基于问题解决视角的“鸡兔同笼”问题优化教学研究

发布时间：2018-03-25 14:13

本文选题：小学数学　切入点：鸡兔同笼　出处：《贵州师范大学》2015年硕士论文

【摘要】：“鸡兔同笼”是一古老的数学名题。它从1500多年前传到现在,从我国走向世界,流传如此久远,且被我国、日本等纳入教材之中,必然有其内在的教育价值。然而,虽然广大教师投入了极高的教学与研究热情,但近几年讽刺挖苦之声甚嚣尘上。因此,为弘扬我国的古典文化,探讨其教育价值,并通过优化教学实现其育人功能就显得十分必要和重要了。本研究通过文献研究法对史料和现代文献进行了研读和梳理;通过案例研究法对有关该问题的解法、教学设计与反思等文献进行了个案分析,并深入课堂听课进行调查研究,在对其历史渊源及当前的教学与研究现状进行分析的基础上,做了以下探讨。首先,探讨了该问题的教学具有如下教育价值:对学生智力及能力的开发价值;对学生思维品质的培养价值;对学生数学思想方法的培养价值;传统文化教育价值,及个性品质培养和陶冶学生情操的美育价值。其次,针对众多的解题方法,进行了归纳分析与整合,揭示了它们的实质是科学发现方法论中的重要方法——尝试。第三,针对枚举、归纳拓展问题应用范围狭窄的问题,应用一般化方法,将其上升为一般问题模型:一些本身固有两方面特征数量的两种事物混合在一起,它们这两方面的特征数量之代数和已知,这两种事物各多少?其实质是所有能列成二元一次方程组的应用题。第四,针对学生备受折磨的各种奇思妙解,将幼儿画画数数解决该问题的过程,提炼为大众都能接受的解决这类问题的一般思维模型;揭示了其实质是二元一次方程组解法的来源;用其可解决所有的二元一次方程组,或可列为二元一次方程组的应用题。第五,从影响优化教学的教师、学生、新课标及教材的角度展开分析,提出了教学应与学生的认知发展水平相适应;与学生的生活经验相结合;以问题解决的教学模式进行教学;自主探究与教师引导有机结合;合作交流与独立思考有机结合;教学应在教材的基础上适当调整与拓展的优化教学的建议。第六,在前面为优化教学扫清了障碍,奠定前提条件的基础上,针对该问题的普适性,为发挥其教育价值,从问题解决教学模式的视角,进行了优化教学设计。
[Abstract]:"Chicken and Rabbit Cage" is an ancient mathematical title. It was passed down from more than 1500 years ago to now, from our country to the world, spread so long ago, and was included in the textbooks of our country, Japan and so on, it must have its inherent educational value. Although teachers have invested a great deal of enthusiasm in teaching and research, satire and sarcasm have been rampant in recent years. Therefore, in order to carry forward the classical culture of our country, we should discuss its educational value. It is very necessary and important to realize the function of educating people by optimizing teaching. This study has studied and combed the historical materials and modern documents through the method of literature research, and solved the problem by case study. On the basis of analyzing the historical origin and current situation of teaching and research, this paper makes the following discussion: firstly, the author makes a case study of teaching design and reflection, and makes an investigation and study in the classroom, and makes the following discussion on the basis of analyzing its historical origin and present situation of teaching and research. The teaching of this problem has the following educational value: the value of developing students' intelligence and ability, the value of cultivating students' thinking quality, the value of cultivating students' mathematical thinking methods, the value of traditional culture education, And the aesthetic value of personality quality cultivation and cultivation of students' sentiment. Secondly, in view of many problem-solving methods, it is concluded and analyzed and integrated, which reveals that their essence is an important method in the methodology of scientific discovery-try. In view of enumerating, generalizing and extending the narrow scope of application of the problem, the general method is used to raise it to a general problem model: two kinds of things which are inherent in the number of features of two aspects are mixed together. How many of these two things are each known and the number of their characteristics is algebraic and known? Its essence is all the application problems that can be listed as binary first order equations. Fourth, the process of drawing and counting children to solve this problem in allusion to the various puzzles that students suffer greatly. A general thought model for solving such problems that is acceptable to the general public; reveals that its essence is the source of solutions to binary first order equations; can be used to solve all binary first order equations, Fifth, from the perspective of teachers, students, new curriculum standards and teaching materials that affect the optimization of teaching, the author puts forward that teaching should be adapted to the level of cognitive development of students; Combining with students' life experience, teaching with problem-solving teaching mode, combining self-inquiry with teachers' guidance, combining cooperative communication with independent thinking; The teaching should be properly adjusted and expanded on the basis of teaching materials to optimize teaching. Sixth, on the basis of clearing the obstacles for the optimization of teaching in front of it and laying down the preconditions, aiming at the universality of the problem, in order to give full play to its educational value, From the perspective of problem-solving teaching mode, this paper carries on the optimized teaching design.
【学位授予单位】：贵州师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G623.5

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