The arts of number
Mathematics
The Quadrivium in modern dress: proof, procedure, and cumulative reasoning worked by hand, taught to fluency in a small class or one to one, K–12.
- Grades K–5
- Grades 6–8
- Grades 9–12
Mathematics at Athena is the Quadrivium in modern dress: the disciplined study of number and quantity, taught as a cumulative art in which each step is earned before the next is attempted. We teach the methods by hand — the algorithms, the constructions, the proofs — because a procedure one can execute without thinking is a procedure one truly owns, and because the hand that has worked a problem remembers it in a way the eye that has only watched does not.
How it is taught
An expert teacher at the board, a small class, and a standard held steadily. New material is demonstrated, worked together, then practiced to fluency; nothing is left half-learned before the class moves on. We prize correctness and the habit of checking one's own work — the quiet competence of a student who knows whether an answer is right without being told.
By grade band
In the early years (K–5): number sense, the four operations to automaticity, fractions, and the beginnings of formal reasoning. In the middle years (6–8): ratio and proportion, pre-algebra and algebra, the transition from calculation to argument. In the upper years (9–12): algebra through calculus, and geometry taught the old way — as a training in proof.
Materials
A workbook where one is used; otherwise paper, pencil, and the board. Roughly $0–25 per course.
Formats
Private 1-on-1 (all grades, in your home), with competition preparation built in, and small-group classes (Kindergarten through 3rd grade, in person in San Ramon).
Begin mathematics with a single class.
See the teaching before you commit to it.