Liberal Art #5—Geometry

Next up in the discussion is Geometry. I think this art should feel more comfortable than some others because it shows up on almost every one’s high school transcript. We all did geometry, right? Unfortunately, we didn’t necessarily do geometry in the the classical tradition.

In The Liberal Arts Tradition, Clark and Jain give us a hint about why geometry is ubiquitous in our syllabus:

From the seventeenth to the nineteenth centuries geometry became synonymous with clear and certain knowledge, the obsession of the modern era.

But classical geometry is and always has been all about Euclid. His Elements was the standard text for centuries, and why shouldn’t we still use it? It’s not like geometry is something today that it wasn’t before, and that tradition alone seems as if it would make classical education come alive for the modern student. Clark and Jain come to the same easy conclusion:

So, for those searching for a classical liberal arts paradigm for the study and teaching of geometry, the answer is found in a return to Euclid.

I don’t think you’ll be surprised to know that Charlotte Mason felt the same way about geometry and Euclid. The Elements appears on the PNEU programmes for the upper forms as part of the work in mathematics. (You’ll want to read what Brandy says about all this at Afterthoughts.) Miss Mason appreciated Euclid for the ideas conveyed in geometry. She wanted the wonder to be a part of the process.

How living would Geometry become in the light of the discoveries of Euclid as he made them! (Philosophy of Education, p. 233)

I feel myself more in need of learning this way than being in a position to suggest how you might teach this way. Clark and Jain urge the practice of drawing the constructions that illustrate the theorems.

Besides Euclid’s focus on deductive proof from first principles, his lessons also contain an element of visual artistry and delight: constructions. Constructions are drawings of the theorems in order to visualize or create them….The constructions aid the reason to conceive the abstract proofs and help connect the wisdom to the wonder.

Timing prevented my being a part of the discussion, but a group discussed this visual presentation of Euclid and did exactly what they are suggesting here—they drew the constructions and shared their work on the AmblesideOnline forum (membership needed to view—easy and free). They used this book, which I still plan to purchase and use with my last high schooler at home.

When so much of recovering the liberal arts tradition is open to doubt and discussion, and educators often find themselves casting about for whys and wherefores as well as ways and means, it’s nice to have something so fixed and accessible among the various liberal arts. Geometry for the win!

Copyright 2018 Karen Glass


Link to all the posts in the Liberal Arts Tradition discussion.

(Some links are affiliate links.)