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Technology can play an important role, but we haven’t had the time or wherewithal to explore it fully. I’m waiting for a breakthrough process, which I think may happen in mathematics. The people at Nintendo figured out billions of dollars ago that you pull kids in, you get them engaged, and that’s the model…
What distinguishes us from cavemen is the level of abstraction we can reach. Abstraction enabled humans to move from barter to money, and from gold coins to plastic cards. These days, what's left of "money" is often just an account record we read on a computer screen, and soon it could just be a line of code in a…
Seneca, the Latin philosopher, wrote, “As long as you live, keep learning how to live.” Centuries later Andre Gide, the French critic and novelist said, “The wise man is he who constantly wonders afresh.” The scientific and technological explosion in this century has caused us all to recognize that learning is a…
The familiar, hierarchical sequence of math instruction starts with counting, followed by addition and subtraction, then multiplication and division. The computational set expands to include bigger and bigger numbers, and at some point, fractions enter the picture, too. Then in early adolescence, students are…
Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art? That's absurd, of course, but it's surprisingly close to the way…
As nearly as I can see, the only secret in popularising science (or anything else) is remembering what thinking went on in your head when you first really understood whatever it is you're now explaining: especially (1) what misunderstandings needed to be cleared away, (2) what metaphors and analogies proved helpful…
In 1905, at a gathering of the world’s greatest minds in the physical sciences, Henri Poincare´ reflected on the rapid progress of scientific inquiry and the means through which the scientific community at the turn of the twentieth century and beyond would refine our understanding of the world. In his historical…
I am miles away from Eric or Linus, but the "curse of the gifted" is very real. Thankfully I wasn't smart or gifted enough that I could ride it for long, but when it comes to math and problem-solving I rode it well into my high school years. I never learned to do algebra "by the book," because I didn't need to. Or…
When you were in college, did you ever meet bright kids who graduated top of their class in high-school and then floundered freshman year in college because they had never learned how to study? It's a common trap. A friend of mine calls it "the curse of the gifted" -- a tendency to lean on your native ability too…
The circulation of accurate and meaningful natural science ideas is of vital concern to our age. These are abundant in science but scarce in society. They should be rendered accessible to all. . . without education in natural science it is impossible to develop a strong intellect.... By placing natural science at the…
Midway through her 9 a.m. Intro to American Literature course Thursday, University of Nebraska-Lincoln Professor Elizabeth Mabrey suddenly realized that her students would accept, without question, literally any words that came out of her mouth as absolute, incontrovertible fact, sources confirmed. “I could say that…
From the evident disposition of children to imitate all the actions of grown persons, from their little scientific propensities to produce in miniature what they see in magnitude, from the delight which they feel, and the deep interest which they take in all their little works and playful amusements, it is certain…
When it comes to biology, Catherine Lacey is a Level 40 Hero. That's her ranking on OpenStudy, where the University of Western Australia student spends up to 30 hours per week answering homework questions posed by students around the world. The level indicates time spent on the site, and Hero is the hardest-to-attain…
Another delightful pastime is overtransforming an information artifact through digital algorithms—useful, if used sparingly—until it turns into something quite strange. For instance, you can use one of the online machine-translation services to translate a phrase through a ring of languages back to the original and…
Or want to strengthen your working memory and ability to multitask? Try reverse mentoring—learning with your teenager. This is the first time in history when children are authorities about something important, and the successful ones are pioneers of a new paradigm in thinking. Extensive research shows that people can…
It can be hard to generalize what people consider jaw-dropping, but Vohs says research demonstrates what consistently creates an awesome experience. Travel ranks high. So does gazing at the cosmos on a clear night or watching a sensational film, as well as anytime we encounter massive quantities: colorful tulips in…
To decrease stress for students Set clear classroom rules with predetermined consequences. Keep students' sensitive information, such as grades and personal issues, confidential. Speak respectfully to students, address them by name, get to know them as individuals, and make each person feel special. Use rubrics for…
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful…
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution…
Now these numbers can be appreciated in many different ways. From the standpoint of calculation, they're as easy to understand as one plus one, which is two. Then one plus two is three, two plus three is five, three plus five is eight, and so on. Indeed, the person we call Fibonacci was actually named Leonardo of…