clarify the subject for undergraduates because the authors apparently felt honor-bound to clutter their presentation of the intuitively accessible ideas by first presenting rigorous justifications of the mathematics.

I contend that the basic ideas are easily understood by students who are probably totally impervious to the justifications. I also contend that students will experience far less discomfort in dealing with infinitesimals from the outset than they presently experience while trying to absorb and utilize the notion of limits and related mathematical underpinnings.

I show in this article how to avoid the early introduction of concepts that, while important to the rigorous development of the subject of calculus, are totally incomprehensible to beginning students. The present approach is, instead, intended to build on students’ intuitive concepts, with mathematical rigor generally left for advanced courses where rigor aids, instead of detracts from, the conceptual development.

The underlying idea (for example in treating difference quotients in finding the slope of a curve), is to treat an extremely small increment of the independent variable (dubbed the ‘dibbl’) as if its square were equal to zero. This idea gives one an occasion to exercise students on the powers of large and small numbers, leading to 