“The essence of mathematics resides in its freedom.”
“To ask the right question is harder than to answer it.”
In 1912, Romiett Stevens studied classroom questions and found that two-thirds of the questions required repeating exactly what was in the textbook. In 1956, Benjamin Bloom looked at classrooms and found that 95 percent of test questions required recalling information—not processing or synthesizing, just recalling. In 1970, Meredith Gall repeated Stevens’s experiment and found that “60 percent of the questions students hear require factual answers, 20 percent concern procedures, and only 20 percent require inference, transfer, or reflection.”1 Nearly forty years later, in the ...