I am of the opinion that students need to learn what a calculator is doing in order to use it properly.
Here’s an example – calculating with decimals can be somewhat tedious and there certainly is a point of diminishing returns with regard to the length of problem sets assigned for practicing concepts.
But, if students don’t develop number sense and don’t really understand what a calculator is doing in a situation as simple as adding two decimal numbers, they can get unexpected results and not be sure whether or not they’ve made a mistake.
Suppose someone needs to add 0.547+0.453
Entered into a calculator, the answer is 1
No big deal – IF you understand how adding decimals works. If you don’t, this answer might be confusing – where did all the other digits go?!
There’s always a balance to be struck between drills and “big picture” ideas and it’s a different balance for different topics and different groups of students.
But, as Professor Wu points out, basic skills vs. conceptual understanding is a bogus dichotomy.