Design And Implementation Of Mathematics Problem-solving System Based On Learning Scaffold

As one of the necessary abilities of a student, the ability of solving mathematics problems is always a hot topic in research of primary and secondary education. In the stage of secondary education, we will meet students with uneven levels of knowledge, as well as some ones having troubles in mathematics learning. They do not have a full and thorough understanding of mathematics conceptions. They always confuse several similar conceptions, and sometimes use an incorrect formula when solving a mathematics problem. In a word, their ability is far away from the request of solving mathematics problems scientifically.On one hand, teachers are accustomed to inculcating the knowledge of mathematics in a subjective way. For example, when they try to explain the method of thinking, they pay more attention to illustrating the whole steps to students while neglecting to clarify the process of attempt before getting the conclusion. As a result, they can not solve a similar problem independently when they meet it in the future. On the other hand, when a student trys to solve a problem by himself, owing to insufficient knowledge, he can proceed to the initial steps only but daunted when meeting some key steps. What's worse, the enthusiasm of learning may be negatively effected accordingly.The thought of Polya's table about how to resolve a problem has been widely accepted and improved by the educators all around the world. When a teacher inculcates the process of problem solving in a mathematics lesson, the table will be so useful to make the students master the knowledge quickly, and will improve their ability of thinking and problem solving as well. In the article, the author thinks the theory will offer a firm support to the students when be used in an informational environment.In view of the above issues, the author designs a Mathematics Problem-solving System which including two main subsystems, the problems compiling one for teachers'use and the problem solving for students'use. In a problem compiling subsystem, a teacher will design a problem-based learning scaffold and a corresponding answer-based learning scaffold。In a problem solving subsystem, a student will utilize the reminder of problem-based learning scaffold and the choosing of answer-based learning scaffold to solve the problems prepared by the teacher.On one side, the usage of the system will provide an essential feedback to the students who are trying to solving mathematics problems after lessons. Furthermore it will promote the students to reconstruct and review the knowledge. Obviously, it will improve the mastering knowledge of a student, as well as transfer the new-learnt external knowledge to the skilled internal one. And it will enhance the thought and ability of a student.On the other side, according to the regulation of the system, all the mathematics problems to be solved by students should be input to the system with whole solving steps and solution. The system will be helpful to avoid teachers'assigning homework purposelessly, and make the teachers have a deeply understanding of problem solving. And it will also change the style of teaching from simplex knowledge transfer one to the one more emphasizes the improvement of the skill and the ability of problem solving. Undoubtedly, the system will observably shorten the course of a fresh teacher transferring to an expert one.