How to Teach Calculus

Calculus is the branch of mathematics that deals with derivatives, infinite series, integrals and limits. It is generally taught no earlier than the first year of college. There is considerable debate about teaching it in high school because calculus represents an enormous advance over anything that has been taught before and it is difficult to introduce the subject gently.

Instructions

1. Ensure the student is prepared. This is essential and must include a thorough grounding in basic algebra, geometry and trigonometry. Many high schools teach preparatory courses that may have titles such as Analytic Geometry or Elementary Analysis and these courses should be taken as well. A college level course in pre-calculus also may be necessary. When assured the student is prepared for learning calculus, each of the following steps must be thoroughly understood before he advances to the next.

2. Start by determining the slope of a tangent line. This is a good way to introduce the idea of limits, which requires the student to understand what happens when a quantity approaches but does not reach some value.

3. Establish the derivative of a function as the slope of a tangent line. This will allow the development of the idea that the derivative is a measure of instantaneous change.

4. Cover infinite series next. This provides the needed foundation for showing integrals as a means of calculating infinite sums.

5. Study integration. This should be the final phase of a first semester course in calculus and the fundamental theorem of calculus can now be introduced. At this point, the integral of a function should be firmly associated with the area under that function when graphed.