Mathematics
	"Euclid alone has looked at Beauty bare."--Edna St. Vincent Millay Our goal in teaching students mathematics is threefold: Math and development of the adolescent The development of abstract thinking is the overarching achievement of the teenage years. Its use in understanding the world can yield order, harmony, and even beauty; it is balm for the turbulent teenage soul. The logic and rigor involved in the study of mathematics supports the development of abstract thinking. Triangles are everywhere around us, for example, but to understand them we must separate them from the physical world. This is sense-free thinking; this is abstract thinking. Mathematics is also fulfilling for the adolescent because there is almost always an exact answer at which we can--with rigor, logic, and thoroughness--arrive. As we develop this skill of "pure" abstract thinking through mathematics, we can apply it to other less exact domains, such as history and literature. Math and the real world No branch of mathematics, no matter how formal or abstract, is without significant applications in understanding the world around us. Knowledge of the physical and social worlds has been advanced and deepened through mathematical modeling and thinking. The connection between abstract math and real world utility is mysterious: Why should the seemingly chaotic real world be amenable to mathematical description in field after field? This profound connection, namely the power of using mathematics to understand the world, is of practical interest for students. No matter what field of study or work they pursue, they will find math useful. The wonder of math Many students arrive at Waldorf believing that they are not capable at math or that math is a dull and dry subject. Essential goals of the math program at Waldorf High School are to build confidence and to reveal the fun and beauty of mathematics.

	Counting and Probability
	Ninth Grade Main Lesson, Mr. Claus
	Counting is the most basic and elementary of all mathematical skills. But counting all the possibilities when a set of objects is grouped together in various ways is not so easy. If an automobile license plate consists of three letters followed by three numbers, how many possible license plates are there? How many different ways can a group of twenty students shake hands? This course introduces the study of combinatorics - the mathematics of combinations of objects in a finite set with specific constraints. Most importantly, by abstracting such a basic and familiar skill as counting, we help students to begin to bridge between natural and abstract mathematical thinking. This lesson will conclude with an introduction to the basic principles of probability.

	Math 9
	Ninth Grade Course, Mr. Claus
	This course begins with a thorough review of basic math and algebra skills. We continue with such algebra topics as inequalities, polynomials, rational expressions, roots and radicals, complex numbers and linear and quadratic functions. Word problems and problem solving are introduced.

	Mathematics and the Greeks
	Tenth Grade Main Lesson, Mr. Claus
	“The primary question is not what we know, but how we know it.” – Thales (ca. 600 BCE) The purpose of this main lesson is to explore one of the great contributions of the Greeks - namely their mathematics and how that helped the Greeks to understand the real world. While earlier great civilizations were interested in using mathematics for practical purposes, the Greek approach to mathematics was more philosophical. The important questions were not “What is true?”, but rather “Why is it true?” or “How can we show this is true?”. Assignments will generally include two parts: 1) a reading from a Greek philosopher or mathematician to be commented upon and 2) a set of related mathematical problems to be solved without the use of modern technological tools such as a calculator. Constructions, numerical analysis, and proofs will all be included.

	Math 10
	Tenth Grade Course, Mr. Claus
	This course is an in-depth study of geometry, focusing on the properties of triangles, quadrilaterals, polygons, circles and solids.  We cover the Euclidean constructions and deductive logic, including reading and writing proofs.  The course may also cover conic sections, symmetry and tessellations.  Ninth grade algebra is reviewed.

	Projective Geometry
	Eleventh Grade Main Lesson, Mr. Raizen
	Projective geometry is essentially a geometry that agrees with our sense of sight. The sides of a square that is moving away from us seem to become smaller. If the square is rotated, the right angles deform, and the square becomes a trapezoid. Parallel lines appear to converge and meet. Projective geometry arose from the attempts by Renaissance artists to accurately capture perspective on a two-dimensional canvas. Projective geometry captures the fundamental principles of such perspectives in simple and elegant ways that can, at the same time, be difficult to imagine. Flexibility of thinking and new concepts of space are developed.

	Math 11
	Eleventh Grade Course, Mr. Oliver/Mr. Claus
	This course is an exploration of analytic geometry and mathematical functions. The general path begins with a thorough review of basic algebra, concentrating on algebraic manipulation, coordinate geometry, and linear and quadratic functions. This path also introduces polynomial, exponential and logarithmic functions. The extended path cover polynomial, exponential, trigonometric and logarithmic functions, as well as introducing dynamical systems and “chaos theory.” Both paths include work with applications, word problems, and problem solving.

	Math 12
	Twelfth Grade Course, Mr. Oliver
	This course is an integrated approach to the study of changing variables with an emphasis on practical, real-world applications. It includes a pre-calculus level study of linear and nonlinear functions, trigonometry, exponents and logarithms, as well as series/sequences and iterated functions and introduction to the basic calculus concepts of the limit, derivative and integral.