I am a postdoc in physics and was in an advisory role in a project with an undergraduate student majoring in math. It was my first time collaborating with someone junior to me. The collaboration was not extremely successful, and I think I need some advice on how to supervise students.
Background information: The project was my proposal but I offered several other options in the beginning and the student picked the current one. It was purely theoretical and I simplified the project into several math problems or calculations so that the student can easily start working on them without the need of advanced knowledge. The math tools required were only basic first-year ones, e.g., calculus and linear algebra. I knew from his CV that he has taken all required courses, so I indeed anticipated a better performance than the current one. He also mentioned explicitly he enjoyed doing these type of analysis.
Student's performance: I was initially confident because the student seemed to understand everything I said and was also highly motivated. He seldom had questions about my notes and was working long hours. However, every time the student wrote up some notes and claimed that he solved one problem, I could always find some obvious loopholes or wrong calculations in the proof. I tried to explain these mistakes and he always quickly absorbed my point. But then the same thing would repeat. He would claim that he solved the problem once again, and then I quickly found out a mistake in his proof. When I asked him to proofread some of his notes himself, he was also not able to spot any mistakes.
After a while, I decided to take the lead and did calculations myself, because maybe he was not well prepared to do calculations by himself. I would let him proofread my notes afterwards and raise questions when he had any. He always claimed that my notes were all correct. It was not a good sign, because sometimes I found out I made some mistakes in my own calculations, but he was never able to spot them.
In the end, I had to finish the project mostly by myself. It was okay, but the experience was kind of intimidating, because I didn't expect a student to act that way. I always imagine a student should either fail to make any calculations or successfully conduct them (like myself), instead of keeping writing notes without knowing they were wrong. It was extremely hard that I was not able to teach him anything because he always acted like he already knew what I said and the mistakes were only a result of carelessness. Still, I find it hard to understand why one can make so many mistakes without knowing.
Question: I was wondering, is there any good method I might adopt if I come across this type of student in the future?