Freshmen and seniors at about 200 colleges across the U.S. take a little-known test every year to measure how much better they get at learning to think. The results are discouraging.

At more than half of schools, at least a third of seniors were unable to make a cohesive argument, assess the quality of evidence in a document or interpret data in a table, The Wall Street Journal found after reviewing the latest results from dozens of public colleges and universities that gave the exam between 2013 and 2016.

At...