A geometry teacher's musings on CS Lewis's discussion of reasoning

Disclaimer: I'm a nerd. This post is just proof.

Our small group is reading CS Lewis's book, "The Weight of Glory" which is a compilation of various lectures he had given during WWII. The lecture we will discuss this week is titled "Why I am not a pacifist" which has very little to do with why it has me so excited but is very interesting considering all of the men in our small group are active duty military. ANYWAY, there is a wonderful discussion of reasoning that has the geometry teacher in me all excited. I am blogging about it now so that in the future if I ever return to teaching, I will remember this! (I wonder if I could make my students read CS Lewis in geometry class? hum...)

Lewis says that there are 3 elements of reasoning:

1) The reception of facts via either experience or authority

2) Intuition (perceiving self-evident truth)

3) The skill of arranging facts to yield a series of intuitions which produce a proof of truth or falsehood

I am particularly interested in #3 considering my graduate thesis is a formative evaluation of an instructional unit I created on proving geometric theorems which is possibly my favorite topic in all of math (and one of the most important topics in all of education IMHO...).

I LOVE the following quote:

"Thus in a geometrical proof each step is seen by intuition, and to fail to see it is to be not a bad geometrician but an idiot." (excuse me, but LOL! wouldn't I love to say this to my students sometimes? I'd probably be fired...) "The skill comes in arranging the material into a series of intuitable 'steps.' Failure to do this does not mean idiocy, but only lack of ingenuity or invention. Failure to follow it need not mean idiocy, but either inattention or a defect of memory which forbids us to hold all the intuitions together."

I personally can empathize with the defect of memory making it difficult to hold all the intuitions together. I guess I have my ADD to thank for that. But I so enjoy the process of untangling logic that once seemed jumbled and confusing in my head.

Furthermore, Lewis notes that corrections of errors in reasoning are corrections of either the 1st or 3rd element of reasoning because the 2nd element (intuition) cannot be corrected, nor supplied if lacking. At first thought, this was a depressing idea to me. I spent a considerable amount of time during my graduate research trying to uncover how to successfully develop deductive reasoning skills in students and to read someone so logically brilliant as CS Lewis claim that logical intuition cannot be taught was initially somewhat disheartening. Except that he follows it up by noting that it is extremely rare for intuition to truly be lacking, which brings me to the next quote I want to store for use with future students:

"Every teacher knows that people are constantly protesting that they 'can't see' some self-evident inference, but the supposed inability is usually a refusal to see, resulting either from some passion which wants not to see the truth in question or else from sloth which does not want to think at all." [emphasis mine]

Yes! One of the most frustrating things as a teacher is the inability to make a student "see" something that is self-evident (i.e. obvious)! And I couldn't agree more with Lewis' statement attributing the problem to sloth! I know that at times I have claimed not to understand something when really, I just didn't care to put in the necessary effort to exercise my brain to work hard enough to understand it.

This may seem like a nasty thing to say to a student, like something a lazy teacher who doesn't want to take responsibility for their student's success would say... but I actually kind of find this idea hopeful. Hopefully because it means that people most likely DO have the ability to understand logic if they are motivated to try. So my objective as a teacher is not so much to impart logical ability to my students as it is to motivate them to utilize the God-given logical reasoning they already have.