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" It still remains unrecognised, that to bring a child into existence without a fair prospect of being able, not only to provide food for its body, but instruction and training for its mind, is a moral crime, both against the unfortunate offspring and against society; and that if the parent does not fulfil this obligation, the State ought to see it fulfilled, at the charge, as far as possible, of the parent. "
― John Stuart Mill , On Liberty
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" The obvious cure for the tragic shortcomings of human intuition in a high-tech world is education. And this offers priorities for educational policy: to provide students with the cognitive tools that are most important for grasping the modern world and that are most unlike the cognitive tools they are born with. The perilous fallacies we have seen in this chapter, for example, would give high priority to economics, evolutionary biology, and probability and statistics in any high school or college curriculum. Unfortunately, most curricula have barely changed since medieval times, and are barely changeable because no one wants to be the philistine who seems to be saying that it is unimportant to learn a foreign language, or English literature, or trigonometry, or the classics. But no matter how valuable a subject may be, there are only twenty-four hours in a day, and a decision to teach one subject is also a decision not to teach another one. The question is not whether trigonometry is important, but whether it is more important than statistics; not whether an educated person should know the classics, but whether it is more important for an educated person to know the classics than to know elementary economics. In a world whose complexities are constantly challenging our intuitions, these trade-offs cannot responsibly be avoided. "
― Steven Pinker , The Blank Slate: The Modern Denial of Human Nature
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" Teachers greatly influence how students perceive and approach struggle in the mathematics classroom. Even young students can learn to value struggle as an expected and natural part of learning, as demonstrated by the class motto of one first-grade math class: If you are not struggling, you are not learning. Teachers must accept that struggle is important to students' learning of mathematics, convey this message to students, and provide time for them to try to work through their uncertainties. Unfortunately, this may not be enough, since some students will still simply shut down in the face of frustration, proclaim, 'I don't know,' and give up. Dweck (2006) has shown that students with a fixed mindset--that is, those who believe that intelligence (especially math ability) is an innate trait--are more likely to give up when they encounter difficulties because they believe that learning mathematics should come naturally. By contrast, students with a growth mindset--that is, those who believe that intelligence can be developed through effort--are likely to persevere through a struggle because they see challenging work as an opportunity to learn and grow. "