Why calculus is hard

Much of the traditional mathematics curriculum in high school is aimed at getting the students to calculus. There are a few more realistic courses, such as consumer math and statistics whose goal is to give students courses that they can use immediately, but many subjects taught in precalculus are there solely to get students to calculus. Such things as trig identities have no use (that I know of) until Calculus II, and only then if the student spends a lot of time on techniques of integration, which is often not done.

Calculus is very cumulative. Even business calculus, which is designed to minimize the algebra and eliminate the trig is very dependent on previous knowledge. The majority of the errors made on tests by calculus students are not calculus errors, but errors in the prerequisite material.

There is one hard concept in calculus: limits. Limits come at the beginning of the course, and if students can get through that and know the prerequisite material well, calculus is easy. There are surprisingly few things requiring memorization. It is logical and makes sense. But students come into calculus with a shaky knowledge of trigonometry and worse skills in algebra, which means they have no chance in calculus.

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4 Responses to “Why calculus is hard”

  1. juanmarqz Says:

    as well there are plenty of fearing students whose primary goal is to make it through no matter how, also there are others who fell in love with, and then perhaps they are going to follow a scientific or technological career, for them calculus is only a stepping stone or a building block. Anyhow we have to learn not to imbue any minimal fear or horror to the subject…

  2. G Says:

    Why Calculus is “hard” varies from person to person, but most likely the one part that is truly hard is the epsilon-delta proofs of limits. Any student who is forced to repeat semester 1 of Calculus might find much of the material is easier the second time through, but the limit proofs likely are still hard, just like they were the first time through.

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