【摘要】：微積分的誕生是數(shù)學(xué)發(fā)展史上一個(gè)劃時(shí)代的成就,為研究函數(shù)和變量提供了重要的方法和手段。二十一世紀(jì)以來(lái),微積分教學(xué)進(jìn)入一個(gè)新的時(shí)期,世界各國(guó)紛紛將微積分引入高中數(shù)學(xué)課程。2003年,我國(guó)教育部頒發(fā)了《普通高中數(shù)學(xué)課程標(biāo)準(zhǔn)(實(shí)驗(yàn))》,將微積分列為高中數(shù)學(xué)的選修課程。但是,新發(fā)行的教科書中并沒(méi)有按照“極限——導(dǎo)數(shù)——積分”的傳統(tǒng)方式編寫,淡化了極限知識(shí)的學(xué)習(xí),將導(dǎo)數(shù)作為一種特殊的極限(增量比的極限)來(lái)處理,直接通過(guò)反映導(dǎo)數(shù)思想和本質(zhì)的具體實(shí)例(如瞬時(shí)速度)引導(dǎo)學(xué)生認(rèn)識(shí)和理解導(dǎo)數(shù)的概念。HPM主要研究如何運(yùn)用數(shù)學(xué)史促進(jìn)數(shù)學(xué)教育,是數(shù)學(xué)教育研究的重要組成部分。目前數(shù)學(xué)教育專家都已經(jīng)意識(shí)到數(shù)學(xué)史在數(shù)學(xué)教育中的重要性,不僅能促進(jìn)學(xué)生課堂學(xué)習(xí)效率,還可以增加學(xué)生的數(shù)學(xué)史與數(shù)學(xué)文化方面的知識(shí),是新課程改革的有效實(shí)踐。本文中,筆者將基于HPM的相關(guān)研究探討在高中導(dǎo)數(shù)教學(xué)中融入數(shù)學(xué)史的教學(xué)設(shè)計(jì)。首先,由于導(dǎo)數(shù)是微積分的重要組成部分,要從歷史的角度提高導(dǎo)數(shù)概念教學(xué)的效率,將導(dǎo)數(shù)概念的產(chǎn)生和發(fā)展過(guò)程有效地滲透于導(dǎo)數(shù)教學(xué)實(shí)踐,必須對(duì)微積分的發(fā)展歷史進(jìn)行系統(tǒng)地了解,全面認(rèn)識(shí)從近半個(gè)世紀(jì)的醞釀到牛頓、萊布尼茨創(chuàng)立微積分,直到十八世紀(jì)柯西等人將微積分嚴(yán)格化的過(guò)程。其次,調(diào)查研究高三學(xué)生導(dǎo)數(shù)學(xué)習(xí)的現(xiàn)狀及理工類大一學(xué)生微積分學(xué)習(xí)的現(xiàn)狀,了解高中導(dǎo)數(shù)的學(xué)習(xí)對(duì)于大學(xué)微積分的學(xué)習(xí)是否有影響。對(duì)高中數(shù)學(xué)教師和高校高等數(shù)學(xué)教師進(jìn)行訪談,了解教師們關(guān)于這部分知識(shí)教學(xué)所持有的觀點(diǎn)。最后,根據(jù)調(diào)查研究,給出融入數(shù)學(xué)史的導(dǎo)數(shù)概念的教學(xué)設(shè)計(jì),并在課堂上實(shí)施檢驗(yàn)其效果,其目的在于為中學(xué)教師在數(shù)學(xué)教學(xué)中融入數(shù)學(xué)史提供參考與借鑒。
[Abstract]:The birth of calculus is an epoch-making achievement in the history of mathematical development, which provides an important method and means for the study of functions and variables. Since the 21 century, the teaching of calculus has entered a new period, and many countries in the world have introduced calculus into the mathematics curriculum of senior high school. The Ministry of Education of our country issued the ordinary Senior High School Mathematics Curriculum Standard (experiment), which included calculus as the elective course of senior high school mathematics. However, the newly published textbook is not written in the traditional way of "limit derivative integral," which weakens the learning of limit knowledge and treats derivative as a special limit (the limit of incremental ratio). Through concrete examples (such as instantaneous speed) which reflect the thought and essence of derivative, students are guided to know and understand the concept of derivative. HPM mainly studies how to use the history of mathematics to promote mathematics education, which is an important part of mathematics education research. At present, mathematics education experts have realized the importance of mathematics history in mathematics education, which can not only promote students' classroom learning efficiency, but also increase students' knowledge of mathematics history and mathematics culture, which is an effective practice of the new curriculum reform. In this paper, the author will discuss the teaching design of mathematics history in derivative teaching based on HPM. First of all, since derivative is an important part of calculus, it is necessary to improve the efficiency of derivative concept teaching from the historical point of view, and effectively infiltrate the process of producing and developing derivative concept into derivative teaching practice. It is necessary to systematically understand the history of the development of calculus, from the brewing of nearly half a century to Newton, Leibniz's creation of calculus, until Cauchy et al. Secondly, we investigate the current situation of derivative learning for senior three students and the present situation of calculus learning for freshmen in science and engineering, and understand whether the derivative learning in senior high school has an influence on the learning of college calculus. This paper interviews high school mathematics teachers and higher mathematics teachers in colleges and universities to find out the teachers' views on this part of knowledge teaching. Finally, according to the investigation and research, this paper gives the teaching design of the concept of derivative into the history of mathematics, and tests its effect in the classroom. The purpose of the design is to provide reference and reference for the middle school teachers to integrate the history of mathematics into the teaching of mathematics.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

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本文編號(hào)：2262342