Research On The Design And Implementation Of Mathematical Task Based On "Classroom Observation"

Since math education is a branch of basic education reform, multiple“Compulsory Education: Math Education Criterion” were published one after another since 2001. Meanwhile, with the deepening of the reform, a series of new teaching theories kept emerging and teachers became an important part of it since they are the receivers and practitioners of these theories. Therefore, nowadays, any proposition of education reform takes teachers’ professional development as the main method to achieve the reform. A teacher’s professional development consists of introspection,teachers’ mutual aid, and expert guide. Among them, introspection and teachers’ mutual aid are the main methods. As the main field for a teacher to practice the teaching theory, class is undoubtly essential. However, the common way of listening and accessing a class can only see the representation, and it is unable to accurately access the cognition level of the teaching tasks that designed by the teacher and its implement effect. Therefore, for those sophisticated teachers, the improvement brought by these ways is limited. However, in recent years, class observation that can supplement this defect was learnt by teachers as a professional way to listen and access the class. But it hasn’t been popularized among first-line teachers due to its deficiency in transforming theory to practice, and it is seldom used as the method to access the daily teaching.This essay is based on the “Math Task Analyze Framework” which is one of the QUASAR research projects of University of Pittsburgh, taking 7 classes given by Teacher Z, a mainstay teacher of a Shanghai public junior high school as the research object through recording and text analysis. By collecting, filing, classifying and comparing the text books, the teaching plan, and the quantity and type of the math tasks assigned during the class, to analyze Teacher Z’s features in designing the math tasks, the change of these math tasks during class and the factors that caused these change. Finally, teaching suggestions will be made based on the above analysis.The conclusions of this research are:Teacher’s feature in designing the math tasks: Teacher Z’s task design features the “teaching structure” with the designed math tasks corresponding to each segment of the “teaching structure”, and extra math tasks will be added based on the teaching content and students learning condition. Teachers shall pay great attention to theimplementation of the “Two Basics”(basic knowledge and basic skill), reviewing old knowledge in the introduction segment of each class and providing summary at the end of the class as well; Besides, the formation process of knowledge is an key point too and math tasks shall be supplemented or refined based on the teaching content;Moreover, class exercises shall focus on the quality rather than quantity; Teacher Z inclines to set the math task of high level cognition level.The implementation of math tasks in the class: Teachers will add or delete math types based on the feedback of homework and math task implementation condition of previous class. It can be caused by 4 reasons, they are 1. The teacher adds the math tasks of reviewing the old knowledge; 2. There appears the reinforce exercise that not exist in the teaching plan during the class; 3. The teacher supplements and refines the math task in the teaching plan; 4. The teacher adds or deletes math tasks due to spare or insufficient time. Influenced by the above reasons, the teacher sets 63% of the high cognition level tasks in the assigning session, but degrades the cognition level in organizing and implementation sessions. Teacher Z’s class ended up with low cognition level tasks accounting for 53% of the total task amount. There are mainly two factors of degrading the cognition level, i.e., “the teacher regularizes the task questions” and “the teacher shifts the key points from meaning, concept, and understanding to the correctness and completion of the answers”. On the other hand,there are three factors of maintaining the high cognition level, i.e., “The teacher‘builds scaffolding’ for the student’s mind and deduction”; “The teacher challenges,judges and/or feedbacks to emphasize the importance of testification, explanation and meaning”; “The teacher sets the tasks based on the student’s current cognition”.