The Effectiveness Of Mathematical Instructional Interaction And "Problem Co-solution Mode" Instructional Design

At present, Reform in international mathematics education highly values students' mathematical communication ability and regards the solving of mathematical problems as the core of the mathematical teaching practice. In China, the new curriculum reform of elementary education starting from the beginning of 21^st century also takes the communication between teachers and students as an very important role in mathematical teaching. The Standard for Full-Time Compulsory Education on New Mathematical Curricular indicates clearly that "Mathematical teaching practice contains mathematical activities and there are a lot of interactions in it between teachers and students who will develop each other." Furthermore, the characteristics of the physical and mental development of junior middle school students also requires that the teacher should give more care and guidance to the students and have a close communication with them in the field of cognition and emotion both in class and outside class. Therefore, in the mathematical teaching practice of junior middle school, it is very necessary for the teacher to launch the method named 'effective instructional interaction' in the mathematic class. The so-called 'effective instruction interaction' is an interaction which requires deep communication and effective understanding between each other. From the effective instructional interaction view, the research in this paper attempts to build up a new mathematical instructional design called "Problem Co-Solution Mode" which takes the solution of problems as the center.At the first part of this paper, the development of current research on interaction and instructional interaction is briefly introduced. This theory research forms the theoretical basis of this paper. Then, the main problems of current instructional interaction in mathematical classes of junior middle schools are summarized according to the experiences gained from actual education practice. And in order to find the standard for effective instructional interaction, five aspects in interaction are investigated, including the subject, the activity, the content, the organization and the effect of the interaction. Based on this standard, a new instructional design called 'problem co-solution mode' is presented, which is following the basic idea of effective instructional interaction and sets the problem solving as the focus. Finally, the basic idea of this instructional design is introduced to teachers from junior middle schools and researchers in fields of educational theory in order to judge the practical value of this design. And an questionnaire is designed from the aspects of effectiveness, feasibility, creativity and operability, which aims at obtaining effective evaluation for this instructional design in 'problem co-solution mode'. From the result of this investigation, it can be showed that junior middle schools and researchers in fields of educational are satisfied with the 'problem co-solution mode'.The main research in this paper including:I. The distinguishing of the concepts between interaction and instructional interaction.II. Analysis towards the main problems of current instructional interaction in mathematical classes of junior middle schools and their possible reasons.III. Searching for the standard of effective instructional interaction.IV. Introducing main idea of new instructional design in 'problem co-solution mode'V. Investigation design to obtain effective evaluation for instructional design in 'problem co-solution mode'...