Just Teach Them To Solve for X

A few people have asked me to keep posting to this blog instead of just consolidating.  So, I'm keeping this bad boy around, but I'll start posting these to my other blog as well. Incidentally, before writing this post (or looking at any comments on blogs), I created a video yesterday that is on my personal blog today dealing with this issue of metaphor. I want to assure you that none of this is ever meant to demean, disrespect or insult anyone - just provoke thought.   

Gertrude the Cognitive Acquisition of Newly Developed Youth Learning Achievement of National Data (CANDY LAND) Specialist approaches me in mid-lesson.

"Your schedule says 'math block' right now and I see your students sketching pictures."

"They're creating metaphors for the concept of 'x.'  So, they start with the picture and then describe the process using the metaphor."

"Why not just teach them to solve for x?"

"I want them to understand how variables work.  Most of them have no idea that 'x' isn't simply a magical number, but actually an independent variable.  If they can't understand how 'x' is used, how will they understand how it is used in life?"

"Look, I see kids drawing pictures of tools and bridges and revolutionary figures.  Why not just teach them to define and use 'x' instead?"

"Metaphors are how we as humans make sense out of the abstract.  It's the bridge between pure abstraction and the concrete, terrestrial reality we experience.  It's used by children and philosophers alike to grapple with a complex universe."

"I don't mind when you have the students replace the slates with paper, Tom.  That's fine with me.  I get it. They can go back and look at previous work."

"Yes, but you miss the full potential of paper when we simply duplicate how we used it with slates.  The genius of paper is how we can use it to construct knowledge rather simply copy processes."

"Your job is to teach them truth.  Cold, hard reliable truth.  Metaphors are messy and muddled and confusing - like a scavenger hunt through a swamp. It should be like clockwork.  Mechanical.  Bits and pieces as clear as day."  I find it odd that he uses two or three metaphors himself to make sense out of his own theory of knowledge.

"What if learning is messy?  What if confusion is the process that leads to clarity?  What if simply memorizing a computational practice does little help students understand how a variable works?"

"Are you arguing that we should make math more confusing?"

"The world's greatest teachers were often confusing.  They understood that truth involves metaphors."

"Like who?"

"Let's start with Locke, Rousseau, Plato, Erasmus, Jesus."

"You aren't Jesus, Tom."

"Good point."

"Look, it's just that metaphors are dangerous.  There's too much room for confusion."

"That's exactly why we need them.  Life is dangerous.  Learning is dangerous.  A bad metaphor can launch a war.  I want my students to know this.  I want them to see that language shapes our perceptions of reality."