The right to do wrong
The right to make mistakes is a fundamental right for any learner. No skill can be effectively learned without making mistakes. The most obvious example is when one tries to learn how play on a musical instrument. First you hear awful sound, then it gets better and if he stick with it, he gets to play. The same thing should be when trying to learn math, but for some reason people get nervous when they make math mistakes. Many people think that there is no room for mistakes when learning or researching math. This attitude take the sandbox out of the learner (or researcher) turning math interaction into a daunting unpleasant task. When one starts to play he knows that he is making awful strange noises, but he continue to play until he get the "right" sound, his ears help him in getting to know when he got it. It seems that a math learner lack "ears", therefore he cannot tell whether he is right or wrong, however this assumption is simply wrong. The role of a good math teacher is to help student to "grow ears" in other words math teacher must help their student to develop skills that will allow him to criticize and evaluate his and others work. But unlike music the "Math Evaluation Skill" or MES is ought to be developed while learning. Some may say that musical hearing skills also developed in musicians and this may be OK if one would like to continue the comparison, but the point is that math teachers are unaware of the importance of mistakes when they teach the subject.