Generative Teaching High School Mathematics Problem Solving Resource Development Problems And Case Studies

The generative resources of problem-solving teaching refers to the following process:in a math class, compared with the relatively static problem-solving methods and the predesigned problem-solving process, the teaching and learning activities go beyond the original thoughts and the teaching plan and dynamically generate some new cases, problems and methods that are helpful in aiding the students to solve the problems and gain unexpected development.Theoretical basis of the research:(1) Wittrock’s generative learning theory.(2)Nimmo’s emergent course theory.(3) The humanism educational theory.(4) The Constructivism theory.Findings from the questionnaires show:Teachers lack a full understanding about the basics of the generative resources, full intention to generate in problem-solving teaching and enough anticipation of the generative resources in class; teacher-controlled classroom behaviors influence the students’learning behaviors and prevent their active generation; teachers lack effective strategies of developing generating resources and enough experience in dealing with emergent cases in class, and they should have more teaching wits.Insights acquired from the case analysis are:excellent teachers timely use quite a variety of strategies of developing generative resources, for example, creating communication scenarios, finding out the reasons for making mistakes when solving problems, kindly dealing with the different opinions in students’group discussions, asking the students to analyze and correct the mistakes and encouraging them to bring up unexpected topics, accumulating the teachers’teaching wits and timely capturing the ingenious thoughts generated in class. All these strategies help to generate new resources in problem-solving teaching.Excellent teachers pay great attention to the development of generative resources in problem-solving teaching:they leave space in their teaching plan, which leaves time and space and creates opportunities for generating teaching. They make an effort in creating a democratic and relaxing teaching atmosphere for developing generative resources. They effectively cultivate the students’awareness to ask questions and reflex so as to reverse the passive state of developing generative resources. They are good at finding out mistakes the students made during classes, and help them to analyze and correct them. They are also capable of taking use of the variants of the exercises to lead in the questions and stimulate the students’inspirations. They also make use of the different solutions to the problem to broaden the students’minds so as to enhance the effectiveness of the math-problem-solving classes.Suggestions for developing the generative resources of problem-solving teaching include: from the perspective of the teaching methods, the heuristic teaching based on generating resources of a problem type, the modifiable teaching based on creative resource generation and the teaching method of providing different solutions to a problem based on generating different resources. From the perspective of the students’learning method, the way of taking the initiative to research should be fostered for the students. The teachers’wits should be sharpened so that they can pay attention to the students’needs when designing the courses, or the learning, which should be planned flexibly instead of rigidly. From the perspective of classroom assessment, a harmonious atmosphere should be created and creative thoughts should be inspired.