The recommended program at The Dragon Academy includes six years of Math, up to Calculus, and six years of Science, covering the three critical branches of Biology, Physics and Chemistry. We reason that these disciplines embody distinct modes of thinking about and knowing our universe. They represent other cognitive faculties which should be developed for a rounded and balanced intelligence. And they are crucial for basic citizenry and participation. You cannot really take part in the modern world without scientific and mathematical literacy.

The ways in which maths and sciences are usually taught makes them seem detached from the student's natural way of thinking about things, requiring considerable quantities of memorization, without readily apparent practical utility. Most people, even those who did well in high school maths and sciences, have little recall of the content of those courses in later years. Those who go on to specialise in these disciplines find that they must considerably revise what they were taught.

Mathematics and the sciences in high school should be foundation studies. Students should not be buried under a mountain of facts which will fade from their memories shortly after their exams. Instead they should discover and truly grasp the great organizing concepts of mathematics and the sciences. These are the concepts which have permitted us to interpret, foresee, and shape our world. These are the concepts which can be used to extend the range of our experience.

These maths and sciences concepts should not be taught in isolation from their historical, philosophical, or aesthetic contexts. These concepts should greatly enrich other areas of study, from the physics of dance, the psychology of myth, the inspirational effect of Newton's Opticks on the imagery of poets, to the religious controversies stirred up by Darwinian theory.

Nor should these concepts be taught once, and then left behind. They should be introduced as accurately as possible given the student's present level of understanding and background, then reappear in increasingly complete and complex forms again and again as the student progresses through the grades of high school.

The Concept of Concepts

The structure of knowledge is web-like, rooted in connectedness and derivation. There is an underlying unity in what we know. One idea follows from another. Critical, at times revolutionary, concepts spring from our deepest values, from how we view humanity and nature.

Mathematical and scientific knowledge are not mere accretions of facts, theories and methods. They have grown organically, moulded by revolutionary discoveries and the concepts that led to and sprang from these discoveries. Each of these great concepts necessitated the re-evaluation of accepted knowledge, admitted new problems for scrutiny, and transformed the ways we conceived of the world.

We believe that the right education emphasizes this structure, allowing students to explore the unity of knowledge, to understand the history of ideas. In the process, they will create an interior culture for themselves, owning what they learn. They will practise, and gain skill, in disciplined inquiry, and through it discover the true and proper rewards of learning—not grades, not admissions, but excitement and confidence.

The progression in our programme is spiral. Key ideas are first presented in a form and language which can be grasped by the student. These ideas are revisited with increasing precision and power until the student is rewarded by mastery.

Mathematical reasoning is not an arcane talent limited to a brainy few. It is something all human beings do naturally, and the failure to develop this ability deprives us of pleasure as well as a necessary skill. We are convinced that proper teaching of mathematics can dispel its mythical "hardness".

Like art, math orders and illuminates the world, but most students of most high school math courses would not believe it.

The best scientists seek the truth but know that one day they may be shown to be wrong. The true scientific attitude, as Stephen Toulmin has suggested, is "that a person's rationality is displayed in how his or her beliefs change in the face of new evidence or experience." Science progresses through conjectures and refutation. We invite our students to discover the best reasons available, in place of the passive acceptance of established facts.

We also encourage, following Kuhn, the study of the framework or paradigm in the context of which scientific work takes place. We look at the historical frames for past discoveries, and we attempt to perceive and clarify our own contemporary paradigm. In so doing, we free students from the tyranny of scientific authority, and so release areas of art and critical interpretation.