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基于发生教学法的对数教学研究与实践

发布时间:2018-06-16 19:12

  本文选题:对数概念 + 发生教学法 ; 参考:《华中师范大学》2015年硕士论文


【摘要】:对数是高中数学课程一个重要的数学概念,是对数函数学习不可或缺的基础知识。一线教师在进行对数的教学时,一般是由指数概念引出对数的概念,这是从逻辑的角度进行教学,这样的方式虽然简洁,但对比发生教学的思想存在以下不足:一是不了解对数的意义,掩盖了对数引入的必要性;二是混淆错用对数运算法则;三是在对数符号接受存在困难。本文从对数思想的起源、对数表的发明、指对关系的揭示三个阶段对对数概念发明的历史进行了深入的研究,找到了促使对数发明的动力,并设计了调查问卷,调查学生对数概念的理解程度及对数符号的接受,在此基础上结合发生教学法的原理,重构了对数发明的历史,设计了对数概念的教学方式,并在一线教师和数学教育研究方向的研究生进行评估。以下是本研究获得的成果:(1)指数教学先于对数教学是合理的。现今教材的编排中,对数的概念安排在指数概念之后,这是因为在学生的知识体系中,指数一直以自乘的形式出现,先接受指数的概念,从逻辑的角度符合学生的认知,故教材出于系统性的考虑进行这样的安排是合理的。(2)直接由指数引出对数是不合理的。从逻辑的角度引出对数,过于注重结果,而忽视了导向结果的过程,从认知的角度来讲是非常困难的。概念的引入过于突兀,学生无法获得深层次的理解。故这种直接从指数出发,进行对数教学的方式是不合理的(3)完全遵循历史进行对数教学亦是不合理。对数的发明几经坎坷,历尽艰辛,倘若完全按照重历对数的发明过程,学生将面临巨大的困难,恐怕教师本身也难以完全知晓其中的关键。(4)对数教学应寻求历史与逻辑的平衡。从逻辑的角度进行对数的教学是存在缺陷的,从历史的角度进行对数概念的教学亦是不可取的。发生教学法注重从学生的认知出发,结合历史与当今的知识体系,通过重构历史,在历史与逻辑之间寻求平衡,促进学生更好地理解对数概念。基于以上的研究结论,本文给出一些教学启示,另有一个完整的教学设计,供一线教师参考。
[Abstract]:Logarithm is an important mathematical concept in high school mathematics curriculum, and it is an indispensable basic knowledge of logarithmic function learning. In the teaching of logarithm, first-line teachers generally derive the concept of logarithm from the concept of exponent, which is taught from a logical point of view. However, the thought of contrasting occurrence teaching has the following shortcomings: first, not understanding the meaning of logarithm, concealing the necessity of introducing logarithm; second, confusing the use of logarithmic arithmetic; third, having difficulty in accepting logarithmic symbols. In this paper, the origin of logarithmic thought, the invention of logarithmic table, the discovery of relationship, and the history of the invention of logarithmic concept have been deeply studied, and the motive force of logarithmic invention has been found, and a questionnaire has been designed. The understanding of logarithmic concept and the acceptance of logarithmic symbols are investigated. On the basis of this, the history of logarithmic invention is reconstructed and the teaching method of logarithmic concept is designed. And in the first line of teachers and mathematics education research direction of graduate students to evaluate. The following is the result of this study: 1) Index teaching is reasonable before logarithmic teaching. In the arrangement of textbooks nowadays, the concept of logarithm is arranged after the concept of exponent. This is because in the knowledge system of students, the index has always appeared in the form of self-multiplication. Therefore, it is reasonable to arrange the textbook for systematic consideration) it is unreasonable to draw logarithm directly from index. It is very difficult from a cognitive point of view to draw logarithm from the logical point of view, pay too much attention to the result, and ignore the process of guiding the result. The introduction of concepts is too abrupt for students to gain a deeper understanding. Therefore, it is unreasonable to carry out logarithmic teaching directly from the exponent) to follow the history completely and carry out logarithmic teaching. The invention of logarithm has been bumpy and arduous. If students follow the process of double logarithmic inventing, students will face great difficulties. I am afraid the teacher himself cannot fully know the key of logarithm.) logarithmic teaching should seek the balance between history and logic. Logarithmic teaching from the perspective of logic is flawed, and it is not advisable to teach logarithmic concepts from the perspective of history. Based on the students' cognition, combining the history with the present knowledge system, the occurrence teaching method seeks the balance between history and logic by reconstructing history, and promotes the students to understand the concept of logarithm better. Based on the above conclusions, this paper gives some teaching enlightenment and a complete teaching design for the reference of teachers.
【学位授予单位】:华中师范大学
【学位级别】:硕士
【学位授予年份】:2015
【分类号】:G633.6

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