There is no one way to learn. Rote memorization is at one end of the spectrum and instantaneous complete understanding and insight of the topic is at the other end. There is a lot in between. People do not learn everything the same way - their own ability to learn changes from moment to moment and subject to subject.
Sometimes material is taught in our schools in a way that expects the student to learn in a specific manner and speed. That's great when those expectations are met. But learning math doesn't always work that way. Math tends to build on previously taught (and hopefully learned) concepts and ideas. A lack of mastery of simpler ideas can create problems and frustration later on when more complex material is presented. Smoothing out those bumps in the learning process is what I am looking to do.
Though I haven't been in the classroom for many years, I continually teach in my job. When a topic doesn't click with someone I am working with, I look for other ways to get the concepts across. I look for a familiar starting point and work and rework the lesson as many different ways as needed.
Only when something has been learned have I the right to say I have taught.
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