The Problem - Based Teaching Research Of High School And The Reconstruction Of Teaching Content

The complex numbers not only has great historical significance in the history of mathematics development, but also has a great influence in scientific epistemology and methodology, and they have extensive application in modern science and technology. Complex numbers chapters in mathematics teaching in high school is a "easier to teach" but difficult lesson. On the one hand, the teaching material content algebraic formalization description, causes the student to complex numbers concept and its calculation can be more easily to obtain the formal memorization and applications, which is why complex numbers content on the surface is relatively easy to teach; on the other hand, it is the results as the starting point of the textbook in the complex numbers, form the complex numbers algebra and formalized definition complex numbers operation, to cover up the origin problem of the development of complex numbers concepts and complex numbers arithmetic, is not conducive to revealed the mathematical characteristics and the thought method of complex numbers and its calculation.This study based on the problem driven of mathematics teaching philosophy,examines the basic status of complex numbers teaching in high school :First of all,combing about the imaginary introduction 、expansion of our concept of number and the complex numbers operation of the current middle school mathematics textbooks,analyzed the problems in the preparation of teaching materials;Compare the difference between teaching requirements and the teaching content related to the secondary complex numbers knowledge in the main developed countries and regions and China, pointing out the gap between China complex numbers teaching requirements in high school. Secondly, in order to grasp the actual condition of middle school on the complex numbers teaching, investigate and research the chapters of the complex numbers teaching through observe lectures and teaching seminars,search and analyzes the problems existing in the high school of complex numbers teaching and its root causes; studied the literature concerning the complex numbersteaching of secondary school teachers, investigation of related understanding about mathematics teachers to the complex numbers teaching problem.Paper further introduces the complex numbers thread of the emergence and development, elaborated the deep physical background of promoting the development of the theory of complex numbers, explores the important thoughts and methods of complex numbers and its calculation, and look at the teaching problems of complex numbers content from the angle of mathematical thought, puts forward suggestions on the reconstruction of high school complex numbers teaching content.Finally, based on the analysis and investigation, reconstruction and preparation the complex numbers teaching content of problem-based driving, hoping to accurately grasp the primitive sexual problems of complex numbers emergence and the development, hoping to deep excavation the questions which can primitive sexual,touch and reveal the nature of the complex numbers, from the commander in understanding the complex numbers,and throughout the problem-driven design and reconstruction of the complex numbers teaching content. Refactoring plan conduct the teaching test and evaluation. New teaching material abandoned the algebra perspective and established the geometrical and physical view to introduce complex numbers, it is a good to answer: why do you want to put forward and introduced a concept of imaginary? How to properly define concept of complex numbers and the complex numbers operation? What are these concepts and operation bring us? Where can reflect the significance and scientific value of complex numbers ?...