Do you find your students trying to stay away from complex mathematical solutions? what is the reason?
Some faculty avoid complex mathematical solutions because they are unable to comprehend concepts involved. It is your job to make it easier for them to get interested. I often ask students to help me formulate problems and guide them through solutions in the advanced courses involving math. These include advanced numerical methods, structural dynamics and advanced soil mechanics.
As a math professor, I often find my students shying away from complicated math problems... meaning just about everything. Math is intimidating to many people and it seems many more are being taught to be afraid of it every day.
That being said, even in cutting-edge research, there is some benefit to hesitating diving into the most complicated problems. First of all, they can sometimes be time-sinks with nothing to show for it at the and but also, a preliminary study of small cases (avoiding the main problem at first) can often shed light on the main problem. A careful study of small cases can lead to clever general arguments.
My two cents. I hope it helps. Cheers!
I contend that in math the differences in students is their rates of learning. If, through the aid of interactive computer-based instruction (with the teacher as mentor), then each student progresses at their own pace, and they can master much of mathematics.
It's when the students in a class have to progress in lock-step, that the slower learners are left behind and, as a result, convince themselves that they are not good at math.
It is also important that a solid foundation is built upon which the next level is dependent.
For example, for university-level courses, it is important to proceed through a systematic step-by-step 2-year sequence of: analytic geometry, differential calculus, integral calculus, and 3rd course calculus; rather than starting with a mix mash of all these in the freshman year. Poor freshman students who are overwhelmed by too many new ideas at once. (I understand that some of the freshman physics classes may be presented with differential and integral calculus, but at what price?)
If they understand the importance of those complex mathematical solutions, I think they will like them. Also, if they can find simpler solutions, they will like them as well.
All the best,
I think the problem lies in the basis of the students, so we need more time and effort to avoid students this problem.
Best regards
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