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Traditionally, mathematics has been taught as a series of isolated subskills, with the emphasis on the product rather than on the problem-solving process. Many students have emerged from such instruction with memorized formulas in their minds but not at their fingertips. Real mathematics, however, is not so cut-and-dried. The practice of mathematics is not merely plugging numbers into an algorithm or a calculator to find a solution, nor is it just a subject in school or a set of rules to memorize. Mathematics is thinking and reasoning, solving problems, making connections, and being able to communicate ideas mathematically.
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Hellwig et al. (2000) studied this question.
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