基于數(shù)學史的高中導數(shù)教學設(shè)計研究
發(fā)布時間：2018-10-10 15:43
【摘要】：微積分的誕生是數(shù)學發(fā)展史上一個劃時代的成就,為研究函數(shù)和變量提供了重要的方法和手段。二十一世紀以來,微積分教學進入一個新的時期,世界各國紛紛將微積分引入高中數(shù)學課程。2003年,我國教育部頒發(fā)了《普通高中數(shù)學課程標準(實驗)》,將微積分列為高中數(shù)學的選修課程。但是,新發(fā)行的教科書中并沒有按照“極限——導數(shù)——積分”的傳統(tǒng)方式編寫,淡化了極限知識的學習,將導數(shù)作為一種特殊的極限(增量比的極限)來處理,直接通過反映導數(shù)思想和本質(zhì)的具體實例(如瞬時速度)引導學生認識和理解導數(shù)的概念。HPM主要研究如何運用數(shù)學史促進數(shù)學教育,是數(shù)學教育研究的重要組成部分。目前數(shù)學教育專家都已經(jīng)意識到數(shù)學史在數(shù)學教育中的重要性,不僅能促進學生課堂學習效率,還可以增加學生的數(shù)學史與數(shù)學文化方面的知識,是新課程改革的有效實踐。本文中,筆者將基于HPM的相關(guān)研究探討在高中導數(shù)教學中融入數(shù)學史的教學設(shè)計。首先,由于導數(shù)是微積分的重要組成部分,要從歷史的角度提高導數(shù)概念教學的效率,將導數(shù)概念的產(chǎn)生和發(fā)展過程有效地滲透于導數(shù)教學實踐,必須對微積分的發(fā)展歷史進行系統(tǒng)地了解,全面認識從近半個世紀的醞釀到牛頓、萊布尼茨創(chuàng)立微積分,直到十八世紀柯西等人將微積分嚴格化的過程。其次,調(diào)查研究高三學生導數(shù)學習的現(xiàn)狀及理工類大一學生微積分學習的現(xiàn)狀,了解高中導數(shù)的學習對于大學微積分的學習是否有影響。對高中數(shù)學教師和高校高等數(shù)學教師進行訪談,了解教師們關(guān)于這部分知識教學所持有的觀點。最后,根據(jù)調(diào)查研究,給出融入數(shù)學史的導數(shù)概念的教學設(shè)計,并在課堂上實施檢驗其效果,其目的在于為中學教師在數(shù)學教學中融入數(shù)學史提供參考與借鑒。
[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.
【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：G633.6
本文編號：2262342
[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.
【學位授予單位】：曲阜師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：G633.6
【參考文獻】
相關(guān)期刊論文 前5條
1 黃友初;朱雁;;HPM研究現(xiàn)狀與趨勢分析[J];全球教育展望;2013年02期
2 王嶸;;五套高中微積分課標教材的比較與分析[J];數(shù)學通報;2010年10期
3 朱衛(wèi)平;;大一學生對微積分基本概念的理解[J];數(shù)學教育學報;2010年04期
4 馮振舉;曲安京;;HPM視野下的數(shù)學新課程內(nèi)容構(gòu)成[J];課程.教材.教法;2007年09期
5 何小亞;;高中數(shù)學新課程微積分的課程設(shè)計分析[J];數(shù)學通報;2006年04期
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