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Effectiveness was generally measured in these studies by higher-than-predicted gains on measures of achievement in math and reading. The emphasis had thus shifted to the behaviours of effective teachers and the relationship between teacher behaviour and pupil learning.

I don't understand the first sentence, especially from the part "by higher-than-predicted gains on measures..." Is the preposition "by" here a part of the passive structure?

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"Effectiveness was generally measured in these studies" — as you recognized, this is a passive construction. The people conducting the studies were measuring the effectiveness of some teaching technique.

"... by higher-than-predicted gains in measures of achievement" — when you teach a student, you expect them to improve in some "measure of achievement" (for example, test scores) because they have knowledge and skills afterwards that they didn't have before you taught them. If students who were subjected to a technique improved even more than the usual without the technique ("higher-than-predicted gains"), the technique was judged effective.

"... in math and reading." — the kinds of "measures of achievement" that they were typically interested in were the ones that measured skill at mathematics and reading comprehension.

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