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This slays large populations of students on that first exam, and seems to be a serious mental block for them: whether g = +9.8 or -9.8 (units suppressed, substitute the English version over metric if you like). I teach that the sign can't be determined unless a coordinate system is defined, which is a separate but critical step in setting up any problem, but they like to rush. Many will inadvertently (or with intent) define a coordinate system (e.g., up is positive), which naturally works the signs into the algebra, but then at the end, will say "well g is always -9.8" and introduce a sign error when they get out their calculators.
I've taken to teaching that g=+9.8 or g=-9.8 is the incorrect way to think about it. Rather, g has merely a value of 9.8, and the sign is an "artificiality" that has nothing to do with g per se. The pushback I get is that "9.8 is the same as +9.8" and I push back in return on that but to skeptical looks.
My question is: is there a good mathematical argument I can cite (aside from a coordinate system) for why +9.8 and 9.8 are not the same thing? Or am I myself wrong?
Stefan Jeglinski
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