Imagine you've drawn large squares on the floor, say ten of them, and numbered them sequentially. Imagine further that you've got a particularly clever dog, and that you train him to trot one box down the row every time you call out 'plus one'. Imagine further still that you train him similarly for 'plus two', 'plus three', et cetera. So if the dog's standing on square four, and you call out 'plus five', he'll move to square nine, effectively adding the numbers. You've taught a dog how to add, right?
Wrong. The dog doesn't know how to add. The dog doesn't understand numbers, addition, or any of the abstract concepts contained therein. The dog may have some innate sense of quantity (two bones is more than one bone) but even that's up for debate. You've programmed the dog to give the illusion of numeracy, but the dog is still, in the final analysis, a dog.
Why do I bring this up? A course I'm taking this semester is taught by a... gentleman... who programs computers the same way this clever hypothetical dog adds numbers. And of course, he is grading me.