • AP Calculus AB

    This course in differential and integral calculus follows the AP Calculus AB syllabus. Topics covered include limits, continuity, differentiation and integration of algebraic and transcendental functions, optimization and related rates, areas bounded by curves, volumes of revolution, techniques of integration, and differential equations. An emphasis on the role of calculus in real-world applications exposes students to the power of mathematics and encourages strong critical thinking skills. This course prepares students to pursue advanced topics in mathematics, science, and business.  Students are required to take the AP Calculus AB exam in May.
  • AP Calculus BC

    In addition to completing the syllabus of Calculus AB, this course completes the preparation for the BC level of the AP exam in calculus. Students are exposed to the power of calculus through examination of real-world applications and interdisciplinary connections. Through this course, students develop the intellectual disposition to continue studying mathematics and related fields. Additional topics include integration by parts and by partial fractions, improper integrals, L’Hospital’s rule, first-order separable differential equations, logistic differential equations, infinite series and power series, and the calculus of parametric, polar, and vector functions. Students are required to take the AP Calculus BC exam in May. 
  • Topics in Linear Algebra and Multivariable Calculus

    This course is designed for twelfth grade students who have completed or are currently taking AP Calculus BC and are interested in studying mathematics or a related field at the college level. Linear Algebra topics include vectors and matrices in 2-space and 3-space, matrix algebra, systems of equations, fundamental subspaces, and a cursory treatment of eigenvalues and eigenvectors. Multivariable calculus topics include derivatives of parametric equations, partial derivatives and applications, double integrals in Cartesian and polar coordinates, and integrals in the plane. Students will explore the history of some of the most important theorems and processes in mathematics such as the Fundamental Theorem of Algebra and Lagrange multipliers. This course will also serve as a way for students to explore the nature of mathematics through reading excerpts from books on some of the most important mathematical developments and discussing mathematical rigor and proof.
  • McCartney Scholars

    During his 15 years as a mathematics teacher at Rivers, Dan McCartney earned a reputation as one of the school’s most engaging, charismatic teachers, with a unique ability to ignite in students a love of math and of learning in general. The McCartney Scholars Program is a special initiative intended to nurture a passion for mathematics among students at Rivers and memorialize a teacher who gave so much of his spirit and energy to Rivers students.
    Those accepted into the program have the opportunity to develop their mathematical skills through access to special advising, additional coursework, and guest speakers with careers in relevant fields. Students who are McCartney Scholars are expected to engage with the community around math which may involve peer support, being a TA, making presentations, and completing a capstone project. . Each year, all rising juniors with a passion for math are eligible to apply to the program, and up to six students are selected. Students will hold the distinction of being McCartney Scholars for their junior and senior years.

Upper School Faculty

  • Photo of David Runkle
    David Runkle
    Math Department Chair, Math TA Program Coordinator
    339-686-2394
    University of North Carolina at Chapel Hill - MS
    Elon University - BS
    2020
    Bio
  • Photo of Elizabeth Wendorf
    Elizabeth Wendorf
    Math, McCartney Scholars Faculty Advisor
    339-686-4494
    Wesleyan University - MA
    Wesleyan University - BA
    2011
    Bio
  • Photo of John Adams
    John Adams
    Mathematics, Director of Technology and Innovation
    339-686-4510
    Bates College - BA
    2015
    Bio
  • Photo of Jean Beecher
    Jean Beecher
    Upper School Math, JV Girls Hockey Assistant Coach
    339-686-4493
    2024
    Bio
  • Photo of Mary Carroll
    Mary Carroll
    Upper School Math, Math Club Advisor
    339-686-2261
    Carleton College - B.A.
    Reed College - MA
    2024
    Bio
  • Photo of Matthew Dias Costa
    Matthew Dias Costa '13
    Mathematics, Varsity Boys' Soccer Assistant Coach
    339-686-2419
    University of Pennsylvania G.S.E. - M.S.Ed.
    Bowdoin College - B.A.
    2019
    Bio
  • Photo of Kristin Harder
    Kristin Harder
    Math, Course Counseling
    339-686-2455
    Dartmouth College - MALS
    Williams College - BA
    Hotchkiss
    2005
    Bio
  • Photo of Klay Johnson
    Klay Johnson
    Mathematics, Admission Interviewer, JV Boys' Basketball Head Coach
    339-686-2360
    St. Lawrence University - MAT
    St. Lawrence University - BA
    2020
  • Photo of Victoria Mizzi
    Victoria Mizzi
    Interim Upper School Dean of Student Life, Mathematics
    339-686-2264
    Queens University - BEd, BS
    2016
    Bio
  • Photo of Christine Pynchon
    Christine Pynchon
    Grade 9 Dean, Mathematics, Varsity Softball Head Coach
    339-686-2459
    Colby College - BS
    2014
    Bio
  • Photo of Alice Sorensen
    Alice Sorensen
    Mathematics, JV Field Hockey & Girls' Ice Hockey Head Coach
    339-686-2451
    College of Charleston - MEd
    Brown University - BA
    2014
    Bio
  • Photo of Kimberly Webster
    Kimberly Webster
    Mathematics, Interim Grade 9 Dean
    339-686-2389
    Williams College - BA
    Boston University - MEd
    2002
    Bio
  • Photo of Keith Zalaski
    Keith Zalaski
    Math, Varsity Boys’ Basketball Head Coach
    339-686-4581
    Amherst College - BA
    Tufts University - MA
    2015
    Bio
333 Winter Street Weston, MA 02493
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