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In some research involving opinion formation, there are some details that have not been studied deeply, just as the role of a person’s self-confidence in opinion dynamics. This small but important detail needs to be cleared up. Hence, in this paper, we want to discuss the self-confidence in opinion dynamics with regard to some common linear and nonlinear models: DeGroot, Friedkin–Johnsen, Deffuant–Weisbuch and Hegselmann–Krause (HK) model. We unfold that (1) A person’s self-confidence assumption has an important impact on the consensus condition in DeGroot model; (2) The relationship between the self-confidence on the initial opinion and the current opinion follows a Kuznets curve in Friedkin–Johnsen model; (3) A person’s self-confidence has a close relationship with the convergence parameter in Deffuant–Weisbuch model, which has little impact on the number of opinion clusters at the stable stage; and (4) A person’s self-confidence varies with time at first and then stays at a certain level finally in the HK model, while the person’s self-confidence does not change with time in above three models.

This chapter begins with a literature review of the role of cram schools and how parents and children perceive them in Taiwan. Interviews were conducted to understand the view of primary school teachers concerning the impact of cram schools on school mathematics learning and instruction. Despite controversial opinions on the merits of cram schools, their growing popularity can be attributed to the increasing demand from parents and children. On the one hand, primary school teachers perceive a positive impact of cram school attendance on children's mathematics learning, as evidenced by better computation skills, completion of homework, and greater self-confidence in mathematics. However, they disagree with rote-learning emphasized in cram school instruction and criticize its failure to develop concepts among children. Cram schools have a negative influence on children's understanding of mathematical concepts as well as flexible application of knowledge. Suggestions for improving children's mathematics ability and learning in cram schools are made.