The real-time learning ability and the fast convergence of the recurrent network model of nonlinear dynamical system have been obtained by introducing the forgetting factor in the objective function and the maximum likelihood estimation principle.

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How to improve self-controlling ability?The research findings show that it is especially important for students to enhance their subjective consciousness, and to have a right math idea, and to have opportunities of experiencing the real math activity process, and to master methods of math thinking, and improve the communication among members in"math learning community". It is the point of break-through to train students to have the consciousness and skills of self-testing, if we want to improve students'self-controlling ability.

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Constructivism advocates "a student-centeredlearning under the guidance of teachers". They agues that knowledge is not taught bythe teachers, but is acquired in a certain situation, that is, in the social and culturalbackground, through the Construction of Meanings by using the necessary materialsfor study, with the help by others (including teachers and learning partners). Theystress to create a variety of real language environments for the students, and pay muchattention to training the students actual ability of using the language. Its theory hasgreat inspiring and guiding significance in organizing teaching and compilingteaching materials.

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