SCIENCE AND MATH

Learning science and math at Steiner takes place in each of the four high school years in rich Main Lesson Seminars, in ongoing courses and electives, and in laboratory experiences.

Major concepts are chosen for presentation and development in each Main Lesson Seminar in a deliberate progression from concrete topics in ninth grade to sophisticated abstract concepts in senior year. In the physics sequence, for example, ninth graders typically engage in hands-on work with combustion engines and electric motors to grasp concepts including force, pressure, and energy while seniors conduct careful observations of optical phenomena and read the words of Newton and Feynman in order to understand wave-particle duality and the goals of quantum mechanics.

Examples of Main Lesson Seminars in Science and Mathematics include, among many others, Engines and Energy (9), Trigonometry (10), Botany (11), and Modern Chemistry (12). In addition to the core work in the Main Lesson Seminars, students are required to take at least three years of mathematics (four years are strongly recommended) and are able to choose from a variety of electives.

COURSE CATALOG

Geometry with Algebra (9)

Algebra with Trigonometry (10)

Math Applications (11/12)

Relations & Functions with Linear Algebra (11/12)

Calculus (11/12)

Calculus II: Vectors, Proofs, and Discrete Math (12)

Computer Science (9/10)

Advanced Computer Science (11/12)

Combinatorics Seminar (9)
The practical aim of this main lesson is to explore the manner of mathematics that arises out of everyday life whenever we make or encounter an ordered arrangement. The theoretical aim is to transform fundamental ideas (basic counting principle, permutation, combination) into deeper structures such as the Catalan numbers. Along the way students encounter some number theory (the φ function), some new notation (n!), and some extensions of ordinary algebra (the Binomial theorem). They also craft narratives that exemplify combinatorics in ordinary experience, refining these until they are true to life rather than to the artificial world of “word problems.”

Geometry Seminar (9)

Conic Sections Seminar (10)

Trigonometry Seminar (10)
This main lesson intends a complete introduction to basic trigonometry. Beginning from student constructions, the course moves rapidly beyond the rudiments (i.e. 30-60-90 and 45-45-90 triangles) by means of 36-54-90 triangles discovered in the regular pentagon. An analysis of arcs and central angles in circles leads to the Law of Sines, which is then a basis for Ptolemy’s theorem; this in turn yields angle addition formulas that enable further trigonometry—now without triangles. The course finishes by introducing spreadsheets as a way to use angle addition formulas to develop a reasonably comprehensive trig table from the angle measures listed above.

Geodesy and Cartography Seminar (11)

Sequence and Series Seminar (11)

Numbers and Values Seminar (12)
Science Elective (10)

Advanced Biology (11/12)

Human Development (12)

Physiology Seminar (9)

Ecology Seminar (10)

Embryology Seminar (10)

Botany Seminar (11)
The Botany main lesson is an in-depth look into the world of plants. Students become familiar with the cellular organization of the plant, as well as the metabolic process of photosynthesis and cellular respiration within the plant. The class discusses the evolution of the plant kingdom by studying the major taxonomic groups of plants with regard to the order in which they evolved and the adaptations that developed. Students conduct a variety of hands-on work that includes growing plants, looking at slides, observing and classifying plants in the park, and exploring the diversity of plant life represented at the New York Botanical Gardens.

Environmental Science Seminar (12)

Evolution and Genetics Seminar (12)
Science Elective (10)

Advanced Chemistry (11/12)

Organic Chemistry Seminar (9)
An introduction to organic chemistry in the 9th grade continues the work of nutritional chemistry done in the eighth grade to greater breadth and depth. Students are taken on a journey through typical organic reactions. Photosynthesis and respiration are presented as basic life processes for plants and animals, providing the rudimentary carbohydrates which eventually create starch and the cellulose of plant structure. Dehydration and hydrolysis produce more complex substances, and carbonization leads to fossil fuels. Following the paths of life processes brings the student an appreciation of the complexity of the chemical processes that bring substance from the external world to the bodies of living beings. Once folded into the Earth those same substances break down forming other compounds antithetical to life processes, hydrocarbons.
The formulae and structures of hydrocarbons provide a challenge for 9th graders exercising abstract thought and visualization. After a study of hydrocarbons, sugars are looked at through the process of fermentation and the slight oxidation of alcohols, aldehydes, and finally organic acids and their place in amino acids and proteins. The synthesis of esters, many of the scents of the natural world, concludes the block. Students learn to recognize the names and formulae of organic groups, synthesize formulae, and balance chemical equations.
Each student is expected to create a main lesson book from essays written for homework while tests and quizzes provide feedback to both student and teacher with respect to the student’s academic progress. Laboratory experiments introduce students to lab equipment and its use, along with the use of significant figures and observation, and the scientific method.

Stoichiometry Seminar (10)

Atomic Theory Seminar (11)

Modern Chemistry Seminar (12)
Laboratory (9)

Advanced Physics (11/12)

Engines and Energy Seminar (9)

Statics & Dynamics Seminar (10)

Electricity & Magnetism Seminar (11)
By eleventh grade, students move beyond the mechanical systems of the earlier years and into the realm of electromagnetic systems. These phenomena are imperceptible to our direct observation, and involve a far higher level of abstraction. These are the foundations that chemistry and mechanics are built upon.
The juniors cross the conceptual divide between the discrete, solid bodies we studied in tenth grade, to the continuous, immaterial field. Now they are challenged to form an exact understanding of an area of effect detectable only by its influence on other bodies. We consider electric and magnetic fields first separately and then united in the phenomena of electromagnetic radiation.

Light & Modern Physics Seminar* (12)
COURSE OFFERING MAY VARY SLIGHTLY FROM YEAR TO YEAR.
CORE COURSES APPEAR IN BOLD.