The Case Analysis Of "Preliminary Algorithm" In Mathematics Of The High School

An introduction to algorithm is one of the newly added materials in the context of China's high school mathematics curriculum, it is the needs of present-day society. As we all know, Algorithm plays a vital role in pure mathematics and applied mathematics. The instruction of an Introduction to algorithm can also be viewed as a special feature of the Chinese mathematics new curriculum. As a result a high school mathematics teacher must point out both the difficulties and importance of algorithms while instructing. As Professor Shangzhi Wang pointed out, the teaching of algorithm is not simply let the student know either programming language or information technology, the key issue is to explain the reason why we compute like this.In the field of teaching algorithms at high-school level, developing new teaching materials is the key to successful teaching, but it seemed difficult for the instructors to develop new teaching materials and apply them in classroom teaching. The cases selected by the teachers must show the chrisma of solving mathematics problems via algorithms, reflect the core concept of algorithms, expressing the valuable idea that algorithms must be taught throughout the hole way of high-school mathematics instruction. In the practice level, teachers pay more attention at whether the cases provided by the textbook are suitable for the teaching practice. The point is that there are many aspects in the high school mathematics textbook needs to be improved. There rise a natural question that what can we do to improve the teaching of algorithms?Our research mainly aims at the following three aspects:1. Following the basic concepts and rules provided by the New National Mathematics Curriculum, based on the previous research by other scholars, we construct the basic principles of developing teaching cases in algorithm teaching.2. Taking the high-school mathematics text book A3 published by PEP press as an example, based on the basic principles, we pointed out the ins and outs of the teaching materials in algorithm teaching.3. We developed some new teaching materials, and analyze them carefully.In this paper, we use the method of case analysis to search, organize, analyze and classify relevant literatures and construct the basic principles of choosing cases in algorithm teaching. On the theoretical basis of this principle, we analyze the typical cases in mathematics textbooks and the quality of cases in algorithm teaching. Then we design some cases in algorithm teaching with typical contents moreover we summarize some characteristics and key points in the design of cases.Relerent conclusions are obtained in this paper:1. Make sure the problem situation is compatible with the contents while disigning algorithm cases.2. Highlight the main characteristics of algorithm while disigning algorithm cases.3. Focus on continuity while disigning algorithm cases.Teachers should bring some practical materials while teaching, let the students imitate, operate and explore something useful, finally reaching the aim that solving problems via the algorithms. As can be seen in the discussion, teaching based on the practical materials, is the soul of teaching, these teaching materials plays a vital role in teaching practice. Our research is based on the design and analysis of cases, we hope that our effort can be helpful developing the level of algorithm teaching, as well as providing some insightful materials to the relative research of high school algorithm teaching.