I am indebted to Professor G.M. Wilson for the title of this paper. In a book entitled What Arithmetic Shall We Teach, which he published through Houghton Mifflin Company in 1926, Professor Wilson says that his findings justify him in recommending a drastic reduction in the amount of computational arithmetic to be taught in elementary schools. He had found in various communities that practical life demands very little training in addition, subtraction, multiplication, and division. It is for the purpose of promoting this idea of, drastic reduction that he wrote his book. The reader is almost persuaded that the book should have been entitled, What Arithmetic Shall We Not Teach.