本文選題：對數(shù)概念 + 發(fā)生教學法　； 參考：《華中師范大學》2015年碩士論文

【摘要】：對數(shù)是高中數(shù)學課程一個重要的數(shù)學概念,是對數(shù)函數(shù)學習不可或缺的基礎知識。一線教師在進行對數(shù)的教學時,一般是由指數(shù)概念引出對數(shù)的概念,這是從邏輯的角度進行教學,這樣的方式雖然簡潔,但對比發(fā)生教學的思想存在以下不足：一是不了解對數(shù)的意義,掩蓋了對數(shù)引入的必要性；二是混淆錯用對數(shù)運算法則；三是在對數(shù)符號接受存在困難。本文從對數(shù)思想的起源、對數(shù)表的發(fā)明、指對關(guān)系的揭示三個階段對對數(shù)概念發(fā)明的歷史進行了深入的研究,找到了促使對數(shù)發(fā)明的動力,并設計了調(diào)查問卷,調(diào)查學生對數(shù)概念的理解程度及對數(shù)符號的接受,在此基礎上結(jié)合發(fā)生教學法的原理,重構(gòu)了對數(shù)發(fā)明的歷史,設計了對數(shù)概念的教學方式,并在一線教師和數(shù)學教育研究方向的研究生進行評估。以下是本研究獲得的成果：(1)指數(shù)教學先于對數(shù)教學是合理的�，F(xiàn)今教材的編排中,對數(shù)的概念安排在指數(shù)概念之后,這是因為在學生的知識體系中,指數(shù)一直以自乘的形式出現(xiàn),先接受指數(shù)的概念,從邏輯的角度符合學生的認知,故教材出于系統(tǒng)性的考慮進行這樣的安排是合理的。(2)直接由指數(shù)引出對數(shù)是不合理的。從邏輯的角度引出對數(shù),過于注重結(jié)果,而忽視了導向結(jié)果的過程,從認知的角度來講是非常困難的。概念的引入過于突兀,學生無法獲得深層次的理解。故這種直接從指數(shù)出發(fā),進行對數(shù)教學的方式是不合理的(3)完全遵循歷史進行對數(shù)教學亦是不合理。對數(shù)的發(fā)明幾經(jīng)坎坷,歷盡艱辛,倘若完全按照重歷對數(shù)的發(fā)明過程,學生將面臨巨大的困難,恐怕教師本身也難以完全知曉其中的關(guān)鍵。(4)對數(shù)教學應尋求歷史與邏輯的平衡。從邏輯的角度進行對數(shù)的教學是存在缺陷的,從歷史的角度進行對數(shù)概念的教學亦是不可取的。發(fā)生教學法注重從學生的認知出發(fā),結(jié)合歷史與當今的知識體系,通過重構(gòu)歷史,在歷史與邏輯之間尋求平衡,促進學生更好地理解對數(shù)概念。基于以上的研究結(jié)論,本文給出一些教學啟示,另有一個完整的教學設計,供一線教師參考。
[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.
【學位授予單位】：華中師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：G633.6

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