Every great how needs a great why and not the other way.
In a TV advertisement for nicotine patch to help quit smoking there is the phrase, " Every great why needs a great how." We got to thinking in this world of flipping things, classrooms and pancakes, that it really should read "Every great how needs a great why." That is what we are about in SIMIODE, the "why" of why we even study differential equations; the "why" of why this equation is suitable for modeling this phenomenon; and the "why" of why this term is even in the differential equations.
We believe that "why" is more important than "how," especially when the "how" can be addressed by technology more and more. Thus "how" becomes less and less important while "why" becomes more and more important. Moreover, the "why" grounds the problem in a context which leads one to see the reasonableness (or unreasonableness) of the solution, however obtained. Whereas the "how" offers a solution strategy which is unmotivated and not memorable.
Children ask "Why is the sky blue?" not "How is the sky blue?" Our students ask, "Why are we studying differential equations?" They do not come to us with "how" questions initially, they come with "why" questions first. If we answer a "why" question with a "how" answer then we are not meeting them at their needs and we are not respecting them. For in so doing we are sweeping away their "why" curiosity and replacing it with our "Here's how." mechanics, rote skills, and solution tricks; all of which they forget and never again recall, whereas "why" discussions ARE remembered.
So next time you address a group of students tell them, "Every great how needs a great why," and join with them to discover the why. It is a lot more fun than showing them the "how" and "why" responses stick with them much longer, for when "how we solve" fails the "why is this so" stays.