The goals of PBAs mathematics program are:
• To develop skills in analytical reasoning and critical thinking
• To encourage precision and elegance in problem solving
• To enhance understanding and develop mastery by connecting the concrete and the abstract
• To foster the love of mathematics
In the third, fourth, and fifth grades, students develop the foundational skills of logical reasoning, arithmetic, and problem visualization through the use of simple diagrams. The curriculum in these grades is based on Singapore Math, designed to develop deep conceptual understanding and mastery without resorting to rote memorization or “drill.” This provides students with a strong base for the pre-algebra and algebra curricula of the seventh and eighth grades.
In sixth and seventh grade, students begin a formal analysis of radicals, exponents, and polynomials, while retaining a firm hold on the concrete and the visual: they develop spatial sense through the study of shapes in two and three dimensions, use coordinate geometry to plot points and curves, and explore data with the help of probability theory and statistics.
Eighth-grade math at PBA is equivalent to Algebra I and Honors Algebra, the first-year math course at most local high schools. Students study linear equations and inequalities, polynomials and their roots, factorization, parabolas, and the quadratic equation. Advanced students may cover additional units in geometry, trigonometry, and introductory calculus. Our recent PBA graduates were placed in Honors Algebra, Geometry, and 11th Grade Algebra Trig as incoming freshmen.
PBA’s math curriculum emphasizes connections: between arithmetic, geometry, and algebra, between math and science, and between math and daily life. These connections help motivate students to explore new mathematical concepts and methods. Drawing a diagram representing the components of an equation illuminates the solution of the equation; studying microorganisms leads to an appreciation of scientific notation; crashing toy cars turns into an analysis of velocity and acceleration and hence also of quadratic functions.
Choristers’ lives are filled with math: buying souvenirs during international tours requires a grasp of unit conversion; music class makes daily use of fractions, cycles, and periodicity. PBA boys do not question the relevance of mathematics in their lives. On the contrary, they have a genuine appreciation of its power to make sense of their world. Learning mathematics is a group activity. Students gather data together, discuss the best ways to solve a problem, collectively correct homework, and give oral presentations of their work to their peers. At the same time, the flexibility of the curriculum allows individuals to flourish. If a student needs to review earlier concepts, he receives support. If a student can consistently work above grade level, he has the opportunity to do so.