Students come to us as energetic and inquisitive problem-solvers, and Roxbury Latin’s mathematics department aims to capitalize on their inherent curiosity. We seek to cultivate in our students an appreciation of the power and utility of mathematics in solving real-world problems and a deep understanding of the logic and beauty that pervade the subject. In addition, we want our boys to enjoy math and to have fun exploring challenging and creative ideas and problems.
In order to navigate an increasingly complex world, students must be effective problem solvers. They must be able to identify a problem, decode relevant information, and devise a strategy to attack the problem. Approaching an unfamiliar problem is perhaps the most intimidating prospect for a student, and we emphasize that the process of grappling with difficult problems, and not shying away from them, is how students improve as problem solvers. Over the course of their time at Roxbury Latin, students develop the skills that enable them to tackle a wide array of problems. In all of our classes, there is no substitute for thorough and careful preparation, and students must take primary responsibility for their learning. While it is natural to see each year of mathematics as distinct, we aim to provide for our students a framework in which they can see their mathematics knowledge growing continuously rather than in discrete steps. Our mathematics teachers are excited and energized by the subject and convey their enthusiasm using a variety of teaching methods and technologies.
Based on prior experience and achievement, students in Class VI are initially divided into advanced and regular sections. Later, the boys are divided into an accelerated section (which reaches AP Calculus BC in Class II); an advanced section (which reaches AP Calculus AB or BC in Class I); and one or two regular sections (which reach AP Calculus AB or AP Statistics in Class I). The groupings are reasonably flexible so that students may move from one section to another when deemed appropriate by the department.
A unique feature of our program is our Class IV course, Math-Science Investigations (MSI). This course, taken by all members of Class IV in heterogeneously grouped sections, provides an interdisciplinary experience for our students.
In addition to coursework, interested students have the opportunity to challenge themselves in outside competitions, both regionally and nationally. These contests include Mathcounts, the Math Madness online competition, and the sequence of American Mathematics Competitions: the AMC-8, AMC-10, AMC-12, AIME, and USA(J)MO.
Math 7 is designed to introduce boys to a variety of new ideas and to solidify crucial concepts and skills. Traditional pre-Algebra topics such as fractions, decimals, signed numbers, percents, area and volume, and ratio and proportion are reviewed in a problem-solving context at different points throughout the year. As a foundation for future math and science work, students are introduced to the fundamental principles of data analysis, probability, and statistics. In the latter part of the year, students learn fundamental algebraic techniques such as solving equations, factoring, and analyzing linear functions.
This course presents a comprehensive overview of the fundamentals of algebra. The course emphasizes algebraic techniques, particularly factoring, solving equations, and analyzing linear functions. Strategies for solving problems form an important component of the course, and an assortment of word problems is covered throughout the year. Other topics covered include real numbers, operations with polynomials and algebraic fractions, inequalities, systems of equations, radical expressions, and quadratic functions. Students explore functions extensively, namely polynomial, rational, exponential, and logarithmic functions. Depending on the section, other topics studied may include conics, sequences and series, and an introduction to trigonometry.
Math-Science Investigations (MSI) is a lab-based course that provides Class IV boys the opportunity to investigate powerful ideas in a hands-on context. Boys do this in an interdisciplinary context, exploring ideas in science, technology, engineering, the arts, and mathematics, collectively known as STEAM. Boys are active learners in this course, discovering concepts through investigation and experimentation and completing projects, often in collaboration, of increasing complexity over the course of the year. They also become immersed in the “maker” culture, building the creative confidence to use newfound skills, tools, and technologies to approach challenging problems.
Geometry provides an introduction to geometric techniques and ideas. Though different sections approach the subject in different ways, all sections develop results involving lines, planes, triangles, circles, polygons, perpendicularity, congruence, similarity, area, and volume. Algebraic techniques are revisited through topics such as inequalities, proportions, and coordinate geometry. Mathematical writing, axiomatic reasoning, and proof form a natural component of the curriculum. Further topics may include vectors, constructions, and similarity transformations. The text for the course is Jurgensen, Geometry.
Analysis continues the development of topics studied in Algebra. Exponential, logarithmic, trigonometric, polynomial, and rational functions are revisited in greater depth. Other topics include sequences and series, probability, conic sections, and polar coordinates. The text is relevant chapters from Brown, Advanced Mathematics.
AP Statistics is the science of collecting, analyzing, and drawing conclusions from data. The course covers four major topics: exploratory data analysis (students use graphs and numbers to describe and analyze data); experimental and sampling design (students discover the proper ways to collect data via sampling and controlled experiments); probability (students learn fundamental principles of random variables and sampling distributions); and statistical inference (students draw conclusions from data using confidence intervals and tests of significance).
AP Calculus is one of the masterpieces of mathematics. In this course students extend the concepts of slope and area to all the nonlinear functions they have studied. This Advanced Placement course is offered at two levels: AB and BC Calculus. Both sections study the derivative and integral in depth, covering topics such as tangent lines, curve sketching, related rates, implicit differentiation, slope fields, optimization problems, areas, volumes, and differential equations. The BC Calculus class also covers advanced integration techniques and Taylor series. The text for the Class I AB and BC courses is Larson and Edwards, Calculus of a Single Variable. The text for the Class II BC course is Stewart, Calculus: Concepts and Contexts.
Advanced Topics in Mathematics
Advanced Topics in Mathematics is designed to equip students with the tools and techniques needed to succeed in college-level mathematics courses such as Linear Algebra, Group Theory, and Real Analysis. In this course, students learn a variety of proof techniques while covering topics whose mastery is essential for success in upper level math courses. These topics include logic and set theory, number theory, counting and induction, relations and functions, and cardinality. In addition, students will be asked to think deeply and creatively, to solve non-standard problems, to formulate conjectures, and to take mathematical risks with the goal of seeing the subject through a lens that reveals its true beauty. The text for the course is Vandervelde, Bridge to Higher Mathematics.
Multivariable Calculus (offered in alternate years) extends the concepts and techniques of AP Calculus to functions of several variables. The course integrates the content of college courses in Linear Algebra and Vector Calculus, and the unified approach emphasizes certain overall themes (e.g., a nonlinear function behaves locally like its derivative). Topics are treated with a high degree of mathematical sophistication and rigor, and most skills from the relevant college courses are covered as time allows. The text is Hubbard and Hubbard, Vector Calculus, Linear Algebra, and Differential Forms.