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Note how this page greets you with whatever name you put into the prompt box earlier. Welcome to the amazing possibilities of interactivity on a web page! So let's get started.
First of all, you need to open your calculator.
If you don't like where the window popped up, you can move
it. At the top of the calculator window, hold the cursor down on the word
Calculator and drag.
If the window isn't big enough, you can resize it. At the
bottom right corner of the calculator window, hold the cursor down on the
slanted grey lines and drag.

Now take that result --
-- and add it to .....
Note how whatever number or words you entered became part of the next paragraph flush left or centered depending on what style class I specified. Try it again with a different word. Click OK. In a similar way, your name passed earlier from the prompt box to the page.
At that point, a teacher can get the form to validate the students' answers. For example, if the students answer one way, they proceed to a certain page. If they answer anything else, they get a gentle "error" message and a redirect to another page. Or whatever.
That's one good reason why students are better off using this form / script combo rather than their graphing calculator or the calculator built into their operating system. The technique illustrated here gives the teacher a way to deal with common errors via the validation methods.
By displaying their answer elsewhere on the page, the teacher can sometimes make the students see how it doesn't fit. If it does fit, they'll get the feeling that they're contributing positively. Either way, it makes them accountable for their answers and makes it impossible for them to gloss over it without understanding it.
Now this is just addition and simple text, but you can do almost any math within the form. After teachers do some usability testing with students, I'll bet that they will develop tutorials that can really help some of them. Some of them won't be able to learn this way ("It's too impersonal."), but others will.
These techniques are in their infancy. It will be interesting to see what some imagination can bring to the process.
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