Images of Math, and Mathematical Images

“Do you see what I mean?”

When we talk about understanding, we often use words associated with vision and sight. Yet there is so much to the concept of “understanding” that does not fit the conventional definition of something that is literally “visible.”

In my first year of teaching, 23 years ago, I asked my students to make “magazines” called “Math Illustrated.”  The purpose: tell your story.  What do the ideas we are learning “look like” to you?   Use words, pictures, graphs, equations,  artwork, poems – whatever else strikes you as useful. You’ve got your own story – just because we were all in the same room today doesn’t mean we all experienced the same thing. The world wants to read about you story!  (Or at least I do!)

This request of my students grew out of my own experiences with learning mathematics up to that point. I found that when I tried to make sense of math, I engaged in dialogues – trading words, metaphors, images with others.  I tried to “see” things from others’ perspectives.  I would “negotiate” meanings, (Is this what that means?  OK, I’ll settle on that for now.)  More often than not, I would come back and reconsider my decisions based upon new information.

Sharing thoughts with others is, for me, a central part of mathematics. Sometimes, the sharing is only with one’s own self.  I trade thoughts with authors past and present, though their written records. I try to see an author’s motivations, trains of thought, and goals, in light of my own experiences.  When I share ideas with colleagues or friends, we talk, write, draw, question each other. We look at each other and ask, “Do you see what I mean?”

Conversing with students, I try to initiate and sustain dialogues focused on building shared understandings, viewpoints, and perspectives,  I seek to find out what the mathematics “looks like” to that student, in light of their experiences.  I wonder if I can I see it the way they are seeing it. I try to make math an ongoing conversation where we’re all looking at something (and maybe not always the same thing!) and have lots of share about what we are “seeing”.

I’m never been quite sure that anyone else “sees” an idea in the same way as another person.  That, to me, makes things really interesting! That will be the goal of this blog – to illustrate stories and experiences of learning math.