Is Precision the Same as Getting the Right Answer?

Screen Shot 2016-08-07 at 11.51.11 AMThere is some very compelling research out there that underscores the importance of making mistakes in learning. It seems like part of the issue in getting kids to have a growth mindset in math (as well as other subjects) is that they consistently get mixed messages.  We tell them that mistakes are okay but then we continue to value the right answers.  We tell them that failure leads to success but obviously failing on a report card is not valued.  If we want students to take risks, make mistakes, be comfortable with frustration and failure then we need to show them that we value these characteristics by the actions that we do in the classroom.

I have been thinking about the idea of precision in math which is frequently equated with getting a correct answer.  Is that really what precision is about? Or is precision dependent on the situation? Maybe it is about the accuracy of the thinking? But in any case does getting the right answer matter in the learning? I mean if a student explains to me that 3×4 means 3+3+3+3 or four groups of three that is precise and accurate, demonstrates conceptual understanding, and doesn’t have a single right answer.  
precisionThe behavior that exhibits the skill of precision would be checking answers or making sure answers are reasonable.  It is these behaviors that lead to precision rather than getting the right answer the first time around, right? It seems that if we train students to have a mindset of accuracy and precision that if they end up being a nurse or an air traffic controller they will train to get it right the first time around.  This level of accuracy is hardly needed for most of the math learned in a K-12 setting.  Could we increase achievement in math if we started holding students accountable for checking their answers and explaining how their answers are reasonable instead of counting right answers? Is it more important to take risks or get the right answers as students learn new concepts?  Can we value precision and mistakes at the same time? More questions than answers I suppose.