What level of calculator use is acceptable for students?

[robertliguori]

Yet another advantage of symbolic answers: When you screw up, it’s easier to find the problem, once you see the answer.

I have a program that takes a decimal, divides it by pi, sqrt(2), and sqrt(3), and tries to convert these results to fractions. Very helpful for that sort of thing.

Calculators have no work to be screwed up. If you can translate a question to calculator form and enter it in, you have solved the problem.

The calculator has become a crutch.

You argue against calculators being left behind, not against being trained to use them.

So students, in your view, should be able to learn to do rough arithmetic by osmosis, just by watching their calculator does without being told how it does it?

Basic math is a prime example. We learned (way back when) that multiplication was addition of a number to itself the number of times that the other number specified. We also had to memorize the multiplication table up to 12. We just as well could have learned the theory and solved the problems with an external look-up table as with the one they forced us to internalize. Learning concepts is a different beast from plugging numbers into anything, be it an equation, a table, or a TI.

Let’s scale back a bit.

Let’s scale back a bit more. A bright calculator user might very well put in X and 1/Y into the product rule function on the calculator. [hijack] (Would this work?) [/hijack]
Getting new formulas to put into the calculator will require math geeks, or even former math geeks. But the average math learner isn’t expected to be able to. And again, if your calculator can call up the power rule, then you have the potential for symbol manipulation that a person who memorized it does.
See again about the user interface. A calculator with a product rule button but no way to see what it is doing does not “know” the product rule. It is unfair to compare it to a person that does.

But I’ve seen those things used as a crutch too often, especially in high-school.

So what? If the purpouse of the activity is to stand, then what does it matter what supports are used?

[There’s a difference] between learning a formula/algorithm and learning how to use a calculator function.

Yes, there is. That is because learning a function != learning how to use a function, just as typing in a function into a calculator does not equal a user interface that lets you plug things into it. A calculator with an integrate button is the same as a student that can integrate but has not memorized the rules. In order to make a comparison between person knowing formula and person + calculator knowing a formula, both need to be able to “recite” the formula. If the formula is hidden from the user, then the user does not “know” the formula. This is not an argument against calculators; it is an argument against data hiding.

[robertliguori]

Dammit. The “The calculator has become a crutch.” should be the list of times where you should have brought a calculator if you need one. The postInsightful() function on my TI needs tweaking.