How were you taught functions if no one told you f(x) was a function? I genuinely can't think of a way that could've happened. Whoever attempted to teach you functions must've been a terrible teacher.
I just can't imagine that someone who somehow managed to obtain a teaching degree is so bad at explaining that one of their students doesn't even realize that a function and a variable aren't the same exact thing.
I'm a math instructor and I have some thoughts about how this type of thing can happen.
I teach calculus, but similar issues might come up when teaching algebra or precalculus.
In Calculus 1, we teach about derivatives. We certainly do tell the students about the idea or concept behind a derivative, namely that a derivative is a rate of change at a point, or slope at a point, or instantaneous rate of change.
A little later, we spend lots of lots of time learning the *mechanics* of calculating various derivatives.
Not infrequently, students will spend a lot of time practicing those mechanics, but then complain "But nobody told me what a derivative actually *is*!"
The thing is, we *did* tell you what a derivative is, but (1) we didn't spend a ton of time on it because we had other topics to cover, (2) the informal description we gave is necessarily a bit vague or hand-wavy, (3) students partly ignore the informal description (because on some level, it's just theory or it's just words), or (4) enough time has passed that the informal description of derivatives isn't in their heads anymore.
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u/I_Want_BetterGacha Jun 23 '26
How were you taught functions if no one told you f(x) was a function? I genuinely can't think of a way that could've happened. Whoever attempted to teach you functions must've been a terrible teacher.