Understanding: If it's demonstrated once, is it enough?

I'm torn. One of my colleagues this year did something called "comping" which is short for compacting. There may be other terms for it, but the premise is that if students understand a concept early on in a unit of study, they don't have to do it again. For example, if they pass a section on a quiz, they are "excused" from having to do it on a project or test. I like the theory of this, as education is methodical and if a student jumps through hoop once (please pardon the expression) why must they do it again and again? My team teacher is sold on the idea, but I still need some convincing.

This is put into play first with a quiz. For most instances, I'll call a quiz a formative assessment mid-way through the unit to check for understanding before going on to more complex applications. My hang-up with this is that:
  1. Quizzes are generally lower level rungs on the ladder of understanding. My quizzes have questions that are accessible and easily understood because I don't want to confuse students early on. For example, a quiz question on area and perimeter might be something like: "Here is a rectangle with a side of 7 meters and a side of 8 meters. What is the area and perimeter?" This feels to me like a low level task of recall and not so much application. Because a student can demonstrate this does not mean that they could apply this to a higher order question like "Joe wants to make a garden with an area of 20 square meters but use the least amount of fencing to build around his garden (perimeter). Using whole numbers, what are the dimensions of the garden that would have an area of 20 square meters but also the least amount of fencing to encircle around the garden? Label the dimensions of the garden and show any mathematical notation to explain your reasoning" Using mathematics in reality happens more like the second question and such understanding is much richer and deeper. 
  2. I have had countless math students that are whizzes with plugging numbers into formulas but fail to apply what they've learned on projects or summative assessments. Some of these students fail to find the underlying relationship between these variables that we want them to discover. For instance, in the problem above, they might learn that with the changing dimensions of a rectangle, a rectangle can have the same area but changing perimeter. For students who are merely number crunchers, they can show a surface level competency, but I can't get my head around on how they would apply such skills to real world situations until they were asked to do it again.
 If we want our students to learn math that is meaningful and useful, I still can't resign myself to having them crank out an equation, plug and chug, and sign them off, decrying them "masters". I've been told that good teaching starts from basic tasks, and spirals up to more complex ones. If students have really mastered something, they should be able to do it again and again. To do so would reinforce their skills. Is it a bad thing that they do it over and over again? What are your thoughts?

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