Formalism in arithmetic programs

Abstract

Much of the adverse criticism of the teaching of arithmetic in the past can be summed up in one sentence. The complaint has been that too often the learning has been “mere formalism.” In this eontext the term “formalism” means that mathematics becomes a game played with symbols according to fixed rules. Little or no attention is paid to the “meaning” of the symbols; that is, the nature of the objects, operations, and relations that are symbolized. Lack of understanding by students, lack of motivation, lack of satisfactory achievement, lack of ability to apply mathematics in problem solving, and other more specific complaints are often attributable, in the last analysis, to excessive formalism.

Mathematics education: What was it, what is it, and what will it be?

“…For him, arithmetic instruction was truly education and the development of young people, not just rote learning. Although Pestalozzi exaggerated with arithmetic exercises in special tables and delved into excessive arithmetic formalism (Hartung, 1962), we must recognize the merits he has for the development of arithmetic instruction. His works inspired numerous educators (e.g., Tillich, Harnisch, Diesterweg, and Grube) of the 19 th century to begin studying and developing arithmetic instruction, thus continually improving it (cf.…”