“That student is taught the best who is told the least.”

– R. L. Moore

“‘Every minute dies a man, Every minute one is born;’  I need hardly point out to you that this calculation would tend to keep the sum total of the world’s population in a state of perpetual equipoise, whereas it is a well-known fact that the said sum total is constantly on the increase.  I would therefore take the liberty of suggesting that in the next edition of your excellent poem the erroneous calculation to which I refer should be corrected as follows:  ‘Every moment dies a man, And one and a sixteenth is born.’ I may add that the exact figures are 1.067, but something must, of course, be conceded to the laws of metre.”

– Charles Babbage, letter to Alfred, Lord Tennyson, about a couplet in his “The Vision of Sin”

“It is the mark of an educated mind to be able to entertain a thought without accepting it.”

– Aristotle

“Over the long run, the non-instructional character of math texts, the lack of concrete and manipulative experiences, the lack of social support such as peer tutoring or cooperative problem solving, and the exclusive reliance on teacher presentations, conspire to divide math learners. Some people get it and are good at it, others don’t, and believe they have no recourse. If faced with math later, as in a statistics course or application, the person assumes he or she should be told what to do. It seems a perfectly natural extension of years of having the teacher ‘tell’ math.”

– Stodolsky, S. S. 
From: Telling Math: Origins of Math Aversion and Anxiety

“Aside from the approximate accumulator that we share with rats and pigeons, our brain probably does not contain any “arithmetical unit” predestined for numbers and math. It compensates this shortcoming, however, by tinkering with alternative circuits that may be slow and indirect, but are more or less functional for the task at hand.”

– Stanislas Dehaene
From: The Number Sense: How the Mind Creates Mathematics