Mathematics

Vanishing HexagonsA major goal in our teaching of math at San Francisco Waldorf High School is to develop the student's capacity for mathematical thinking in a creative, rigorous, and comprehensive way in addition to building the traditional skills of algebra, geometry, and calculus.

High school mathematics is taught in the block system as well as in ongoing track classes. The track classes meet four times a week for a period of fifty minutes each session throughout the year. These classes develop mathematical reasoning and problem solving through the traditional topics of algebra, geometry, advanced algebra, pre‐calculus, calculus, and advanced calculus. The blocks, on the other hand, are four weeks long and meet during the usual main lesson time. Here, the teaching of mathematics has a different focus. Thanks to this brief but intense immersion into the world of mathematics, the students have time to explore mathematical ideas in a more creative way and within a historical context.

Some of the blocks include the ninth grade Permutations and Combinations block which looks at the many faces of chance: fate, destiny, randomness, risk. The tenth grade Trigonometry block begins with determining when two polygons are similar. Once introduced, the sine, cosine, and tangent functions are used in calculations involving right triangles and eventually in deriving the Law of Sines and the Law of Cosines for (not necessarily right) triangles. In the eleventh grade, the Projective Geometry block formalizes one of the central principles of perspective art: parallel lines meet at infinity. This block includes elements at infinity, the principle of duality, perspectivities and projectivities, projective generation of point and line conics, cross‐ratio and invariance, and, more specifically, study of the theorems of Desargues, Pascal, Brianchon, and Pappus, as well as the Fundamental Theorem of Projective Geometry. The twelfth grade Calculus/Chaos block introduces the historical and mathematical development of calculus and includes elementary aspects of both differential and integral calculus.