John Green Quotes

He that gives a portion of his time and talent to the investigation of mathematical truth, will come to all other questions with a decided advantage over his opponents.

Learning is more than the acquisition of the ability to think; it is the acquisition of many specialized abilities for thinking about a variety of things.

Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

In college, you learn how to learn. Four years is not too much time to spend at that.

What I knew was I liked math and science, and I never wanted to memorize everything. I wanted to understand where it came from.

My students may have dexterity with the equations they're required to know, but they lack the capacity to apply their knowledge to real-life problems. This critical shortcoming appears in high school and possibly in elementary grades - long before college.

The reason the gifted students of the world like Khan Academy is because we don't say, 'Memorize this formula,' but say, 'Let's try to derive it from core principles,' or, 'I forgot my trig identity, so I'm going to just try to prove this to you.'

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

Reason in a creature is a faculty of widening the rules and purposes of the use of all its powers far beyond natural instinct; it acknowledges no limits to its projects. Reason itself does not work instinctively, but requires trial, practice, and instruction in order gradually to progress from one level of insight to another.

There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being.

True learning must not be content with ideas, which are, in fact, signs, but must discover things in their individual truth.

But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.

To study is not to consume ideas, but to create and re-create them.

We owe it to our kids to inform them and train them how to think, not what to think.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

Synthesize new ideas constantly. Never read passively. Annotate, model, think, and synthesize while you read, even when you're reading what you conceive to be introductory stuff. That way, you will always aim towards understanding things at a resolution fine enough for you to be creative.

All of us were slowly losing that intellectual light that allows you always to tell the similar from the identical, the metaphorical from the real.

My investment of time, as an educator, in my judgment, is best served teaching people how to think about the world around them. Teach them how to pose a question. How to judge whether one thing is true versus another.

It must be remembered that the purpose of education is not to fill the minds of students with facts... it is to teach them to think.

The education is the answer to everything, really, and on so many different levels. The minutiae of life require analytical skills that you learn in being educated, an ability to navigate the very systems that constitute life. They all require some degree of education, and if you don't get it, you're at a real disadvantage.

How hard would it be to ask children what they see in their heads? How big should the house be in comparison to the family standing in front of it? What is it about the anatomy of the people that doesn't look right? Then let them try it again. Teach them to learn how to see and ask questions.

Even if individual researchers are prone to falling in love with their own theories, the broader process of peer review and institutionalized skepticism are designed to ensure that, eventually, the best ideas prevail.

Today much of what we call education is merely knowledge gathering and remembering. Problem solving and thinking, never strong parts of our educational system, have been downgraded in all but a few scientific subjects.

Be sensitive to your mistakes. Put it on the wall for a couple of weeks. It may be that you can learn more from the study of your own work than from others.

I am passionate about everything in my life--first and foremost, passionate about ideas. And that's a dangerous person to be in this society, not just because I'm a woman, but because it's such a fundamentally anti-intellectual, anti-critical thinking society. --bell hooks