The Problem with Age-Segregation in Schools

A new class of 6-year-old children will soon begin to share similar ways to think and behave. Then, next year, when they are 7 years old, most of those pupils will still remain in that group—and thus will tend to perpetuate those same patterns of activity. The next year, they will be 8-year-olds, but will continue to share many attitudes, values, and cognitive strategies. So as those children proceed through their K-12 grades, large portions of their ways to think will remain much like th...

 A Sonata as Teacher

Music makes things in our minds, but afterward most of them fade away. What remains? In one old story about Mozart, the wonder child hears a lengthy contrapuntal mass and then writes down the entire score. I do not believe such tales, for history documents so few of them that they seem to be mere legend, though by that argument Mozart also would seem to be legend. Most people do not even remember the themes of an evening's concert. Yet, when the tunes are played again, they are recognized. So...

 English Spelling Risks Becoming Like Chinese Ideograms

Indeed, the present tendency in the scools is to dis- regard the fonetic basis of English spelling, and to treat the written and printed words as ideografs like Chinese the pupils being taught to recognize a word by its appearance as a whole, rather than by a f util attempt to analize the supposed sounds of the letters composing it. Vast amounts of mony and incalculable years hav been spent in efforts, never wholly success- ful, to teach children to memorize the intricate and unreaso...

 Prescriptivism and Descriptivism

So, you seem to be at an impasse. On the one hand, you have generations of grade school English teachers rightly warning their pupils that people might chuckle at them if they use the word ‘irregardless’. On the other hand, you have the scientific rigor of the modern linguistic community touting descriptivism as the torch-bearer of truth and enlightenment. Are you doomed to choose between a democracy of solecisms and a library of thousand-page tomes of writer’s regulations? Are things r...

 Mathematicians Who Can Only Generalize or Specialize

A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditiona...

 Teaching is a Waste of Time

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 preciou...