AT Classic: A Philosophy of Arithmetic Instruction

Abstract

Fehr covers a wide range of topics in this article by necessity, because of his broadly conceived view of arithmetic instruction. He reminds us that arithmetic instruction must be determined by a set of several interrelated concerns: societal and children's needs, the structure of the discipline, and a knowledge of how children learn. Perhaps more than anything, though, I consider this article a classic because of Fehr's discussion of problem solving. To Fehr, problem solving is the ultimate goal of arithmetic instruction—a position that has a very familiar, contemporary ring. However, Fehr's views about how to develop problem-solving ability. which were an outgrowth of his commitment to field theories of learning, are less familiar and largely ignored. Since some recent studies tend to support Fehr's views, they warrant the attention of classroom teachers and researchers alike. By reprinting this article from April 1955. it is hoped that another perspective will be injected into the debate on how to teach problem solving. (The reader is referred to another classic by Fehr, “Theories of Learning Related to the Field of Mathematics,” in The Leaming of Mathematics: Its Theory and Practice, the Twenty-first Yearbook of the NCTM.)