Mathematics Education Quotes & Sayings

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world. — Keith Devlin

Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession. — Mary Everest Boole

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart? — David Eugene Smith

When we are young, we spend much time and pains in filling our note-books with all definitions of Religion, Love, Poetry, Politics, Art, in the hope that, in the course of a few years, we shall have condensed into our encyclopaedia the net value of all the theories at which the world has yet arrived. But year after year our tables get no completeness, and at last we discover that our curve is a parabola, whose arcs will never meet. — Ralph Waldo Emerson

What I know is that if I was asked to teach mathematics in French for a week to young kids, I would do my homework and I think I could do a decent job. I don't think a degree in education would make me a better teacher. I sometimes teach in college. I don't teach for long periods of time, but I give workshops and I think I can communicate stuff. So, it's about communicating. — Philippe Falardeau

Adaptability to change is itself a hallmark of successful education. — Peter Hilton

A good student is one who will teach you something. — Irving Kaplansky

If I were again beginning my studies, I would follow the advice of Plato and start with mathematics. — Galileo Galilei

I mean that they (students) should not play life, or study it merely, while the community supports them at this expensive game, but earnestly live it from beginning to end. How could youths better learn to live than by at once trying the experiment of living? Methinks this would exercise their minds as much as mathematics. — Henry David Thoreau

A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school. — John Gresham Machen

The habit of looking at life as a social relation - an affair of society - did no good. It cultivated a weakness which needed no cultivation. If it had helped to make men of the world, or give the manners and instincts of any profession - such as temper, patience, courtesy, or a faculty of profiting by the social defects of opponents - it would have been education better worth having than mathematics or languages; but so far as it helped to make anything, it helped only to make the college standard permanent through life. — Henry Adams

For the things of this world cannot be made known without a knowledge of mathematics. — Roger Bacon

What are the objects of an useful American education? classical knowlege, modern languages & chiefly French, Spanish, & Italian; Mathematics; Natural philosophy; Natural History; Civil History; Ethics. — Thomas Jefferson

I write rhymes with addition and algebra, mental geometry. — Ice-T

The ultimate goal of mathematics is to eliminate all need for intelligent thought. — Ronald Graham

Education is worth little if it teaches only how to make a living rather than how to make a life. — Mary Hatwood Futrell

I haven't had any formal education. Through the grace of god, I am gifted in mathematics and the English language. — Shakuntala Devi

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began. — Albert Einstein

In mathematics, the art of asking questions is more valuable than solving problems. — Georg Cantor

Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive. — Ronald Graham

In the online math class, there was almost no meaningful student/teacher or student/student interaction. To equate this type of online learning with a real-world classroom experience is a major stretch. — Ian Lamont

Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles? — Paul Lockhart

Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play! — Constance Reid

I couldn't claim that I was smarter than sixty-five other guys
but the average of sixty-five other guys, certainly! — Richard Feynman

The continuous transformation of a school into an elite Science, Technology, Engineering and Mathematics (STEM) institution prepares students to become 21st century-ready.
STEM embeds college-, career-, and citizen-ready skills into the curriculum.
For our nation, we must succeed. Yet we cannot step into this new world without inspiration and commitment. So we cobble
together ideas and actions to create our own recipe for success. — Aaron Smith

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected. — Edward Griffith Begle

One of the best examples of a polymath is Leonardo da Vinci. Born in Italy in 1452, Leonardo was a sculptor, painter, architect, mathematician, musician, engineer, inventor, anatomist, botanist, geologist, cartographer and writer. Although he received an informal education that included geometry, Latin and mathematics, he was essentially an autodidact, or a self-taught individual. — James Morcan

I had the most beautiful set of theories you ever knew when I started out as a schoolma'am, but every one of them has failed me at some pinch or another. — Anne Shirley

What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant. — Laurent Schwartz

I had done quite a bit of research about math education when I spoke before Congress in 2000 about the importance of women in mathematics. The session of Congress was all about raising more scholarships for girls in college. I told them I felt that it's too late by college. — Danica McKellar

I needed to wander ... whenever and wherever I wanted! I'd found myself at the end of my rope as far as school was concerned; there seemed no particular reason for me to stay. The teachers didn't want to teach, and I didn't want to learn - from them. I wanted my education to come from living life, getting out there in the world, seeing and doing and moving amongst the other vagabonds who had had the same sneaking suspicion that I did, that there would be no great need for high-end mathematics, nope ... I was not going to be doing other people's taxes and going home at 5:37 p.m. to pat my dog's head and sit down to my one meat and two vegetable table waiting for Jeopardy to pop on the glass tit, the Pat Sajak of my own private game show, in the bellybutton of the universe, Miramar, Florida. — Johnny Depp

A totally new kind of education is needed in the world. The person who is born to be a poet is proving himself stupid in mathematics and the person who could have been a great mathematician is just cramming history and feeling lost. Everything is topsy-turvy because education is not according to your nature: it does not pay any respect to the individual. It forces everybody into a certain pattern. — Osho

Well, part of it is a longstanding belief - it's been in our education establishment at least since the 1930s - that somehow children should be allowed to discover knowledge for themselves, that they should construct their own knowledge. This has surfaced most recently in connection with mathematics instruction, where the idea is that they need to discover how to add for themselves. Rather than being taught how to add, they should construct this knowledge on their own. — Lynne Cheney

How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play. — David Van Dantzig

I was perplexed by the failure of teachers at school to address what seemed the most urgent matter of all: the bewildering, stomach-churning insecurity of being alive. The standard subjects of history, geography, mathematics, and English seemed perversely designed to ignore the questions that really mattered. As soon as I had some inkling of what 'philosophy' meant, I was puzzled as to why we were not taught it. And my skepticism about religion only grew as I failed to see what the vicars and priests I encountered gained from their faith. They struck me either as insincere, pious, and aloof or just bumblingly good-natured. (p. 10) — Stephen Batchelor

The only time a question should be asked is when all other possibilities of finding the answer for yourself have been eliminated. — Benjamin Franklin

What would mathematics have amounted to without the imagination of its devotees-its giants and their followers? There never was a discovery made without the urge of imagination-of imagination which broke the roadway through the forest in order that cold logic might follow. — David Eugene Smith

The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few primarily those who are independently motivated and who will learn under any conditions. — Lynn Steen

When Mathematics unfold through Origamis,
when video games target Medicine and Education,
when architecture embraces nature,
when we defy gravity,
when physics dance, and dance clubs play Einstein,
when we stop playing war,
when TV starts saying something,
when we produce without wasting,
when engineering meets humanity's primary needs,
when all of these are not just casualties,
but a standard we all live UP to:
Then we'll know.
I'll know:
we really live in the 21st century — Natasha Tsakos

I suppose you are two fathoms deep in mathematics, and if you are, then God help you. For so am I, only with this difference: I stick fast in the mud at the bottom, and there I shall remain. — Charles Darwin

The teacher will never be a parent. The parents are the parents. But they have to engage in some sort of active education beyond just teaching mathematics and French and English because the kids spend more time there than they do with their parents at that age. We have to accept that other adults will be part of our children's education and they will have bad teachers. That's going to happen. — Philippe Falardeau

A man may possess a profound knowledge of history and mathematics; he may be an authority in psychology, biology, or astronomy; he may know all the discovered truths pertaining to geology and natural science; but if he has not with this knowledge that nobility of soul which prompts him to deal justly with his fellow men, to practice virtue and holiness in his personal life, he is not truly an educated man.
Character is the aim of true education; and science, history, and literature are but means used to accomplish the desired end. Character is not the result of chance work but of continuous right thinking and right acting. — David O. McKay

Because much of the content of education is not cognitively natural, the process of mastering it may not always be easy and pleasant, notwithstanding the mantra that learning is fun. Children may be innately motivated to make friends, acquire status, hone motor skills, and explore the physical world, but they are not necessarily motivated to adapt their cognitive faculties to unnatural tasks like formal mathematics. A family, peer group, and culture that ascribe high status to school achievement may be needed to give a child the motive to persevere toward effortful feats of learning whose rewards are apparent only over the long term. — Steven Pinker

Our teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed. — Ian Stewart

In no other branch of mathematics is it so easy for experts to blunder as in probability theory. — Martin Gardner

Speaking of Newton but also commenting more broadly on education and the Enlightenment: I have seen a professor of mathematics only because he was great in his vocation, buried like a king who had done well by his subjects. — Voltaire

[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on. — Paul Lockhart

There is one thing only which a Muslim can profitably learn from the west, the exact sciences in their pure and applied form. Only natural sciences and mathematics should be taught in Muslim schools, while tuition of European philosophy, literature and history should lose the position of primacy which today it holds on the curriculum. — Muhammad Asad

Teaching mathematics, like teaching any art, requires the ability to inspire the student. Inspiration requires marketing, and marketing requires stirring communication. — Hartosh Singh Bal

Without mathematics, your world becomes foggy! For a clear vision, you need to be educated in the Temple of Mathematics! — Mehmet Murat Ildan

There isn't an education system on the planet that teaches dance everyday to children the way we teach them mathematics. Why? Why not? — Ken Robinson

There is no place for [the Bantu] in the European community above the level of certain forms of labour ... What is the use of teaching the Bantu child mathematics when it cannot use it in practice? That is quite absurd. Education must train people in accordance with their opportunities in life, according to the sphere in which they live. — Hendrik Verwoerd

I recognize that I have a unique position to be a role model to young girls because I am doing something that they consider glamorous, which is acting, and yet I took a time to really get my education and study mathematics, and I think math is the cat's meow. — Danica McKellar

Winfree came from a family in which no one had gone to college. He got started, he would say, by not having proper education. His father, rising from the bottom of the life insurance business to the level of vice president, moved family almost yearly up and down the East Coast, and Winfree attended than a dozen schools before finishing high school. He developed a feeling that the interesting things in the world had to do with biology and mathematics and a companion feeling that no standard combination of the two subjects did justice to what was interesting. So he decided not to take a standard approach. He took a five-year course in engineering physics at Cornell University, learning applied mathematics and a full range of hands-on laboratory styles. Prepared to be hired into military-industrial complex, he got a doctorate in biology, striving to combine experiment with theory in new ways. — James Gleick

However, the new Istanbul would not be a closed off society built on strict religious grounds. Influence from Middle Eastern kingdoms during that time did not spell cultural collapse, but usually the opposite, as historically the old Islamic empires were known for preservation of antiquities and a push toward topics like science, mathematics, and education. Although initially Constantinople was a ransacked, broken city, it would gradually turn into a new cultural center, where even former enemies (Christians) were allowed to re-enter and live among Muslims (although they were taxed for their faith). — Ayaz Babacan

The forms of mathematics, the harmonies of music, the motions of the planets, and the gods of the mysteries were all essentially related for Pythagoreans, and the meaning of that relation was revealed in an education that culminated in the human soul's assimilation to the world soul, and thence to the divine creative mind of the universe. — Richard Tarnas

We all love stories, even if they're not true. As we grow up, one of the ways we learn about the world is through the stories we hear. Some are about particular events and personalities within our personal circles of family and friends. Some are part of the larger cultures we belong to - the myths, fables, and fairy tales about our own ways of life that have captivated people for generations. In stories that are told often, the line between fact and myth can become so blurred that we easily mistake one for the other. This is true of a story that many people believe about education, even though it's not real and never really was. It goes like this: Young children go to elementary school mainly to learn the basic skills of reading, writing, and mathematics. These skills are essential so they can do well academically in high school. If they go on to higher education and graduate with a good degree, they'll find a well-paid job and the country will prosper too. — Ken Robinson

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade? — Paul Lockhart

Me, and thousands of others in this country like me, are half-baked, because we were never allowed to complete our schooling. Open our skulls, look in with a penlight, and you'll find an odd museum of ideas: sentences of history or mathematics remembered from school textbooks (no boy remembers his schooling like the one who was taken out of school, let me assure you), sentences about politics read in a newspaper while waiting for someone to come to an office, triangles and pyramids seen on the torn pages of the old geometry textbooks which every tea shop in this country uses to wrap its snacks in, bits of All India Radio news bulletins, things that drop into your mind, like lizards from the ceiling, in the half hour before falling asleep
all these ideas, half formed and half digested and half correct, mix up with other half-cooked ideas in your head, and I guess these half-formed ideas bugger one another, and make more half-formed ideas, and this is what you act on and live with. — Aravind Adiga

My early education was in the public school system of Omaha, where, retrospectively, I realize that my high school training served me in good stead for the basic subjects of mathematics, English, foreign languages and history. — Lawrence R. Klein

Education is like a diamond with many facets: It includes the basic mastery of numbers and letters that give us access to the treasury of human knowledge, accumulated and refined through the ages; it includes technical and vocational training as well as instruction in science, higher mathematics, and humane letters. — Ronald Reagan

If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done-I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education. — Paul Lockhart

The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge. — W.W. Sawyer

College is the grinding machine of the Mathematical Establishment, a conveyor belt that takes individuals from one cookie cutter to another so that the product comes within tight control limits out of the assembly line. — Bill Gaede

I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature. — Ian Stewart

The more I work and practice, the luckier I seem to get. — Gary Player

The issue, then, is not, What is the best way to teach? but, What is mathematics really all about? ... Controversies about ... teaching cannot be resolved without confronting problems about the nature of mathematics. — Reuben Hersh

I had been to school most all the time, and could spell, and read, and write just a little, and could say the multiplication table up to six times seven is thirty-five, and I don't reckon I could ever get any further than that if I was to live forever. I don't take no stock in mathematics, anyway. — Mark Twain

Every education system on Earth has the same hierarchy of subjects: at the top are mathematics and languages, then the humanities, and the bottom are the arts. — Ken Robinson

The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device. — John Kenneth Galbraith

It is said that there comes a point in every mathematics student's education when he hears himself saying to the teacher, "I think I understand"-- and that's the point at which he has hit a wall. Making sure that all gifted students hit their own personal walls is crucial for developing the empathy with the rest of the world. When they see their less lucky peers struggle academically, they need to be able to say "I know how it feels,"-- and be telling the truth. — Charles Murray

Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things they said: 'I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.' -Robert Sachs, Ph.D., George Mason University ... 'I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for future columns.' -W. Robert Smith, Ph.D., Georgia State University ... 'If all those Ph.D.'s were wrong, the country would be in very serious trouble.' -Everett Harman, Ph.D., U.S. Army Research Institute — Mark Haddon

We the undersigned, intend to establish an instruction and training institution which differs from the common elementary schools principally in that it will embrace, outside of (in addition to) the general and elementary curriculum, all branches of the classical high school, which are necessary for a true Christian and scientific education, such as: Religion, the Latin, Greek, Hebrew, German, French and English languages; History, Geography, Mathematics, Physics, natural history, Introduction to Philosophy, Music, and Drawing. — C.F.W. Walther

Mathematics is a vast adventure; its history reflects some of the noblest thoughts of countless generations. — Dirk Jan Struik

The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving ... The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense. — George Polya

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels. — Richard Askey

Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself. — George Polya

I started attending community college when I was 14 or 15, just doing general education stuff like history and mathematics. Then I went on to California State University Long Beach to pursue a degree in journalism. And then I ended up dropping out to found Oculus. — Palmer Luckey

Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him. — Blaise Pascal

I had a liberal arts education at Amherst College where I had two majors, mathematics and philosophy. — Stephen Cole Kleene

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time. — Carl Friedrich Gauss

To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. — Hilda Phoebe Hudson

My elementary education was at Christ Church infant school and St. Stephen's junior school. At St. Stephen's, I encountered my first real mentor, the headmaster Mr. Broakes. He must have spotted something unusual in me, for he spent lots of time encouraging my interest in mathematics. — Richard J. Roberts

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education. — Henri Poincare