Quotable Mathematics

"True Dialogue occurs when teachers ask questions to which they do not presume to already know the 'correct answer'." (Jay...

  "By showing us the extreme diversity of the factors involved  in scientific creativity, the history of science teaches us that  we sh...

"Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is...

"If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula...

"This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations...

"Two types of graphic organizers are commonly used for comparison: the Venn diagram and the comparison matrix [...] the Venn diagram pr...

"If we are to be effective mathematics teachers, we should endeavor to understand students’ values and students’ goals. Not to mention ...

"A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should r...

"Teaching is just pointing out what you cannot see without help." (Issai Chozan, "The Mysterious Skills of the Old Cat" ...

"The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of defini...

"Some people believe that a theorem is proved when a logically correct proof is given; but some people believe a theorem is proved only...

"It has been said, often enough and certainly with good reason, that teaching mathematics affords a unique opportunity to teach demonst...

"Science is a magnificent force, but it is not a teacher of morals. It can perfect machinery, but it adds no moral restraints to protec...

"The chief end of mathematical instruction is to develop certain powers of the mind, and among these the intuition is not the least pre...

"[…] mathematical verities flow from a small number of self-evident propositions by a chain of impeccable reasonings; they impose thems...

"Often I have considered the fact that most of the difficulties which block the progress of students trying to learn analysis stem from...

"All thinking and all actions are influenced by conclusions that have been consciously or unconsciously drawn." (Jacob W A Young, ...

"The best review of arithmetic consists in the study of algebra." (Florian Cajori, "Teaching and History of Mathematics in U....

"Finally, students must learn to realize that mathematics is a science with a long history behind it, and that no true insight into the...

"The impossibility of separating the nomenclature of a science from the science itself is owing to this, that every branch of physical ...