My teaching philosophy is to always teach qualitative before quantitative in math and science. In other words, I believe that understanding the concepts behind equations and ESPECIALLY shortcuts is essential to fully grasping a concept in order to move to the next level within that subject area. Once a shortcut is taught, there should always be an assessment that requires the student to demonstrate the appropriate conceptual understanding of the problem separate from solving problems using the shortcut. If the conceptual understanding is missed, it should put a hard STOP on moving on, even if it was only a portion of the concept that was erroneously demonstrated. The process can be quick using a simple correction technique and requiring the student to explain where their mistake originated. Gauging conceptual misunderstandings cumulatively over time can provide valuable information regarding each student's process of conceptualizing regarding strengths and weaknesses. Finally, it is essential for my understanding of a concept to be thorough enough to explain the same concept using at least three examples.