A Study Of Units Instruction Designing For "Mathematical Induction"

How to make unit teaching design in mathematics, there are many researchers have conducted studies, some research results have been applied to teaching. "Mathematical induction" is an important part of the high school mathematics. In the content system, Mathematical induction is a profound mathematical thinking method. Early researchers found that student only made use of mechanical application simply and they can’t understand the principle. Based on this, the author using the idea of unit teaching design, designs the "Mathematical induction", which can promote students to understand the essence of the "Mathematical induction" better, and make learning into practice.On the basis of the literature and teaching practice, the author thinks that the core of mathematics unit teaching design is mainly made up of six elements: mathematics, teaching material elements, learning elements, standard, target elements and structural elements. Based on the author’s cognitive level, this paper mainly discusses the elements of teaching materials, learning element and standards. Material elements analyze the content characteristics, structural characteristics and content expectation of four different versions of textbooks, which show the mathematical induction. Four different versions of textbooks include A version and B version of People Education Press, version of Beijing Normal University Press and version of JiangSu Education Press. In this paper, the author integrates the advantages and makes teaching design properly. As for the learning element, The author uses questionnaire investigation modeling after the Philippines and Egil research method to investigate three classes of grade 3 who have already finished the mathematical induction, these three classes include experimental classes, major work class and regular class. Through the questionnaire, the author can find out the students’ psychological difficulties after learning mathematical induction and then the author can feedback the results to other teachers to make students learn mathematical induction better and accumulate experience for teacher’s teaching design. Standard elements mainly analyze problems from the perspective of the evaluation. It investigates the recent five years college entrance examination papers involved in the mathematical induction and makes use of analysis comparison of Bao Jiansheng to analyze its changes in test difficulty. Through the guiding role of college entrance examination, the author reflect the way of handling problems to grasp the difficulty of teaching contents of the unit in the design and related questions scientifically.The focus of the work is based on the unit objectives, teaching arrangement, logic analysis and design of reflection to complete the teaching design of the unit.Under the guidance of unit teaching design, the author constructs four class teaching design by unit teaching designed systematically. The process of each class teaching design includes teaching aim, teaching difficulties, teaching methods, teaching process and teaching reflection. According to the arrangement of unit teaching and the design of the four classes are: the introduction of the principle of mathematical induction, avoid mathematical induction certificate error, deep understanding of the principle of mathematical induction, the use of mathematical induction to solve problems. The core of the design is to "understand". Fistly, understand the "Mathematical induction" principle, and gradually accept the principle of recursive thinking. Improve the level of students’ mathematical thinking and mathematical perspective. Secondly, understand the way to solve the problem, that is to say, summarized it first, then guess it, at last, prove it. This approach is not only applied to solve mathematical problems but also applied to other disciplines. It highlights the mathematical thinking method to solve the problem and make students know the origin of the mathematical conclusion, ways mathematicians creating ideas and improve the students’ confidence and maths accomplishment. The difficulty of four class unit design is several links more than loops at every level, from understanding the principle to application then to understand mathematical thinking. The aim of it is not only to teach students practice but also hope that it can help teachers making use of mathematics thinking method in the teaching.