Education encompasses both thoughts and practical applications. One subject that is universally accepted as requiring a great deal of “thought” is mathematics. Since the ancient times, mathematics has been a subject taught at schools. The degree of emphasis on the subject has varied over time. Plato believed that mathematics, aside from its application, was the gateway to absolute truth and a necessity for the development of the mind. He advised that arithmetic, plane geometry, and solid geometry be taught in childhood (see age 254 of this edition of The Republic). Considering that plane geometry was still an active area of research (Euclid’s Elements was not written until approximately 80 years after the publication of The Republic) and solid geometry was in its infancy, Plato’s mathematical curriculum was radical, if not (by today’s standard) ludicrous! Cicero, Plato’s Roman counterpart, on the other hand, believed that mathematics was subordinate to oratory. According to him, “anyone who wants to display the fullest significance of [mathematics] cannot possibly do so without calling upon the resources of the orator.” (see page 258 of this edition of The Good Life)
Dewey Was Wrong About Mathematics
The “Progressive Education Movement,” of which Dewey was a central figure, was based on the philosophy of pragmatism, whose emphasis on “practical effects,” was at odds with mathematics. Contrary to Plato, Dewey writes “Numbers are not objects of study just because they are numbers, but because they are factors upon which the accomplishment of our purposes depends.” (see page 134 of this edition of Democracy and Education) And on page 143 of the same book he says, “Mathematics, even in its higher branches, when undue emphasis is put upon the technique of calculation, and science, when laboratory exercises are given for their own sake, suffer from the same evil.”
These statements are consistent with Dewey’s tenet that if a theory has no practical application, it is “practically useless.” However, history contradicts these statements repeatedly. As Galileo discovered, mathematics is the language of Nature. There is a strong symbiotic relationship between mathematics and the laws governing Nature. The study of Nature creates mathematics (as in the creation of geometry in ancient Egypt and Babylon and calculus in 17th century), and mathematics, pure and abstract mathematics, developed by the human brain finds application in the study of Nature.