We propose an alternative to the standard introduction to the derivative. Instead of using limits of difference quotients, students develop Taylor expansions of polynomials. This alternative allows students to develop many of the central ideas about the derivative at an intuitive level, using only skills and concepts from precalculus, and…

Students sometimes have difficulty in mathematics because they solve problems mechanically, without understanding the ideas represented by their equations. This brief note provides mathematics instructors with ideas for rectifying this fundamental flaw in students' paradigm of problem solving. (Contains 1 footnote.)