Mathematics Education
The best therapy for emotional blocks to math is the realization that the human race took centuries or millennia to see through the mist of difficulties and paradoxes which instructors now invite us to solve in a few minutes.
— Lancelot Hogben (1936), English zoologist, medical statistician, popularizer of math and science, author of Mathematics for the Million
The teaching of mathematics should maximize the inner organization of the contents; it should present the contents as a meaningful, coherent, interconnected exploration of a few clearly significant topics.
At the same time, the teaching should maximize autonomous intellectual activity by the student - in- sight, understanding, creative problem-solving, active intellectual analysis and synthesis of genuinely interesting mathematical situations.
— Alexander Wittenberg (1964), German-Swiss mathematician, educator, philosopher, author, reformer
...Mathematics and mathematical thinking are not only part of a special science, but are also closely connected with our general culture and its historic development of mathematical thinking, a bridge to the so called Arts and Sciences and the seemingly so non-historic exact sciences can be found
...Our main purpose is to help build such a bridge. Not for the sake of history but for the genesis of problems, facts and proofs, for the sake of the decisive turning points of that genesis...
By going back to the roots of these conceptions, back through the dust of times past, the scars of long use would disappear and they would be reborn to us as creatures full of life.
— Otto Toeplitz (1926), German mathematician, author, popularizer of mathematics
Recognize that you are probably better at math than you think. There’s a tendency for adults to label the math that they can do (such as identifying patterns, choosing between competing offers in a supermarket, and challenging statistics published by the government) as “common sense”
and labeling everything they can't do as “math”— so that being bad at math becomes a self-fulfilling prophecy…
— Rob Eastaway (2010), contemporary English engineer, math educator, author, popularizer of math
— Mike Askew (2010), contemporary mathematician, educator, author, popularizer of math
But also here is a message to any older person who has never given a thought to mathematics or science during their school days or afterwards : You may be ready to start. Starting can be intellectually thrilling...
— Barry Mazur (2005), contemporary American mathematician, educator, author, popularizer of mathematics
Other people are less interested in specific statements than in well-built theories, in fruitful ideas, in the logical or even psychological value of relations...
In this state of mind,...it is possible to make contact even with mathematics far above our level, mathematics whose power and beauty, even though barely glimpsed, are a fountain of enrichment for the mind and an opportunity for long reflections on our modest activities as users or teachers of elementary mathematics.
— Lucienne Felix (1960), French mathematician, author, popularizer of mathematics
We believe that large numbers who would become active and effective in higher mathematical research are now lost to the cause simply by reason of the fact that there are no intermediate steps by which they can climb to these heights.
— Herbert E. Slaught (1914), American mathematician, educator, a founding father of the Mathematical Association of America
As teachers of mathematics, and even more so as historians of mathematics, we are the carriers of the mathematical culture. It is our solemn responsibility to transmit this culture to our students. It is not sufficient that we simply present the mathematical details.
Our responsibility is much greater. We would be derelict in our duties as teachers if we presented mathematics as a fully developed discipline, a discipline that seemingly appeared millennia ago in perfect form.
— V. Frederick Rickey (1996), contemporary American mathematician-historian, logician, educator
Mathematics is the result of a cumulative endeavor to which many people have contributed, and not only through their success but through half-formed thoughts, tentative proposals, partially worked solutions, and even outright failure.
No part of mathematics came to birth in the form that it now appears in a modern textbook: mathematical creativity can be slow, sometimes messy, often frustrating.
— Jacqueline Stedall (2011), British mathematician-historian, author, popularizer of mathematics
It is regrettable that the importance, for the progress of science and mathematics, of good exposition, of revealing underlying beauties, as a foundation for the future, is little understood in research assessments. There is a difference between `advancement of knowledge' and `advancement of understanding'. Yet the latter is often a motivation for young people to study mathematics at various levels.
— Ronald Brown (1999), British mathematician, author, popularizer of mathematics
Taking a realistic view of the facts, anyone but an indurated bigot must admit that mathematics has not yet made out a compelling case for democratic support, so that the men and women who pay the bills which make mathematics possible can see clearly what they are asked to pay for.
This must be done, and immediately, if mathematics is to survive in America.
— Eric Temple Bell (1935), Scottish-American mathematician, popularizer of mathematics, author of Men of Mathematics
In describing the way that most mathematicians view mathematics Maxime Bôcher stated, that they represent “only the dry bones of the subject…it may perhaps be said that instead of inviting you to a feast [they] have merely shown you the empty dishes and explained how the feast would be served if only the dishes were filled.”
— Maxime Bôcher (1867 – 1918), influential American mathematician, educator, author, a founding father of mathematical research in America
Even if practice does not necessarily make perfect, it is clear that practice is an essential element of perfection. There is no way to become a good swimmer, a good musician, without putting in the hours to get the feel of the activity…Is there a danger that the baby of practice has been thrown out with the bath water of rote learning?
— Ronald Brown (1999), British mathematician, author, popularizer of mathematics
If a list of objectives is developed to too great degree of refinement, an actual handicap can be imposed upon good teachers.
Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.
— Edward G. Begle (1970), American mathematician, educator, author, reformer, head of School Mathematics Study Group
The mathematical student needs to use the telescope as well as the microscope, even if the latter instrument is the more important for those who desire to become experts along mathematical lines.
— George Abram Miller (1916), American mathematician-historian, educator, author of Historical Introduction to Mathematical Literature
Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding
— Gian-Carlo Rota (1980), influential Italian/American mathematician, educator
No mathematical idea has ever been published in the way it was discovered.
— Hans Freudenthal (1973), German/Dutch mathematician, founder of Institute for the Development of Mathematical Education
I believe that math is in grave danger of joining Latin, Greek, and other subjects, which were once deemed essential but are now, at least in America, regarded as relics of an obsolete, intellectual tradition…
. . . (Math) must not be taught as a series of disconnected, meaningless technical procedures from dull and empty textbooks.
— attributed to Evelyn Boyd Granville (ca. late 1990s), American mathematician, educator, author, reformer
A change of attitude of mathematicians towards public awareness of their discipline is vital...We have to reach a wider audience to show the real value of present and past mathematical results.
We have to be more appealing always maintaining a sufficient standard of accuracy, avoiding excesses and cliches, and creating astonishing situations with the right mixture between science and entertainment, that is ultimately the heart of the communication strategy.
— Andrea Capozucca (2017), contemporary Italian mathematician, educator, author, popularizer of mathematics