Mathematics

The mathematics department teaches skills necessary for success in an increasingly technical world and prepares students to think carefully and productively about patterns, figures, numbers, functions, and applications. The department believes each student learns best and feels most successful and confident when she covers the material at an appropriately challenging pace. Consequently, beginning in Class III, sequential courses of differing pace are presented to meet the needs of individual students; the faster-paced sections study the material in more depth. In the Upper School, three years of mathematics and one semester of quantitative reasoning are required; it is strongly recommended that students take mathematics through Class VIII and almost all students do.

Mathematics Courses 2007-2008

Class I

Students study arithmetic using whole numbers, fractions, and decimals to understand concepts and strengthen skills. Manipulatives are used to help illustrate concepts. Other topics include measurement, geometry, estimation, and problem solving. Mental and written computation is emphasized but calculators or computers are used for appropriate activities.

Class II

The mathematics curriculum includes fractions, decimals, percents, number theory, order of operations, measurement, 2 dimensional geometry, statistics, probability, and an introduction to negative numbers and equations. All topics involve individual and group activities and solving a variety of problems. Scientific calculators are introduced. Computer spreadsheets are also introduced and used during the study of graphing and statistics. This is the first year participation in the Elementary School Math Olympiads is offered.

Class III

Using a curriculum that emphasizes strong conceptual understanding, Class III students study algebraic expressions, 2 and 3 dimensional geometry, exponents and scientific notation, negative number arithmetic, and solving equations. They learn financial literacy through a computer simulation project and creative problem solving by participating in the Middle School Math Olympiad.

Class IV

Algebra 1
The course includes solving and graphing linear equations, exponents, polynomials, and solving and graphing quadratic equations. During the year students develop and refine their problem-solving and critical thinking skills. Students use scientific calculators regularly. Four sections of the course are offered, with two sections covering all standard Algebra 1 topics and two other sections covering topics at a faster pace.

Class V

Algebra 2
All students will study the core topics of Algebra 2: functions (linear, quadratic, polynomial, radical, exponential, and logarithmic), systems of equations, and some analytic geometry. The uses of the TI-84 graphing calculator will be introduced. All sections will study a unit on Data Analysis. Trigonometry will be included if time permits. The algebraic and graphical aspects of each topic will be emphasized.

Class VI

Geometry, Probability and Statistics
This course begins with a study of probability, combinatorics, and statistics. Then students study Euclidean geometry, including the properties of triangles, polygons, parallel lines, and circles. They solve problems involving similar figures, areas, volumes, symmetry, and triangle trigonometry, and learn the principles of logic by writing formal deductive geometric proofs.

Class VII

Precalculus
In this course students continue to study functions, including polynomial, rational, exponential, logarithmic, and circular functions, and their applications. Graphing calculators are used throughout the course. More traditional analytic and algebraic methods are also emphasized so that students will understand different approaches and techniques. Other topics covered include transformations of graphs and inverses of functions, solving equations and inequalities, and trigonometry. In addition, polar coordinates, conic sections, sequences and series, and parametric equations are introduced if time permits. The department usually offers Precalculus sections that move at three different paces; the fastest pace is designated Honors Precalculus.

Class VIII

Calculus AB and BC, Introduction to Calculus and Statistics and Data Analysis courses meet the requirement for a quantitative course during senior year. In addition, the mathematics department offers second semester 8-week mathematical seminars.

AP Calculus
AB and BC Calculus are both AP courses, and students are required to take the AP test in May. BC Calculus is a faster paced, more demanding course. Beginning with the concepts of limits and continuity, students go on to learn the definition of the derivative and its applications, and progress to theory, techniques, and applications of integration. Additional topics are included as prescribed by the AP syllabus. Graphing calculators are used as a tool to enhance understanding of the concepts and facilitate problem solving.

Introduction to Calculus
Students study the crucial concepts of the derivative and the integral, including their meaning in relation to both graphs and formulas. They also study applications of both concepts to a variety of real-world situations.

Statistics and Data Analysis
Students study the fundamental concepts, techniques and applications of statistics and data analysis, including reading, analyzing, and producing graphical representations of data, making valid inferences based on data, and detecting misleading uses of statistics. Contemporary examples from other subjects such as social science, biology, and environmental science are included.

Computer Science

Computers are essential tools in higher education and in the job market. Students are introduced to computer applications throughout the Winsor curriculum and the math department offers a course in programming.

Computer Programming
Students learn the specific details of the C++ and Matlab computer programming languages, strategies for approaching programming problems, and general algorithmic (systematic, step-by-step) thinking. Programming requires an ability to think precisely and symbolically, and a fascination with problem solving.