Main Question or Discussion Point
If math professors observed that their students who don't perform well in their foundation to proofs class and abstract algebra class, there not going to do well in any other math course? My math professor told me about a study of 200 students who did not do well in their analysis class who previously perform badly in their foundation to proofs class and abstract algebra class. I was in agreement with my professor in the study. But what she and the study failed to provide is explanations for why the students did not do well in the proofs class. its like she and the study were implying that improvement in writing mathematical proofs is virtually nonexistent. Its like singing or being a good basketball player. my professor seemed to be implying that writing mathematical proofs is innate, just like being a good basketball player and a good singer, you either know it or you don't. now I think its safe to say that we are all in agreement when I say that their are just some people who are just gifted in mathematics or physics , based on the way that individual's brain is structured. but I think that most mathematicians worked to become guru's in math or just to become mathmaticians. now back to my main point: What the study I initially mentioned was if failed to provide whether or not students changed their study habits or students did not show any effort to try hard. I personally think if you changed your study habits, you will improved at writing proficient mathmatical proofs. Finally , I want to know the general consensus among math professors whether they are in agreement with my professor and the study , or do all of you (math professors) think students that did bad in the proof class just were lazy or needed to change their study habits to help them improve at writing mathmatical proofs? Please I asked for the honest truth and not for any of you responders to sugar coat your replies. Thank you.