Our school shall have no faith-based math. Before I set off an Internet flame war (or is it too late already?!): I'm not talking about religion right now. Except maybe I am?
The Calvin & Hobbes strip above really nails the experience of many students in math class. Doing well in math amounts to taking things (formulas, for instance) on the authority of the textbook. Students who do well in math class are those who can best memorize these bits of dogma.
Obviously, this has nothing to do with actual mathematical understanding.
I know that this idea sounds incontestable — and, well, it is. Of course students should understand what they're doing in math!
Yet this principle is broken in nearly every textbook, in nearly every class.
I'm reminded of this today as I prepare my economics lesson for the afternoon. We're reading a popular book on economics — I won't mention the title — and are trying to understand how supply and demand curves shift when products are taxed.
The students are struggling to understand it. They're model students: reading carefully, testing their comprehension. But they're frustrated. I should be able to help them, because I should have a full understanding of the topic at hand.
The thing is: I don't. And the book is no help.
The book — at least this portion of the book — is, in effect, faith-based. It doesn't explain taxation the way it claims to. It doesn't matter how hard the reader works: they're stuck in faith-based math (or, in this case, faith-based economics). They're forced to kowtow to the author, and simply assume the theory makes sense.
I'll see what I can do for the class — I may need to bring in an outside economist to help us make sense of this. I'll certainly own up to my own non-understanding, and help the students explicate the gaps in their understanding.
That is, I'll help them see what they don't see.
And that's useful, in the short-term. But here's a long-term promise we can make for our school:
When studying any analytical, reasoning-based subject, students will never be expected to take anything on faith. We'll inculcate them in the truth that, if some idea (a math formula, an economic concept, a chemistry… chemically-thing!) has been understood by someone else's mind, it can be understood by their mind.
And we'll rear them in the conviction that achieving this understanding — capturing its complexity in their own head — is one of the most beautiful experiences available to us humans.