I take pains to break down and explain my lessons in simple vernacular (of course,while using correct mathematical terminology)and model problems in step by step fashion. I am fascinated by the students who leave the lesson with complete understanding vs. those with little or none of the same.What did I say that resonated with some students? And didn't with others? Would a different approach to the lesson have made a difference? so I am vexed by this thought exercise: -let x represent the % of students who leave the lesson with understanding and perhaps a reasonable mastery of the skill and/or standard covered that day. -let y (or 1-x) be the % of students who leave with little or no understanding of the skill and/or standard being taught. -obviously, x + y = 1.00 or 100% Can you envision a scenario wherein 2 teachers would have 100% completly different results? i.e, for teacher A and teacher B, the kids who fall into the X group for teacher A become the Y group for teacher B...and vice versa? this question has perplexed me for some time and I am curious as to the opinions of my colleagues.