Abstract
The careful use of notation and language in the statement of both the definitions and problems of calculus can begin the process of making students mathematically literate while allowing them to enjoy working on challenging problems and applications without the aid of numerous examples. Engaging the students to participate in the precise use of the language inculcates a philosophy of careful use of language that benefits all students regardless of major. Not only will this benefit those few students who decide to major in mathematics, but the precision of language will especially benefit both majors and non-majors outside of their mathematical studies. This pedagogical piece exhibits anecdotal evidence that such an approach provides motivation to students, better preparation for “proofs” classes, and a desire to pursue higher mathematics. Examples of calculus problems presented in the traditional fashion alongside subtly more precise presentations illustrate the process.
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