What is the purpose of computers in education?
To cut the feedback time down.
That is all they can do, and all they should do.
Why? Feedback is vital for learning. Without feedback, you have nothing that most people would think of as "learning".
Proper use of computers in education requires some "out-of-the-box" thinking. Proper use of computers would largely eliminate the test structures we have now, but anybody who proposes that is promptly shot as a heretic. (Have you noticed this schizophrenic approach to education reform, where we all agree that schools really need reform, but consider the way schools are doing things now holy, such that any significant reform is immediately discarded?)
What if, instead of spelling tests, we required students to always use a proper spellchecker? A proper spell checker is one that dynamically underlines misspelled words immediately, instead of being run as a discrete process at the "end" of writing something. Proper spell checkers provide immediate feedback. A traditional spelling test provides feedback after a day or more, long after it is too late to learn anything from the test.
From experience, I know this is an extremely effective way to learn spelling. It has certainly improved my spelling, and I am very surprised that more programs have not adopted this technique. (Certainly my Iron Lute, when it gets a spell checker, will do this!) If you haven't used this type of spell checking, you might think that people will just lean on it, but it doesn't work that way. You want to avoid seeing the red underlines, and you get a sort of odd pleasure from typing an entire paragraph without seeing any red underlines. Where the "check at the end" spell checkers breed dependence, the "immediate feedback" spell checkers breed independence.
Suppose we just spot-check the students on spelling? Suppose, trusting in the students constant exposure to immediate feedback, we just take spelling for granted in all but the toughest cases? After all, every time the student types something is a spelling lesson, from their first essays to their final Senior Essay. That's far more time spent on spelling overall then the current education system can boast!
This is the place of computers in education; not to entertain the student, not to play stupid "learning" games that fail to teach anything useful, but to provide immediate feedback that no human can, all the time, every time, not merely augmenting but replacing many mechanisms we've grown attached to.
Sure, it's obvious that computers can't do certain things. Computers don't do a good job of detecting homonyms, for instance. But just because computers can't do one job isn't a reason to discard all the other things they can do better then a human! The need for humans in the education process isn't going to go away anytime soon, but their time is valuable. Instead of arithematic and spelling drilling, they should be doing the tricky stuff.
The "homonym" example demonstrates the other pitfall of computers in education: They absolutely must not be used for more then they can do! The students will learn from the computers what the computers are teaching, and it is very important to ensure that what the computers are actually teaching matches what the humans intend to teach. One can use a "grammar checker" to check for most homonyms (few homonyms are the same part of speech), but grammar checkers are very bad, teaching a very simplified and incorrect version of English. Grammar checkers should definately not be used like the spell checkers are, because they teach the wrong thing. (They might be useful to a teacher to assist in grading, but even then I'd be very cautious about it.)
There are a lot of other benefits to this approach; for instance, see the conclusions section of this paper for a real life example of a computer education system that fits with this idea. But I'm proposing an even finer-grained feedback cycle, starting as early as possible, and carefully tuned to what computers are good for, and what humans are good for. Let the computers do what they can do, and let the humans do what they can do.