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The value of hard work and persistence
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Formal discipline theory led to views that learning Latin and geometry were important, even if few students would use these skills in their lives, because by their formal character they acted as the ideal dumbbells for mental strength training.
Training on one task didnāt help much with training on dissimilar tasks. Identical elements theory suggested that in order for training in one skill to apply to another, the two problems must share common elements.
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Provided a person has the ability to see the correspondence, the problems āthree times threeā and ā3 x 3ā are the same, even if they look different. In short, an idea, as a more abstract, general notion, can influence your thinking on a wider range of problems than a procedure you memorize.
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The easy-to-spot ideas in a field may really just be the tip of an iceberg of invisible tacit knowledge. Wanting skills that float freely of any specific use, we may end up making ideas that are detached from all uses.
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Few keys to acquiring more broadly useful skills:
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