The authors express their appreciation of the helpful criticism they have received from students in the Newton (Massachusetts) High School; ...
Is it grammatically correct to use the definite article before the proper name of a high school?
pretty much none at all. You just have to memorize it. For instance, most state universities in the USA don't use "The" in the title, but a few do.
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The use of "The" in front of schools and universities makes about as much logical sense in