The point isn ' t to demean people who make stupid mistakes . The point is to ensure they understand they made a stupid mistake . When someone says xy x y and you point out that this is problematic , you get two types of responses Oh wow . I can ' t believe I did something that stupid . But what ' s wrong with doing that ? The first reflects a performance deficit , where someone understands but doesn ' t do something correctly . The second reflects an understanding deficit . What matters here is how feedback is structured and what we do with mistakes . I ' ve had plenty of students give the first response followed by I suck at math I ' ve had several who genuinely didn ' t see a problem but were very open to explanation when given constructively . I agree about freshmen not quite understanding their own limitations or lack of preparedness . However , I ' ve found that here are some things you can do to develop your understanding is fundamentally different and much more effective than you are in really bad shape . What you ' re saying is that students need to know when their understanding is flawed I ' m saying there are lots of ways to do that , but understanding is fairly subtle , and comes and goes rather than being fixed once and moved on from . As an example , my stats students are going to do fine on our cumulative final because the content really is structured to build one section from the next . My algebra students will have trouble because the content is largely a mishmash of procedures for solving equations with functions they will later need to differentiate , with no discernible order , structure , or connection . Grade inflation aside , I think it ' s easy to pass without understanding because of two things Understanding is pretty difficult to measure directly , therefore we measure it by performance . While performance may be necessary for understanding , it ' s not sufficient , so students can pass the class by memorizing procedures and rules without making any connections .