I honestly hadn’t meant for them to trap themselves. It just happened that way.
I was in front of a class of future elementary teachers many years ago.  We were discussing the four basic arithmetic operations we all learn in elementary school.  More specifically we were discussing alternative algorithms for these operations.  That is, we were discussing different paper/pencil procedures that could be (and have been) used besides the specific procedures we typically learned.
As happened every year with this topic, the students were amazed that there were other procedures that would produce correct answers in these situations, and they weren’t sure whether to be excited or disconcerted, especially when they liked some of the ‘newer’ procedures better than the ones they learned.
Common reactions were always “Are you sure it’s OK to do it this way?” or “Why didn’t we learn these other methods in school?”  (A perennial favorite was the Austrian Algorithm for subtraction – a procedure which requires no ‘borrowing’!)
We discussed these reactions at some length, along with the pros and cons of the procedures, how and when they might be used in a classroom, and how different procedures could help different youngsters.
That particular class period, as they were becoming more comfortable with the various algorithms and indeed, with the very idea that such different procedures/algorithms even existed, one of these future teachers remarked “Well, the important thing is helping a student be able to get the right answer.  If they can do that, then I guess it doesn’t matter so much which procedure they use to get it.”
The whole class nodded in agreement, as if the obvious had somehow been stated, and they were all pleased with the ‘bigger picture’ perspective they now had about ‘basic skills’.
As I said, I hadn’t really planned it this way, but I couldn’t let the opportunity pass.  “Excellent point,” I said.  “After all, if your real-world problem calls for you to subtract, it doesn’t matter whether you use the common algorithm, or the count backwards trick, or the Austrian algorithm we just learned, or . . .” (big pause here) “or the newest and easiest of all procedures – a calculator.”
The almost-but-not-quite-amused silence that followed was so ‘pregnant’ I almost felt guilty.  Almost.  On the other hand, it was one of the most effective arguments about what basic skills are (and aren’t) that I had seen – and they had made it themselves!
Normally, when I tell this story, I move on to make my usual calculators-aren’t-evil point.  But I’ve done that in this space (too?) often recently, so, I’d like to close with a slightly different observation.
Almost always, when folks talk of ‘basic math skills’, they are speaking of addition, subtraction, multiplication, and division.  Most of us would agree, and there is much truth there.  But too often, when we say that, what we are usually talking about is the specific set of paper/pencil procedures we learned.  We say ‘addition, subtraction, etc’, but what we are often visualizing is ‘carrying, borrowing, times tables, lining up rows’ and so on. And many of those things aren’t necessarily needed in various answer-getting procedures.   I’ve seen future teachers do these procedures perfectly by rote, only to later discover they don’t really understand the concepts of regrouping, place value, etc, which are crucial to student learning/understanding.
The point is both a small one and a huge one.  The ongoing discussions of which/whether ‘basic math skills’ are still needed in today’s technological world is made easier if we understand that these same skills/operations are not specific rote procedures.