Weapons of Math Instruction

Tentative Sequence

The following can be telescoped for students who demonstrate greater ability.

Grades Coursework
1–4 Euclidean geometry (Trachtenberg) arithmetic
5–6 Euclidean geometry prealgebra
7 Euclidean geometry elementary algebra
8–9 linear algebra elem. alg. & analytic geometry
10 linear algebra elem. alg. & trigonometry
11 linear algebra calculus
12 lin. alg. & diff. eq. calculus

Possible Texts

The Trachtenberg Speed System of Basic Mathematics (Die Trachtenberg-Schnellrechenmethode), Jakow Trachtenberg, tr. Ann Cutler and Rudolph McShane.

Elements of Algebra (Vollständige Anleitung zur Algebra), Leonhard Euler, ed. Christopher James Sangwin.

Elements (Στοιχεῖα), Euclid, tr. T. L. Heath (vol. 1, vol. 2).

Geometry (La Géométrie), René Descartes, tr. David E. Smith and Marcia L. Latham. Note: preceded in the foundation of analytic geometry by Omar Khayyam’s Discussions of the Difficulties in Euclid.

Algebra, I. M. Gelfand and A. Shen?

Textbook to be written after Divine Proportions: Rational Trigonometry to Universal Geometry, N. J. Wildberger.

2 responses to “Weapons of Math Instruction

  1. Bending and Stretching Classroom Lessons to Make Math Inspire. Thought you’d enjoy this article at nyt.com today as well as the related videos.

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