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Old 06-26-2008, 04:21 PM   #8 (permalink)
Calculusaurus
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Calculus is hard on students for two reasons.

1. depth of understanding is rewarded over rote memorization of problem solving techniques. Any fool can do algebra. (e.g.) Memorize the quadratic formula and apply it without questioning where it came from or what it means. In calculus, you're rewarded for asking questions like "what does the integral actually mean?" Probing those questions will be critical to your success.

2. Calculus is our first encounter of difficult abstract concepts with no "grounding". Our brains were better suited get an intuitive grasp of algebra and geometry (though some evolutionary psychologists consider even those to be social conditioning). Calculus is hard because at first glance it seems like an arbitrary set of pointless rules and techniques (it's not).

According to Jean Piaget, the fourth and final stage of cognitive development is the Formal Operations Stage, which is characterized by the ability to think in the abstract reasoning and understand logical proofs. According to some studies, something like 70% of the population never reach this stage, but I wouldn't take a dead Swiss philosopher's theory too seriously.
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