Action research is a methodology that has been found to be valuable as a problem-solving tool. It can provide opportunities for reflection, improvement, and transformation of teaching. The purpose of this study is to better understand these claims about the benefits of action research. Several research questions stand out: How is action mathematics education research and work in the emerging cognitive sciences opened up a spectrum of research methods and foci that expanded the scope of the enterprise in tremendously productive ways. For instance, compared with the corresponding linear case, the solutions of the nonlinear problem can obtain rapid 2 RESEARCH PROPOSAL This project will carry out a systematic research on the challenging topics to study the inﬂuence of the nonlinear term in the asymptotic behavior of solutions.
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