BullsEye Who has not seen a child riding upon and whipping his father’s walking-stick, as if he were mounted upon a real horse? There we have a proof of “imagination” in the child! What pleasure it gives to children to construct a splendid coach with chairs and armchairs; and while some recline inside, looking out with … Read more
Suppose that we should find ourselves among a race of giants, with legs immensely long and bodies enormously large in comparison with ours, and also with powers of rapid movement infinitely greater than ours, people extraordinarily agile and intelligent compared with ourselves. We should want to go into their houses; the steps would be each … Read more
Age mixing is Sudbury Valley’s secret weapon. I never could make heads or tails of age segregation. People don’t live their lives in the real world separated by age, year by year. Kids don’t all have the same Interests or abilities at a particular age. Anyway, we soon found out how children mix when they … Read more
We have to be careful with words. It’s a miracle they ever mean the same thing to any two people. Often, they don’t. Words like “love,” “peace.” “trust,” “democracy” — everyone brings to these words a lifetime of experiences, a world view, and we know how rarely we have these in common with anyone else. … Read more
Every thinking educator has grappled with the basic questions that have dogged the profession from earliest times: What is the best way to teach, or to learn? What subjects should children learn? How responsible are children? How much of a say should they have in what they do? How should schools be run in a … Read more
Though calculus represents a new sophistication in the understanding of sequences, that idea, like so many others, had already been familiar to the Greeks. In the fifth century b.c., in fact, the Greek philosopher Zeno employed a curious sequence to formulate a paradox that is still debated among college philosophy students today, especially after a … Read more
State governments tend to ignore arguments about the possible bad effects of lotteries. That’s because, for the most part, they know enough about mathematical expectation to arrange that for each ticket purchased, the expected winnings—the total prize money divided by the number of tickets sold—is less than the cost of the ticket. This generally leaves … Read more
A few years ago Canadian lottery officials learned the importance of careful counting the hard way when they decided to give back some unclaimed prize money that had accumulated. They purchased 500 automobiles as bonus prizes and programmed a computer to determine the winners by randomly selecting 500 numbers from their list of 2.4 million … Read more
In the two-daughter problem, an additional question is usually asked: What are the chances, given that one of the children is a girl, that both children will be girls? One might reason this way: since it is given that one of the children is a girl, there is only one child left to look at. … Read more
Unfortunately, it is hard to achieve quantitative dexterity when you’re juggling VIIIs and XIVs. In the end, though Roman law had a certain legal rationality and coherence, it fell short of mathematical validity. In Roman law, for example, two half proofs constituted a complete proof. That might sound reasonable to a mind unaccustomed to quantitative … Read more
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