mathematics as an innate ability. You either have “it” or you don’t. But to Schoenfeld, it’s not so much ability as attitude. You master mathematics if you are willing to try. That’s what Schoenfeld attempts to teach his students. Success is a function of persistence and doggedness and the willingness to work hard for twenty-two minutes to make sense of something that most people would give up on after thirty seconds. Put a bunch of Renees in a classroom, and give them the space and time to explore mathematics for themselves,

I deal with writer’s block by lowering my expectations. I think the trouble starts when you sit down to write and imagine that you will achieve something magical and magnificent — and when you don’t, panic sets in. The solution is never to sit down and imagine that you will achieve something magical and magnificent. I write a little bit, almost every day, and if it results in two or three or (on a good day) four good paragraphs, I consider myself a lucky man. Never try to be the hare. All hail the tortoise.

A Connector might tell ten friends where to stay in Los Angeles, and half of them might take his advice. A Maven might tell five people where to stay in Los Angeles but make the case for the hotel so emphatically that all of them would take his advice. These are different personalities at work, acting for different reasons. But they both have the power to spark word-of-mouth epidemics.

The “IQ fundamentalist” Arthur Jensen put it thusly in his 1980 book Bias in Mental Testing (p. 113): “The four socially and personally most important threshold regions on the IQ scale are those that differentiate with high probability between persons who, because of their level of general mental ability, can or cannot attend a regular school (about IQ 50), can or cannot master the traditional subject matter of elementary school (about IQ 75), can or cannot succeed in the academic or college preparatory curriculum through high school (about IQ 105), can or cannot graduate from an accredited four-year college with grades that would qualify for admission to a professional or graduate school (about IQ 115). Beyond this, the IQ level becomes relatively unimportant in terms of ordinary occupational aspirations and criteria of success. That is not to say that there are not real differences between the intellectual capabilities represented by IQs of 115 and 150 or even between IQs of 150 and 180. But IQ differences in this upper part of the scale have far less personal implications than the thresholds just described and are generally of lesser importance for success in the popular sense than are certain traits of personality and character.

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If we want to, say, develop schools in disadvantaged communities that can successfully counteract the poisonous atmosphere of their surrounding neighborhoods, this tells us that we’re probably better off building lots of little schools than one or two big ones.

Greenberg wanted to give his pilots an alternate identity. Their problem was that they were trapped in roles dictated by the heavy weight of their country's cultural legacy. They needed an opportunity to step outside those roles ... and language was the key to that transformation.

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