Wow, that is a difficult problem indeed. I think this might be the fear of every instructor and I'm not sure if there is a single answer to address this. If the student presents this openly in the classroom as opposed to a one-on-one confrontation, then the problem is significantly compounded. My personal experience with this came when I took over an algebra class from a former instructor who had problems. On my first day of class when I was challenged by one of my students, he presented a question regarding factoring equations which was way beyond the capability of any of the other students at that time and I offered to discuss the problem after class. He took it as if I didn’t know how to do the equation and became loud. Of course the other students now became focused on our discussion. I halted our discussion at that time and addressed the class assigning them some reading and problems to work on as a team. Subsequently, I readdressed the problem presented by the upset student and explained the steps involved in the calculation. I then gave him a similar problem to work on, but he was unable to solve it. By showing him how to approach the solution and talking with him, he became one of my best students and supporters. Of course, the rest of the class was watching closely, but I had to meet the challenge and build the students’ confidence in me. For the remainder of the quarter we had a great time.
