本文關(guān)鍵詞： 三角函數(shù) 概念教學(xué) 現(xiàn)狀 改進　出處：《四川師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：數(shù)學(xué)概念教學(xué)一直受到廣泛的關(guān)注,新課程標(biāo)準(zhǔn)更加重視數(shù)學(xué)概念的形成過程,提倡揭示概念的本質(zhì)、背景以及蘊含的數(shù)學(xué)思想方法�！叭我饨堑娜呛瘮�(shù)”概念歷史發(fā)展悠久,其單位圓定義體現(xiàn)了高中數(shù)學(xué)最重要的數(shù)形結(jié)合思想。本研究以三角函數(shù)知識和概念教學(xué)的理論知識作為研究的基礎(chǔ),一方面,對“任意角的三角函數(shù)”教學(xué)進行現(xiàn)狀調(diào)查：訪談教師對三角函數(shù)知識的理解,觀察教師實際的教學(xué)課堂并檢測其教學(xué)質(zhì)量,分析教學(xué)問題以及原因,對有關(guān)三角函數(shù)的教學(xué)研究有一定參考作用。另一方面,在現(xiàn)狀調(diào)查的基礎(chǔ)上,改進“任意角的三角函數(shù)”概念的教學(xué)方案,并在課堂中實施、檢測、對比分析,旨在優(yōu)化“任意角的三角函數(shù)”概念教學(xué),對教師的實踐教學(xué)具有現(xiàn)實意義。具體的研究內(nèi)容與結(jié)論如下：首先,對“任意角的三角函數(shù)”和“概念教學(xué)”進行文獻研究。從三角函數(shù)的歷史發(fā)展與教學(xué)內(nèi)容對“任意角的三角函數(shù)”解讀,并簡述數(shù)學(xué)概念及其教學(xué)理論,將數(shù)學(xué)概念教學(xué)理論知識作為本研究的理論基礎(chǔ)。然后,在理論基礎(chǔ)上,通過訪談、課堂觀察、試卷測試重點調(diào)查了“任意角的三角函數(shù)”概念教學(xué)的現(xiàn)狀.現(xiàn)狀表現(xiàn)為：(1)大多數(shù)教師對“任意角的三角函數(shù)”概念的認(rèn)識限制于教材中呈現(xiàn)的知識邏輯。(2)教師對教學(xué)內(nèi)容的認(rèn)識基本上達到了教學(xué)要求,但是對教學(xué)內(nèi)容的處理缺乏技巧。(3)教師對教學(xué)內(nèi)容的呈現(xiàn)順序與教材呈現(xiàn)的順序一致。(4)教學(xué)方法主要以“講授法”為主,“引導(dǎo)-問答-講解”的教學(xué)模式。最后,與教師交流,將教學(xué)內(nèi)容的處理方式,教學(xué)方法進行分析和改進,設(shè)計教學(xué)方案并實施,得到研究結(jié)論：(1)以師生活動為主的問答法和討論法的教學(xué)方式,更容易引起學(xué)生學(xué)習(xí)興趣。(2)從函數(shù)角度認(rèn)識銳角三角函數(shù),并通過類比學(xué)習(xí)任意角的三角函數(shù)概念,可以消除舊知識對新知識獲得的負(fù)遷移作用。(3)以單位圓定義為中心,利用單位圓解決三角求值,符號判斷等問題可以突出教學(xué)重點,促進“任意角的三角函數(shù)”概念的形成。
[Abstract]:Mathematics concept teaching has attracted extensive attention, the new curriculum standard pays more attention to the forming process of mathematics concept, advocate explain the essence of the concepts, background and ways of thinking mathematically. "Trigonometric function" arbitrary angle concept of the long history of development, the definition of the unit circle is the most important high school mathematics Shuoxingjiehe thinking of this. Study on the theoretical knowledge of trigonometric function knowledge and concept teaching as the basis of the study, on the one hand, the investigation of "teaching trigonometric function" arbitrary angle: interview the teachers' understanding of the knowledge of the trigonometric function, observation of teachers' actual teaching and test the quality of teaching, analysis of teaching problems and reasons, have a certain reference study on the teaching of trigonometric function. On the other hand, on the basis of the survey, the teaching plan to improve the "trigonometric function" arbitrary angle concept, and in the classroom In the implementation, testing, comparison and analysis, in order to optimize the teaching of "trigonometric function" arbitrary angle concept, it has realistic significance to the teaching practice of teachers. The specific research contents and conclusions are as follows: firstly, research literature on "trigonometric function" arbitrary angle and "teaching". From the historical development and the teaching content of triangle the function of interpretation of "trigonometric function" arbitrary angle, and the mathematical concepts and teaching theory, the teaching theory of knowledge of mathematical concepts as the theoretical basis of this study. Then, on the basis of the theory, through interviews, classroom observation, test papers focusing on the investigation of the "trigonometric function" arbitrary angle of concept teaching status the status quo. Performance: (1) most of the teachers' understanding of the "trigonometric function" arbitrary angle limits of the concept of logic of knowledge in the teaching materials presented. (2) the teachers' understanding of teaching content basically achieve the teaching However, the lack of teaching content processing skills. (3) the same teachers show the order sequence and teaching materials for the presentation of teaching content. (4) the main teaching method in "teaching method", "Guide - Q - explanation" teaching mode. Finally, to communicate with the teacher, will teach the way of learning content the teaching method is analyzed and improved, teaching design and implementation, the research conclusion: (1) to students based question answering and discussion teaching method, easier to arouse students' interest in learning. (2) acute angle function from three known function angle, and by analogy learning trigonometric functions of arbitrary angle that can eliminate the negative transfer of old knowledge to new knowledge obtained. (3) to the unit circle is defined as the center, using the unit circle to solve the triangle evaluation, symbol judgment can highlight the focus of teaching, promote the "trigonometric function" concept of arbitrary angle Formation.

【學(xué)位授予單位】：四川師范大學(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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