On Teaching (Unsourced)

"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 require some ‘dreaming’ time." (Howard W Eves)

"A great teacher is not simply one who imparts knowledge to his students but is one who awakens their interest in the subject and makes them eager to pursue it for themselves. An outstanding teacher is a spark plug, not a fuel line." (Norman J Berrill)

"A good teacher protects his pupils from his own influence." (Bruce Lee)

"A teacher is a compass that activates the magnets of curiosity, knowledge, and wisdom in the pupils." (Ever Garrison)

"All explanations should be given in a language that pupils understand." (John A Comenius)

"An extremely odd demand is often set forth but never met, even by those who make it; i.e., that empirical data should be presented without any theoretical context, leaving the reader, the student, to his own devices in judging it. This demand seems odd because it is useless simply to look at something. Every act of looking turns into observation, every act of observation into reflection, every act of reflection into the making of associations; thus it is evident that we theorize every time we look carefully at the world." (Johann Wolfgang von Goethe)

"[Education carries an impact] as long as the student has a need for it and applies it to some situation of his own. Every new idea should be worked out in application." (John A Comenius)

"[…] education is not something which the teacher does, but that it is a natural process which develops spontaneously in the human being." (Maria Montessori)

"Education is teaching our children to desire the right things." (Plato)

"Great teachers do not act important; they make their students feel important." (Todd Whitaker)

"Great teachers see challenging students as a reason to try that much harder." (Todd Whitaker)

"Great teachers have high expectations for their students, but higher expectations for themselves."  (Todd Whitaker)

"Great teachers treat their students the way their best teacher treated them." (Al Burr)

"Hypotheses are lullabies with which the teacher lulls his pupils to sleep. The thinking and faithful observer learns to know his limitation more and more; he sees that the further knowledge extends the more problems arise." (Johann Wolfgang von Goethe)

"I consider the teaching and study of the historical development of science as indispensable. [...] Our textbooks fail in this respect." (Richard Willstätter)

"It is not sufficient that the teacher should have a competent knowledge of the subject which he professes [...] he must (in addition) have considered his science from the point of view at which it appears as a human acquisition." (T F Nunn)

"It appears to me that if one wishes to make progress in mathematics, one should study the masters and not the pupils." (Niels H Abel)

"Life is good for only two things, discovering mathematics and teaching mathematics." (Simeon-Denis Poisson) [in Mathematical Magazine, Volume 64, Number 1, February 1991]

"Most students have to do some work to resuscitate their childlike curiosity. The best way to do that is to start asking questions again - lots of them." (Hal Gregersen)

"Only he who knows what mathematics is, and what its function in our present civilization, can give sound advice for the improvement of our mathematical teaching." (Hermann Weyl)

"Poor is the pupil who does not surpass his master." (Leonardo da Vinci)

"Science, as usually taught to liberal arts students, emphasizes results rather than method, and tries to teach technique rather than to give insight into and understanding of the scientific habit of thought. What is needed, however, is not a dose of metaphysics but a truly humanistic teaching of science." (Harry D Gideonse)

"Show all these fanatics a little geometry, and they learn it quite easily. But, strangely enough, their minds are not thereby rectified. They perceive the truths of geometry, but it does not teach them to weight probabilities. Their minds have set hard. They will reason in a topsy-turvy wall all their lives, and I am sorry for it." (Voltaire)

"Students shall themselves seek, discover, discuss, do, and repeat by their own efforts, examine everything themselves without abdicating to the teacher's authority. The teacher should be left with the task of seeing that the task is completed." (John A Comenius)

"Teaching is not about information. It's about having an honest intellectual relationship with your students." (Paul Lockhart)

"The best teachers make every decision based on what is best for their students." (Al Burr)

"The more abstract the truth you wish to teach, the more you need to seduce the senses to it." (Friedrich Nietzsche)

"The more the teacher 'teaches,' the less the student learns." (John A Comenius)

"The most important outcome of education is to help students to become independent of formal education." (Paul E Gray)

"The only instruction which a professor can give, in my opinion, is to think in front of his students." (Henry Lebesgue)

"The secret of education is respecting the pupil." (Ralph W Emerson)

"The teacher, if indeed wise, does not bid you to enter the house of their wisdom, but leads you to the threshold of your own mind." (Kahil Gibran)

"Those who have had the good fortune to be students of the great mathematician cannot forget the almost religious accent of his teaching, the shudder of beauty or mystery that he sent through his audience, at some admirable discovery or before the unknown." (Charles Hermite [according to Paul Painlevé])