I wholeheartedly agree, I used to tutor calculus in college and getting students to focus on the fact that the derivative was the slope of the curve or the rate of change and the integral was the area under the curve and the significance of that made calculus so much easy. Drawing the unit circle to explain the cos, sin, and tan was also so enlightening to students. Most students just see a list of characters when the see math problem, but "math people" understand what is going on underneath and become excited to solve a problem and see multiple paths of potentially solving it. If you can unleash that excitement the problem solves itself.
Once you understand the why, the how becomes so much easier.
Once you understand the why, the how becomes so much easier.