# Mathematical Blunder #5

Vector products are non-associative. Apparently a neuron misfired as I wrote out the properties for the cross product of two vectors. Fortunately, one student was on their toes and asked, “Are there more properties than are in the textbook?” To be honest, there are but the one of the ones I happened to list was not. Nevertheless, board blunders are gateways to great explorations. I had fun demonstrating the concepts with two long sticks, a stack of dry erase markers and my thumbs.

By the way, to my wife who researched the usefulness of technology in math instruction, that is a key place where technology does improve math instruction. Don’t you think a computer visual in 3d would be more effective than my thumbs? It seems like my training in OpenGL (3d computer visualization toolkit) would come in handy just for this.

## 5 thoughts on “Mathematical Blunder #5”

1. You know, just the funniness of the situation will probably stick this thing in students’ minds. So yes use broomsticks, sponges, thumbs, anything.

I don’t know about college students, but in lower leves kids certainly need opportunity for some hands-on experimentations themselves. I’ve used pencils to illustrate to kids how an angle can ‘open’ and be bigger or smaller. I can just see my daughter, when she’s ready for that, trying all sorts of objects to do the same thing.

But computers are VERY good too. They just aren’t always there, whereas pencils or thumbs usually are!

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2. When i was teaching the cross product this last semester, I did so by having individual students represent vectors using their bodies; one student would lie on the floor; another would stand where the first student’s feet were, and a third student would have to come up and try to place himself at the correct location and angle. (The scaling is way off, but you can’t do anything about that.)

So this is a situation where 3D computer visualization is nice but I happen to think that 3D *physical* visualization is better.

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3. I think you both make a great point. Technology does not REPLACE other instruction methods, but can augment it.

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4. The other problem is that with physical manipulatives you can get a spontaneous response generated a lot faster. That’s why when I give a class using beamer slides, I still like to be able to go to the board and write a bit more.

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5. It’s important to remember the definition of technology. It is so broad! Especially in terms of education. In my research, I even found an article where technology was defined a triangular (or as Timothy would say, trinangler) pencil grip. Using technology does not mean staring at a TV / computer screen! Though that is always good too…

Good for you, dear, for using some creative techniques in a college classroom! Your students are so lucky!

🙂

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