We should not speak so that it is possible for the audience to understand us, but so that it is impossible for them to misunderstand us.
— Quintilian paraphrased (ca. 95 CE), Roman rhetorician, educator, author
First, despite how commonsense, commonplace it may seem, teaching is far from simple work…Doing it well requires, as Congressman Kildee said, detailed knowledge of the domain for which you are responsible for teaching the students and a lot of skill in making it learnable…Teaching also requires good judgment and a tremendous capacity to relate to a wide range of young people.
— Deborah Loewenberg Ball (2010), contemporary American professor of education, math educator, author, reformer
To give simplicity of form with depth of thought is one of the qualities of the difficult art of teaching.
— Charles Laisant (1898), French mathematician, politician, author, popularizer of mathematics
When we come to the very close of life, we cannot transfer, in a single moment, that knowledge of the world and of human nature which an experience of 70 years has afforded us.
If, therefore, from any cause whatever, we have not already dealt it out to those around us, it is likely to be lost;—and lost for ever.
— William A. Alcott, (1833), American educator, reformer, physician, author
…We have to make it harder to become a teacher but easier to be one. And right now we are actually doing the opposite.
— John Merrow (2017), contemporary American journalist, author, educator
Unlike any other species, human beings deliberately teach each other in settings outside the ones in which the knowledge being taught will be used.
Even if we are the only species that “teaches deliberately” and “out of the context of use,” this does not mean that we should convert this evolutionary step into a fetish.
— Jerome S. Bruner (1996), American psychologist, educator, a founding father of cognitive psychology, author of The Process of Education
The effective teacher recognizes that giving the students material to master is the mental equivalent of giving them packages to carry. With only one package, they can make a lot of progress in a hurry.
If they are loaded down with many, they stagger around, have a lot more trouble, and can’t get as far. And when they experience the mental equivalent of many packages dumped on them at once, they are squashed flat and can’t learn anything.
— Carl Wieman (2007), contemporary American physicist, educator, Nobel laureate, author
Do not try to satisfy your vanity by teaching a great many things. Awaken people's curiosity. It is enough to open minds; do not overload them. Put there just a spark. If there is some good inflammable stuff, it will catch fire.
— Anatole France paraphrased (1895), French novelist, writer, journalist, man of letters, critic, Nobel Laureate
Inspired teaching is the canny art of intellectual temptation.
— Jerome S. Bruner paraphrased (1962), American psychologist, educator, a founding father of cognitive psychology, author of On knowing; essays for the left hand
The most important single factor influencing learning is what the learner already knows. Ascertain this, and teach him accordingly.
— David Ausubel (1968), American psychologist, educator, author
A mathematics teacher is midwife to ideas.
— attributed to George Pólya, Hungarian-Swiss-American mathematician, popularizer of mathematics, author of How to Solve It
If some subject can be taught this does not imply that it should be taught.
— Hans Freudenthal (1973), German/Dutch mathematician, educator, author of Mathematics as an Educational Task
…We’ve got to do fewer things in school. The greatest enemy of understanding is coverage. As long as you are determined to cover everything, you actually ensure that most kids are not going to understand.
You’ve got to take enough time to get kids deeply involved in something so they can think about it in lots of different ways and apply it…
— Howard Gardner (1993), contemporary American developmental psychologist, educator, author of Multiple intelligences: The theory in practice
It is my belief that the thing which we should cultivate in our teachers is more the spirit than the mechanical skill of the scientist; that is, the direction of the preparation should be toward the spirit rather than toward the mechanism.
— Maria Montessori (1912), influential Italian educator, physician, reformer, author
A bad teacher is a small-scale disaster that wreaks havoc as long as he lives.
— Morris Kline (1977), American mathematician-historian, popularizer of mathematics, author of Why the professor can't teach : mathematics and the dilemma of university education
People who have sought to teach critical thinking have assumed that it is a skill, like riding a bicycle, and that, like other skills, once you learn it, you can apply it in any situation. Research from cognitive science shows that thinking is not that sort of skill.
The processes of thinking are intertwined with the content of thought (that is, domain knowledge). Thus, if you remind a student to “look at an issue from multiple perspectives” often enough, he will learn that he ought to do so, but if he doesn’t know much about an issue, he can’t think about it from multiple perspectives.
You can teach students maxims about how they ought to think, but without background knowledge and practice, they probably will not be able to implement the advice they memorize.
Just as it makes no sense to try to teach factual content without giving students opportunities to practice using it, it also makes no sense to try to teach critical thinking devoid of factual content.
— Daniel Willingham (2012), contemporary American psychologist, educator, author