高中生對極限概念理解的研究
發(fā)布時間：2018-11-16 15:57
【摘要】：隨著新課標(biāo)的出臺和實施,極限概念與極限思想的教學(xué)已經(jīng)被大眾所忽視,而極限理論是微積分學(xué)昀基礎(chǔ),“極限思想”是微積分產(chǎn)生和發(fā)展的最重要、最基本的數(shù)學(xué)思想。高中階段若能較好的理解極限概念,可為后續(xù)學(xué)習(xí)微積分理論奠定重要的基礎(chǔ)。本文利用APOS理論,通過問卷調(diào)查和訪談的方法研究高中生在極限概念的理解上的差異,探索高中生在理解中存在的問題以及理解困難的成因,以期為學(xué)生的學(xué)習(xí)和教師的有效教學(xué)提供參考和建議。得到如下結(jié)論：首先,高中生對極限概念的理解在APOS的四個階段整體水平較低,并且沒有性別差異。在得分率最高的活動階段也僅有63.3%的學(xué)生能理解幾何背景下的極限概念；其次,高中生在極限概念理解中表現(xiàn)出對“∞�！钡睦斫饫щy,“∞�！弊鳛橐粋�數(shù)在學(xué)生頭腦中根深蒂固的存在；高中生對極限概念的理解中表現(xiàn)出對極限的過程和極限結(jié)果的精確性的理解的困難,70.05%的學(xué)生認(rèn)為“無限”一直在構(gòu)造中,永遠(yuǎn)完成不了的；學(xué)生對“極限觀”的應(yīng)用意識非常薄弱,知識的聯(lián)結(jié)方面的能力也較弱,很難上升到圖式階段。最后,影響學(xué)生對極限概念理解的主要原因是日常用語的干擾,難以理解極限的過程與極限的精確結(jié)果間的辯證關(guān)系和認(rèn)知結(jié)構(gòu)定勢。基于以上發(fā)現(xiàn),筆者對高中數(shù)學(xué)教師以及高中數(shù)學(xué)概念教學(xué)提出相應(yīng)的建議,以期為我國數(shù)學(xué)概念教學(xué)提供一定的參考。
[Abstract]:With the introduction and implementation of the new curriculum standard, the teaching of limit concept and limit thought has been ignored by the public, and limit theory is the foundation of calculus. Limit thought is the most important and basic mathematical thought for the generation and development of calculus. If the concept of limit can be well understood in senior middle school, it can lay an important foundation for further study of calculus theory. Based on the APOS theory, this paper studies the differences in the understanding of the limit concept of senior high school students by means of questionnaires and interviews, and explores the problems existing in the understanding of senior high school students and the causes of the difficulties in understanding. In order to provide reference and suggestions for students' learning and teachers' effective teaching. The conclusions are as follows: firstly, high school students' understanding of the concept of limit is relatively low in the four stages of APOS, and there is no gender difference. Only 63.3% of the students can understand the concept of limit in the geometric background in the stage of the highest score. Secondly, the high school students show "鈭，
本文編號：2335950
[Abstract]:With the introduction and implementation of the new curriculum standard, the teaching of limit concept and limit thought has been ignored by the public, and limit theory is the foundation of calculus. Limit thought is the most important and basic mathematical thought for the generation and development of calculus. If the concept of limit can be well understood in senior middle school, it can lay an important foundation for further study of calculus theory. Based on the APOS theory, this paper studies the differences in the understanding of the limit concept of senior high school students by means of questionnaires and interviews, and explores the problems existing in the understanding of senior high school students and the causes of the difficulties in understanding. In order to provide reference and suggestions for students' learning and teachers' effective teaching. The conclusions are as follows: firstly, high school students' understanding of the concept of limit is relatively low in the four stages of APOS, and there is no gender difference. Only 63.3% of the students can understand the concept of limit in the geometric background in the stage of the highest score. Secondly, the high school students show "鈭，
本文編號：2335950
本文鏈接：http://www.sikaile.net/jiaoyulunwen/chuzhongjiaoyu/2335950.html
最近更新
教材專著
