高中圓錐曲線的概念教學(xué)探究
發(fā)布時間：2018-09-04 15:49
【摘要】：圓錐曲線是高中平面解析幾何的核心內(nèi)容,它借助平面直角坐標(biāo)系用坐標(biāo)法研究平面幾何圖形的方程,并從方程出發(fā),研究平面幾何圖形的性質(zhì),把數(shù)和形緊密結(jié)合在一起,充分展示了數(shù)形結(jié)合的思想方法。本文從圓錐曲線的歷史出發(fā),基于阿波羅尼奧斯(Apollonius,約公元前262～190年)的《圓錐曲線論》,從數(shù)學(xué)史的角度考察圓錐曲線的產(chǎn)生和發(fā)展過程。結(jié)合筆者多年的教學(xué)實踐和領(lǐng)會,就大綱版高中數(shù)學(xué)教科書和新課標(biāo)高中數(shù)學(xué)教科書(人教版)中各知識點的具體要求和變化進行探析,同時對現(xiàn)行人教版教科書(A版、B版)、蘇教版、北師大版教科書進行簡單比較,發(fā)現(xiàn)在由應(yīng)試教育向素質(zhì)教育轉(zhuǎn)變的今天,不應(yīng)“重解題,輕概念”,造成數(shù)學(xué)概念與解題相脫節(jié),概念含糊不清則知識體系將不完整,這不符合素質(zhì)教育的要求,也影響學(xué)生的思維品質(zhì)。數(shù)學(xué)概念是學(xué)生學(xué)習(xí)數(shù)學(xué)知識的起點,是導(dǎo)出數(shù)學(xué)定理和數(shù)學(xué)相關(guān)知識的邏輯前提,是基礎(chǔ)知識、基本能力教學(xué)的核心,是數(shù)學(xué)教學(xué)的重要組成部分,深刻理解概念的內(nèi)涵與外延是掌握這些重要圓錐曲線的前提,因此要讓學(xué)生動手、動腦、動口,對知識進行主動探索、主動發(fā)現(xiàn)、自主學(xué)習(xí)。通過比較分析,提出了圓錐曲線概念教學(xué)的處理方法：通過實例激發(fā)學(xué)生的學(xué)習(xí)興趣；借助多媒體和數(shù)學(xué)教室展示圓錐曲線形成過程；用準(zhǔn)確的語言文字描述圓錐曲線的概念并將其符號化；將概念運用到問題解決中,在概念教學(xué)中滲透數(shù)學(xué)思想方法；歸納典型題及教師如何合理地使用數(shù)學(xué)教科書中的內(nèi)容等。在理解概念和應(yīng)用概念上,采取活動式教學(xué)為主讓學(xué)生主動參與其中,并結(jié)合從形到數(shù)、再從數(shù)到形的例題,充分地理解概念并進行相關(guān)的問題解決。教學(xué)中合理使用數(shù)學(xué)教科書中提供的例題和習(xí)題,通過深入挖掘進行變式訓(xùn)練、一題多解等培養(yǎng)學(xué)生的解題能力。
[Abstract]:Conic curve is the core content of plane analytic geometry in high school. It studies the equation of plane geometry by using coordinate method with the aid of plane rectangular coordinate system, and studies the properties of plane geometry from the point of view of equation, which combines the number and shape closely together. The thought method of the combination of number and form is fully demonstrated. Starting from the history of conic, based on the theory of conic by Apollonius, (about 262 ~ 190 BC), this paper investigates the generation and development of conic from the point of view of the history of mathematics. Combined with the author's teaching practice and understanding for many years, this paper probes into the specific requirements and changes of the knowledge points in the syllabus edition of senior high school mathematics textbooks and the mathematics textbooks in the new curriculum marking (people's Education Edition). At the same time, a simple comparison is made among the current textbooks for the education of people (A edition, edition B), the Soviet edition, and the edition of Peking normal University, and it is found that in today's transition from examination-oriented education to quality-oriented education, we should not "pay more attention to solving problems than to concepts." This will lead to the disconnection between mathematical concept and problem solving, and the ambiguity of concept will result in incomplete knowledge system, which does not meet the requirements of quality education and affect the thinking quality of students. The concept of mathematics is the starting point for students to learn mathematical knowledge, the logical premise for deriving mathematical theorems and related knowledge, the core of basic knowledge and basic ability teaching, and the important part of mathematics teaching. A deep understanding of the connotation and extension of the concept is the premise of mastering these important conic curves, so students should be allowed to start, use their brains, move their mouth, actively explore knowledge, discover actively, and learn independently. Through comparison and analysis, the paper puts forward the teaching methods of conic curve: arousing students' interest in learning through examples, displaying the forming process of conic curve by means of multimedia and mathematics classroom; The concept of conic curve is described and symbolized with accurate language and characters; the concept is applied to the problem solving, and the mathematical thinking method is infiltrated in the concept teaching; the typical problems and how to use the contents of the mathematics textbook reasonably are summarized. In terms of understanding concepts and applying concepts, active teaching is adopted to let students take part in them actively, and combined with examples from form to number, then from number to form, the concept is fully understood and the relevant problems are solved. In teaching, the examples and exercises provided in mathematics textbooks are used reasonably, and the students' ability to solve problems is trained by digging deeply and solving many problems.
【學(xué)位授予單位】：內(nèi)蒙古師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：G633.6
本文編號：2222631
[Abstract]:Conic curve is the core content of plane analytic geometry in high school. It studies the equation of plane geometry by using coordinate method with the aid of plane rectangular coordinate system, and studies the properties of plane geometry from the point of view of equation, which combines the number and shape closely together. The thought method of the combination of number and form is fully demonstrated. Starting from the history of conic, based on the theory of conic by Apollonius, (about 262 ~ 190 BC), this paper investigates the generation and development of conic from the point of view of the history of mathematics. Combined with the author's teaching practice and understanding for many years, this paper probes into the specific requirements and changes of the knowledge points in the syllabus edition of senior high school mathematics textbooks and the mathematics textbooks in the new curriculum marking (people's Education Edition). At the same time, a simple comparison is made among the current textbooks for the education of people (A edition, edition B), the Soviet edition, and the edition of Peking normal University, and it is found that in today's transition from examination-oriented education to quality-oriented education, we should not "pay more attention to solving problems than to concepts." This will lead to the disconnection between mathematical concept and problem solving, and the ambiguity of concept will result in incomplete knowledge system, which does not meet the requirements of quality education and affect the thinking quality of students. The concept of mathematics is the starting point for students to learn mathematical knowledge, the logical premise for deriving mathematical theorems and related knowledge, the core of basic knowledge and basic ability teaching, and the important part of mathematics teaching. A deep understanding of the connotation and extension of the concept is the premise of mastering these important conic curves, so students should be allowed to start, use their brains, move their mouth, actively explore knowledge, discover actively, and learn independently. Through comparison and analysis, the paper puts forward the teaching methods of conic curve: arousing students' interest in learning through examples, displaying the forming process of conic curve by means of multimedia and mathematics classroom; The concept of conic curve is described and symbolized with accurate language and characters; the concept is applied to the problem solving, and the mathematical thinking method is infiltrated in the concept teaching; the typical problems and how to use the contents of the mathematics textbook reasonably are summarized. In terms of understanding concepts and applying concepts, active teaching is adopted to let students take part in them actively, and combined with examples from form to number, then from number to form, the concept is fully understood and the relevant problems are solved. In teaching, the examples and exercises provided in mathematics textbooks are used reasonably, and the students' ability to solve problems is trained by digging deeply and solving many problems.
【學(xué)位授予單位】：內(nèi)蒙古師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：G633.6
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