"Calculus is definitely more easily understood with infinitesimals vs. limits (ask any physics major or engineer)." I don't think this is true, and suffers fro

"Calculus is definitely more easily understood with infinitesimals vs. limits (ask any physics major or engineer)." I don't think this is true, and suffers from the same fallacy as the opposite statement that limits are easier to understand than infinitesimals. For example, I've always found limits very easy to understand and infinitesimals confusing, even before I was asked to work with them rigorously using epsilons and deltas. I'm also a math major. In the physics classes I took, I sucked at mechanics (like, almost-failed sucked) but love relativity and QM. Talk to me in terms of Lie algebras and invariant subgroups and I'll be ten steps ahead of you. I realize that's not usual, I'm just pointing out that there's no absolute "easiest way" to understand something. Warning: personal theories of learning and pedagogy ahead, stated with more certainty than warranted. I think a key to understanding is presenting the same idea using multiple models/representations. The learner already has some picture of the idea you're trying to explain in their head. The picture might be confused and poorly formed, but there's some version of it nonetheless. I'd say, for that learner the "easiest way" to understand something is to find an accurate picture of the idea you want to explain and relate it to an idea the learner already understands clearly. I have a picture I want to put into your head. Your version of that picture is fuzzy and confused. I need to relate the clear picture I want to give you to clear pictures of other ideas you already have in your head. Ceci n'est pas une pipe, the map is not the terrain, the signifier is not the signified, etc. http://www.brandonbird.com/signifier_signified.html http://www.brandonbird.com/signifier_signified.html