3D Geometry

From our last two posts on math education and teaching geometry in grades 5-7, you should understand that math education is about developing the capacity to think. By 8th grade, we move into 3D geometry which capitalizes on previous skills and carries them further. Yet, it is important we do this not just through head-exercises but through hands on skills. (There is a connection between what the hands do in youth and how an adult thinks later on.)

3D geometry centers around the Platonic Solids. These forms are logical forms that cannot be constructed any other way than they are and therefore represent eternal truths. 8th grade geometry teaches the forms through clay and paper modeling as well as drawing.

The Deeper Reason for Teaching 3D Geometry

Math is a method for developing pure thinking. Consider the cube above. Imagine you were asked to develop a 2D layout which would later be cutout and put together as a 3D cube. Could you do it? If so, what would it look like?

The above is what it would look like, including little flaps that would form the hinges which join the different parts of the form together.

By doing exercises like these, we form in the students the capacity for projective-imaginative thinking. In other words, they build the muscle to think through a problem to the end in pure concepts. Then, they join that with a tangible, real-world expression in the form of the 3D cube.

The History of Pure Thinking

After the practical geometry of the Egyptians and Babylonians, the Greeks advanced geometry as a tool to cultivate the mind. These intrepid thinkers strove to discover perfection. Geniuses like Plato wanted to discover the divine, eternal principles underlying the visible world. It was felt that mastering the world of thought made one simultaneously a moral and beautiful human being. This took place as an inner, super-sensory process. In other words, mastering the good, beautiful, and true depended on one’s ability to develop a purely inner capacity.

If we look at the arc of Egypto-Chaldean practical geometry to the theoretical and 3D geometry of the Greeks, we see a shift from the sensory to the super-sensory. This is not without tremendous implications when you consider that pre-Greek cultures were virtually all authoritarian in one or another way. Either the pharaoh, king, or priest told everybody how to live their lives. With the Greeks dawned a new impulse. In many cases, they threw off their kings, began debating in the public square, and even questioned the gods. The city-states were all fiercely independent from one another and tolerated no tyranny. This was arguably the first step towards FREEDOM, and it all depended on cultivating the capacity for super-sensory thinking.

What is our goal in teaching 3D geometry?

Few, if any, modern people I know would tolerate Ancient Egyptian-Babylonian-style authoritarianism – benevolent, though it may have been intended in those past ages. After all, we in the west have no more kings, and ordinary citizens rail against any hint of such. We all want freedom, but freedom is not merely outer. No amount of license to act nor money nor any other sort of power will make a difference if we ourselves cannot direct our freedom with moral intuition. It is the good, beautiful, and true which ultimately free us from the shackles of a purely animal existence, which we can – and often do – descend to as human beings. Yet, in order to realize it, we have to touch something that doesn’t exist in the outer sensory world. We have to touch something divine and eternal in ourselves, something which we can only sense if we have developed the super-sensory organ of thinking. And, that is why we practice 3D geometry in 8th grade.

How we can help you

Enkindle Academy offers prerecorded and live lessons for students in grades 5-9. We teach all academic subjects plus fine arts, creative writing, and empowerment groups for teens. We also offer 1-on-1 tutoring on all subjects including fine arts. Visit our website for more info and for free sample lessons, and remember to subscribe for weekly updates, tips for homeschooling, and special offers.