More than Processing: Math in Word
by Excerpted with permission
In his book, author Bob Johnstone presents a collection of teachers' stories about computer use. What follows is the account of John Vincent, a veteran teacher who worked for ten years with laptops in elementary classrooms. John's ideas for using Word to explore geometry open the door to a vast world of play and learning in math, using what we typically think of as only a word-processing program.
My background really is that I've always been fascinated by the possibility for technology to impact teaching and aid learning. I'm not interested in what the technology is, this goes way back before computers to video recorders and overhead projectors.
Word basically works with a nineteenth-century concept of the way that we communicate. It says, here's a page, here's where you write—you start at the top left-hand side, and you write down the page. It's very hard to break out of that unless you use a special graphic element like a text box. And it's very difficult to put pictures into your page without breaking your formatting and messing everything up; you've got to be quite skillful with the tool to even begin to cope with putting pictures into Word. And when it comes to putting in moving images, sounds, and so on, then you really are running into considerable difficulties, because Microsoft never thought of those concepts, it thought of Word purely as a word processor.
But the kids we teach don't receive information like that anymore. For our young people, receiving information through solid words is an unusual method of reception. They receive information through television, from computer games, via moving images. We have grown up with words, but even we now receive most of our information visually or aurally. Microsoft has never caught up with the fact that what we actually want to do on the page is to slide words around, to slide information around, to be able to rearrange our pages in a flexible way.
Ironically, if you go to Word's drawing tools, you've got exactly the opposite situation. The drawing tools are totally free—you draw something on the page wherever you want it to be, not where the program wants you to; you move the object around, you press Ctrl and drag it and Copy it, you change its size and rotate it at will.
So inside a nineteenth-century word processor, you've got a twenty-first-century understanding of what you actually need in a very simple drawing and graphics package, including a whole lot of mathematical understanding.
For example, if I draw a line and click on it, I can get it to report to me its exact size. If I draw a shape like a triangle [from AutoShapes on the Format menu], I can get it to report not only its size, height, and width, but also the angle of rotation that I've got it at. I can rotate my line and therefore I can get accurate angles. So if I want to do a forty-five degree angle, I can put it at exactly forty-five degrees. Now you're starting to get all sorts of geometric accuracies. And because you've also got exact sizes you can use this to do things like draw a completely accurate scale map of the classroom.
Again, with shapes [click on Basic Shapes from the AutoShapes toolbar], if I press the shift key I get an equilateral shape, which I can then distort—all sorts of mathematical language comes into this. I can also rotate the shapes, and turn them into 3D. Now I've got a whole range of 3D shapes as well, which themselves can then be rotated. So with the drawing tools in Word there are these amazing geometric, scale, and aspect relationships. It's middle-years math basically.
I discovered these tools by playing and experimenting with the program. I can remember the day I found the 3D shapes, because another teacher asked me if I knew anything that did 3D shapes. And I thought I'd seen something like that on the menu bar. But I had no idea that it could do this sort of thing. I've always thought it extraordinary that a word processor should have all these mathematical capabilities.
One of the beauties about when you draw a map of the classroom with Word is that everything is floating, nothing is fixed. So you can do scale maps of all the furniture in the classroom, then rearrange it. I used to get the kids to organize our classroom virtually, before we actually rearranged the furniture in the room. They actually came up with designs for the classroom that they were going to live in for the year. This was grade five or six, ten- or eleven-year-olds.
You can fix things to the screen, but most of the time everything's floating. That's why you can tessellate, fit things together with no gaps between them. The simplest one is an equilateral triangle. Then the next question is "Why do triangles tessellate and pentagons don't, however much you rotate them?" And of course the answer eventually lies in the number of degrees in these angles. If they don't add up to 360, then you're never going to get tessellation.
You can build irregular shapes that tessellate, too. There's all sorts of things you can do with this; it's a question of where your imagination stops, really. That's why I became interested in Word's drawing tools, and that's just scratching the surface, really.
As well as the creative stuff, you can also do things on a more formal level.
For example, if you're studying polygons, you can create a library of polygons. And because Word's text boxes are also graphics, you can also construct meanings and descriptions around the polygons as well. So I would get kids to make a library of polygons (and a library of 3D shapes as well), the program has every shape up to an octagon. Then I would ask them to construct their own nonagon and decagon. (I would use this in conjunction with MicroWorlds, which is a more dynamic program, and we would actually open out the angles, and investigate the internal and external angles.)
One thing that I think is not used enough in Word is text boxes, which can fit together with things like this. So I would be asking students, having experimented on a page doing various things with triangles, to reflect on them using text boxes. Or, you can make a hyperlink to another file, where you can show all your tessellations with the triangle.
For the very visual kids, and kids who want to be very visual, there are other elements here, too. You've got a whole lot of menus that no one knows very much about. For instance, you can bring in pictures from the clip gallery or another file. So, for example, you can create 3D shapes with faces on them.
The very first time I had a class with laptops, as with most classes, there were a number of kids who were every weak with words, very poor at communicating verbally. They found it very hard to put sentences together to say what they wanted to say, and they found it incredibly hard to write. So much so that, after five years of compulsory school they had stopped writing, because that was not their thing.
Interestingly enough, like so many of these kids, they would draw, or they would have a very fine sense of humor, or they would be very dramatic, or something. At the time I was reading a lot of stuff on learning styles, beginning to put two and two together. Then I got the laptops, found MicroWorlds, and put it on the computers. We experimented with telling a story through a multimedia format using moving pictures, animations, and sounds. And these kids just went wild, these same kids who had so much trouble with writing.
It became more and more clear to me that what we were looking at was a deprived group of children. We condemn them to fail in school, because they can't communicate in words, but in fact they have enormous skills of communicating in multimedia.
It's really a matter of equality, of equity in the classroom—both in math and in literacy; we must give these children the opportunity to work multi-modally, not just mono-modally. But what so few people [understood] is that it's the computer that will let us do this. Because with the computer, you can allow children to work in a much more multimodal way; it provides the opportunity to differentiate learning. Especially when you've got one-to-one computing as in the laptop classes. Or a pod of, say, fifteen computers between two or three classrooms, where you don't need the computers all the time, but the children can be accessing them much of the time.
So now, instead of saying to the kids, "This is what you're going to use, and this is the way you're going to do it," you can say, "This is what's available; see what you can do with it."
In medicine, if a technology that offers very great potential comes along, or a new medication, and a doctor refuses to deal with it, or associate with it, or experiment with it, or actually use it, that doctor very quickly ends up out of a job. In teaching, by contrast, we have license to completely subvert every new technology that comes in, or just to ignore it. We may pretend to accept it, while actually pushing it to one side, and we can still be lauded as a good teacher.
To cope with new technologies, you need to be so adaptive. The teacher is so crucial in the equation—you can't just sit back and let it happen. No matter what the technology is, it needs hard work. And if you're not prepared to put in the hard work, it won't happen. And that is particularly true with computers.
Few teachers are able to work with a weak pedagogical framing because most of us are insecure. But if you throw a computer into the mix, you've got to have weak pedagogical framing, otherwise you never discover what's possible, you never discover the creativity. And in today's schools, it's often a matter of security. The secure way of doing things is to make sure you know exactly what's going to happen. And that doesn't work with computers.
Reprinted with permission from I Have Computers in My Classroom—Now What? by Bob Johnstone. Copyright© 2006. Published by Heinemann, Portsmouth, NH. All rights reserved.
Excerpted with permission