Theoretical And Experimental Study On Learning From Mathematical Example

This study carries on following the three parts of research around mathematical examples: the first part, study on cognition of mathematical examples, including argumentation on that learning from mathematical example should become one important way of mathematics independence study and mathematics teacher and learner's cognition on mathematical examples; second part ,study on transfer result and influence of mathematical example, including the study in transfer results of different kinds of mathematical examples, and the characteristics of learning from mathematical example; the third part, design of material of those kinds of learning from mathematical example and the study of principle on learning from mathematical example.To improve mathematics classroom instruction efficiency is one basic task of study on mathematics education. Studies have shown that one of the most effective teaching strategies is to study independently by students; Through acting on one's own hard, reach the respective and different goal separately. No matter what kind of independent study way, reading the study material should be the first key link. In order to let students be able to study mathematics effectively through reading, the establishment of study material should be a key. The study material content in mathematics is roughly divided into three major parts: first, introduction of knowledge (situation open) and its analysis and explanation (understand and obtain the knowledge); second, the application example of knowledge; third, the arrangement and design of the exercise. The scientific and rational designs for the three parts are the strong guarantee of one's own successful study through reading. Among them, knowledge application is a key ring, which main form is worked example, so it is an important component of the study material of independence to design mathematical examples. Learning from mathematical example is a kind of study way, which students study by kinds of examples and in kinds of examples. And with the aid of already existing knowledge foundation or cognitive structure, students understand the example and construct a scheme voluntarily and form a kind of knowledge voluntarily. And it should become a kind of important way of independent study.The questionnaire investigation to teachers and students about learning from mathematical example shows that the main view of teacher's cognition about examples is that an example is not merely only a" model" for imitating, and an example still can play a role in explaining the concept, principle, formula, etc.. And an example can help students to understand the concept, strengthen the memory, and let students know how to use the principle or the formula to solve a problem. An important function of example about principle use can offer one example that how match the marriage partner's example among the principles, especially in a situation that the principle is comparatively abstract. One group examples used to lead orsummarize general principle or method except for having function that example release, which is regarded as abstract target also, from which support learner summarize general principle or schemas, and then applied it to the new problem.The cognition of the students' learning from example is different, but students can realize the function and importance of examples on mathematics study. The basic cognition has two respects: on the one hand, learning from example can help oneself understand knowledge, understand what ground application it will be; on the other hand, learning from example can help students to solve exercises further, and play a role in forming solving standard. Generally speaking, student's cognition of the example is still deeper. But to the individual it is not complete. For example, some students only think that the example just shows the standard form of solving problem, and some students think that the example is the basic question type that should be mastered, etc. In most students' eyes, the example in the current textbook is t...