Students in classical schools became masters of their own thoughts and words through the arts of the Trivium. Through the four mathematical arts of the Quadrivium, they began to gain knowledge about the world.
Geometry contains amazing truths about shapes, arithmetic about the kinds of numbers. Both of these disciplines were considered delightful because of the truths they taught, and useful because they developed strength of mind. Astronomy and Music showed that abstract mathematical truths can make sense of the motions of the heavens and of the human heart in response to rhythm and harmony. These studies opened up wider vistas leading to questions about the nature of the Maker of the Heavens, and the human soul.
Because mathematics requires little experience to see the truth of its starting points, students can come to know them with certainty and clarity. Schools should choose texts in these areas that begin from clearly known first principles to argue step-by-step to remarkable conclusions.
Yet the role of the Quadrivium has to be a matter for particular discussion in schools today. Algebra was unknown to ancients, yet it occupies the central role in the modern mathematical curriculum. Do algebra and calculus reveal truth and arouse wonder? Or are they merely problem-solving techniques that train student to think and respond like computers?
Quadrivium Resources Online
Euclid’s Elements – The complete Elements on-line with helpful notes.
Geometry: Seeing, Doing, Understanding. A proof-based text praised by many home educators. Jacobs also has an Algebra text.
The Key to Algebra series teaches basic algebra techniques and applications through workbooks that are not intimidating and easy on the eye.
Beyond the Test, the Institute Newsletter (January 2009, on The Quadrivium)