I am researching about contradiction, cognitive conflict or contradiction in teaching-learning process about triangle inequality. Are there any research about this feature?
You might try the proceedings of the annual PME conference; for example, there is this paper which might be of interest (and there may be more):
Alatorre, S., Flores, P., & Mendiola, E. (2012, July). Primary teachers’ reasoning and argumentation about the triangle inequality. In T. TY (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 3-10).
To access the PME proceedings, follow the instructions at: