The Failure of Arts and Crafts

Every once in a while I’ll do what might be called a manipulative project with a class. No, that doesn’t mean I teach them to manipulate those around them. These are teenagers and they’re already plenty good at that. What it means is that the students work with some solid object- manipulate it if you will. In pre-Algebra, we use something called Algebra tiles to connect math concepts to physical objects. In trigonometry it might involve using a compass and measuring angles in a circle. In Geometry, which has a more obvious connection to the physical world, we do a variety of things.

This week, we were studying medians. The medians of a triangle are the line segments connecting each vertex (corner) of the triangle to the midpoint (what it sounds like) of the opposite side. There are 3 of these in every triangle. Medians have certain properties, and they happen to all 3 cross at a single point. This is called either the median or the centroid of a triangle. This point, almost magically, is exactly 2/3 of the way from the vertex to the opposite side. It’s also the center of gravity of a triangle, which means the triangle will balance on your finger if you put your finger on that point.

So here’s the project:
1. Draw a triangle (I provided rulers to help).
2. Cut it out (scissors provided)
3. Find the midpoint of each side by folding across and matching up the corners.
4. Draw lines from the 3 midpoints to the opposite corners.
5. Measure the lines to see that the place where they all cross is 2/3 of the way from the vertex to the opposite midpoint.

Pictorial directions are given in the book. The book suggests that this activity should take between 15 and 20 minutes, which seemed a bit optimistic, but I am at a loss to describe exactly what happened when we tried to do this. Let me start by saying that in a room full of normal, reasonably intelligent students, that I was the only one to complete this task in a 30 minute period.

When the period ended, the room looked like a confetti factory and everyone was alternately laughing and tearing their hair out. Some people drew teeny triangles and couldn’t work with them. Some people completely folded the triangle and drew no lines. Some people connected the vertices with random points on the opposite side. Some connected the midpoints to random points on one of the other sides. Some made a drawing mistake and started making new triangles instead of just turning the paper over. I can say with conviction that everyone at least drew triangles and cut them out. Beyond that, your guess is as good as mine.

I blame the system for this epic mini-disaster. These kids have clearly been deprived of the requisite arts and crafts training required to complete tasks requiring small motor skills. My own skills were honed by years of gluing popsicle sticks to each other, making collages, creating potholders with loops, flowers out of tissues and weaving paper baskets. The changeover to electronic toys and the rise of cell phones are yielding disastrous results. Not being a trained arts and crafts professional, as my mentors clearly were, I am at a loss to say how we can improve this situation. I fear for our future.