Teaching should be individualized, not one size fits all.
How do we do this? I agree, but how?
I think the answer comes from enthusiasm. Simply put: enthusiasm.
To be enthusiastic in what you’re teaching, that is how: questions, interest, desire for more, excitement to continue: all come into fruition.
It is not the facts spoken from mouth to ear, but the energy behind them all. The desire of the teacher themselves to continue learning.
Multiplying x^2 by any coefficient will make it steeper by a factor of that coefficient. This is given to us as the whole, yet it is only just a small part!
What if a parabola is stretched out completely, is it a line?
What larger picture is a parabola part of? What are its smaller parts?
These questions, this desire. It all comes flooding out when enthusiasm saturates the words.
I use math because many people find it boring, but the same is true for all topics.
Teaching and learning: the key is enthusiasm.