Children must be taught how to think, not what to think. Margaret Mead
The role of the teacher is to create the conditions for invention rather than provide ready-made knowledge. Seymour Papert
Only awareness is educable. Caleb Gattegno
The roots of education are bitter, but the fruit is sweet. Aristotle
Teaching to solve problems is education of the will. George Polya
The best way to learn is to do; the worst way to teach is to talk. Paul Halmos
Minus times minus is plus,
The reason for this we need not discuss.
W H Auden
Complete success would mean that every individual felt, “I enjoyed the mathematics that I had time to learn. If I ever need or want to learn some more, I shall not be afraid to do so.”
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Understood or not, tapping the aesthetic component of mathematics is a crucial and neglected component of mathematical education. See Simon Fraser mathematical educator Nathalie Sinclair’s 2006 book Mathematics and Beauty: Aesthetic Approaches to Teaching Children. Given that basing mathematical education on utility and importance has not worked very well, perhaps introducing the aesthetic is past overdue.
It is impossible to be a mathematician without being a poet in soul.
One cannot be a mathematician if one does not have the soul of a shaman.
It’s my contention that not only is the aesthetic component of maths neglected but also the historical and cultural components. Maths is a subject created by human beings to meet human ends, whether it be the need to balance the books, or the need to understand or uncover a truth of nature.
Along with other maths educators I contend that what maths education is weak at is providing a believable context; believable, that is, by the consumers of mathematics education ie school kids. That is the challenge of teaching and tutoring this important subject.
…mathematics in the Chinese curriculum is not seen as an elite subject. It is viewed as an essential of life, and one in which everyone can be highly competent if you work at it. ‘Maths gets you everywhere’ is a common phrase used in China and far from turning pupils off the subject, this focus and respect for it gives their pupils confidence and purpose.
Sean Harford HMI, National Director, Initial Teacher Education, Ofsted Maths teaching in China…
Whatever it is you seek, you have to put in the time, the practice, the effort. You must give up a lot to get it. It has to be very important to you. And once you have attained it, it is your power. It can’t be given away : it resides in you. It is literally the result of your discipline.
Ian Malcolm (fictional mathematician in the Jurassic Park novels of Michael Crichton)
Learning and creating mathematics is indeed a worthwhile way to spend one’s life.
Garrity and Pederson “All the mathematics you missed”
But let’s keep things in perspective:
Music and poetry are more important than carburettors and calculus, because both the bus driver and I would be better human beings if we had more in common because we could then collaborate better to live in a saner world.