Even if we did carefully define the arithmetic operations so that there was a unique correct answer to every sum, or at least a well-defined understanding of whether an answer was correct or not, I really don't envy the primary school teacher who has to make sure the children understand what's going on. (And you wouldn't be proposing teaching them some rules by rote, would you?) Notice that addition now has no identity and no inverses (because uncertainty always increases when you do an arithmetic operation, so you never get back to exactly where you started).
Which, going all the way down the rabbit hole, makes this the PERFECT time to discuss the meaning of "degrees of freedom" and their relative loss, doesn't it??
I agree that the whole reveal is not a good idea.
I think that where Val and I are coming from is that there's no compelling reason to teach students something that they will have to
unlearn later on in almost every other discipline they enter.
This is a serious problem for high school and undergraduate students-- and many of them
never quite manage to "unlearn" that business of "just add a trailing zero" which leads to errors even in college-educated STEM individuals, frankly. Their errors on this point have some pretty significant consequences (if you'll pardon the pun).
I don't see any compelling REASON to add zeros to 2.5 just so that I may add the value 1.689 to that value.
Simply align the decimals correctly and
add them, YK?
Maybe most 3rd-5th grade students really can't manage to keep this straight without the zeros-- but I guess I can't really wrap my head around that particular idea. Maybe that is my problem; I'm assuming ability that many students don't have, perhaps.
