Education absolutely increases IQ test scores but wether its an increase in intelligence itself whatever that may be is questionable.
There is some alignment between IQ tests and academic work; an academic background gives you a few tricks for solving those kinds of problems.
It's also not just the case that the "bottom is being raised", but also that the whole distribution was shifting.
I think these kinds of things make it unlikely education is explaining at least the rise part of the curve. To the extent the fall is in a subset of these types of measures of settings it also might not be (but it could be).
The more recent decline has been less well-documented although there are multiple studies using multiple measures that have shown this, so I believe it is a trend at least in some regions of the world (developed, western). I have a fuzzy memory that the decline is stronger with verbal measures (as opposed to nonverbal) but I might be misremembering that.
Education is strongly related to IQ/g/general cognitive ability but they're not perfectly correlated. I think when I looked this up a week ago or so, the best estimates were like 0.50 in a general population sample.
Clinically a discrepancy between IQ and educational achievement is important, as it points to someone not getting resources they need etc.
So yes, they're related, and yes, education could explain general population trends over time, but no they're not the same.
"I'm not sure what an I.Q. is. Dr. Nemur said it was something that measured how intelligent you were--like a scale in the drugstore weighs pounds. But Dr. Strauss had a big argument with him and said an I.Q. didn't weigh intelligence at all. He said an I.Q. showed how much intelligence you could get, like the numbers on the outside of a measuring cup. You still had to fill the cup up with stuff."
Maybe that stuff is education.
[1]https://www.reddit.com/r/slatestarcodex/comments/oh6115/perf...
At the least I’d like to see something like an instrumental variables analysis.