發(fā)布時間：2019-06-19 05:30

【摘要】：三角函數(shù)是學生在高中階段應該掌握的一類基本初等函數(shù),是高中數(shù)學中的重要知識,三角函數(shù)有廣泛的應用,可見其重要性。本研究從高中生學習三角函數(shù)的認知特點出發(fā),了解和掌握高中生在三角函數(shù)學習中可能出現(xiàn)的認知錯誤及成因,并對典型性錯誤的案例進行詳細分析,尋求糾正錯誤的有效方法。本研究以文獻分析、訪談、調(diào)查、教學實踐研究等方法進行,通過編制三角函數(shù)錯誤類型測試卷,對2014-2015第一學期我校六個班級236名學生實施測試,針對測試結(jié)果,選取部分測試者進行非標準化訪談,再將測試和訪談結(jié)果進行歸納、總結(jié)、研究,發(fā)現(xiàn)高中生學習三角函數(shù)在概念和運算等方面出現(xiàn)的錯誤類型,總結(jié)、概括為四大類：(1)三角函數(shù)概念方面的錯誤；(2)三角函數(shù)圖象、性質(zhì)方面的錯誤；(3)基本公式運算方面的錯誤；(4)忽視條件限制方面的錯誤等。從高中生的認知結(jié)構(gòu)出發(fā),分析各種錯誤的成因,得出學生出現(xiàn)的錯誤多屬于知識性錯誤和認知策略性錯誤,總結(jié)出以下四種錯誤成因：(1)認知原因；(2)思維原因；(3)缺少反思；(4)其他原因,例如原有基礎(chǔ)知識不牢固、新知識體系不完善、新舊知識體系混淆、不良學習習慣的影響、思維定勢的消極作用,以及學生的畏難情緒等等。通過“防錯”與“糾錯”的實際教學案例,匯總學生在三角函數(shù)學習中容易出現(xiàn)的一些錯誤,并針對這些錯誤進行分析和更正,彌補知識上和心理上的不足,避免再次出錯。針對研究結(jié)果,結(jié)合高中生的特點提出了對三角函數(shù)這部分內(nèi)容在教學方面的一些建議,希望能通過三角函數(shù)的學習,有效地提高學生的探究能力和數(shù)學水平,能為一線教師積累一些經(jīng)驗,提供一些參考。
[Abstract]:Trigonometric function is a kind of basic elementary function that students should master in senior high school. It is an important knowledge in senior high school mathematics. Trigonometric function has a wide range of applications, so it can be seen that it is important. Based on the cognitive characteristics of senior high school students learning trigonometric functions, this study understands and grasps the possible cognitive errors and causes in trigonometric function learning of senior high school students, and analyzes the cases of typical errors in detail, so as to find an effective way to correct the errors. This study is carried out by means of literature analysis, interview, investigation and teaching practice research. 236 students from six classes in our school in the first semester of 2014 / 2015 are tested by compiling trigonometric function error type test paper. according to the test results, some testers are selected for non-standardized interviews, and then the test and interview results are summarized, summarized and studied. This paper finds out the types of errors in the concept and operation of trigonometric functions in senior high school students, and summarizes them into four categories: (1) the errors in the concept of trigonometric functions; (2) the image of trigonometric function, the error of property, (3) the error of basic formula operation, (4) the error of neglecting the limitation of condition, etc. Starting from the cognitive structure of senior high school students, this paper analyzes the causes of all kinds of errors, and concludes that most of the mistakes made by students belong to intellectual errors and cognitive strategic errors, and the following four causes of errors are summarized: (1) cognitive causes, (2) thinking reasons, (3) lack of reflection, (3) lack of reflection, (2) thinking reasons, (3) lack of reflection, and (3) lack of reflection. (4) other reasons, such as the original basic knowledge is not firm, the new knowledge system is not perfect, the new and old knowledge system is confused, the influence of bad learning habits, the negative effect of thinking stereotype, and the students' fear of difficulties and so on. Through the actual teaching cases of "error prevention" and "error correction", this paper summarizes some mistakes that are easy to occur in trigonometric function learning, and analyzes and corrects these errors, so as to make up for the lack of knowledge and psychology and avoid making mistakes again. According to the research results, this paper puts forward some suggestions on the teaching of trigonometric function according to the characteristics of senior high school students. It is hoped that through the study of trigonometric function, the students' inquiry ability and mathematics level can be effectively improved, and some experiences and references can be accumulated for front-line teachers.
【學位授予單位】：天津師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：G633.6

【相似文獻】

相關(guān)期刊論文 前7條

1 郭木生;;教師要善于經(jīng)營學生的認知錯誤[J];教育實踐與研究(A);2011年03期

2 ;最大的危險是無知[J];東西南北(大學生);2005年12期

3 余嘉元;運用規(guī)則空間模型識別解題中的認知錯誤[J];心理學報;1995年02期

4 杜文才;;美麗的錯誤,無價的資源[J];中學課程輔導(江蘇教師);2012年22期

5 唐秋美 ,曹中昌 ,高曉翠;改變認識走出低谷[J];心理與健康;1995年06期

6 周穎;;攻擊性幼兒的認知錯誤及矯正策略[J];教育導刊(下半月);2013年12期

7 ;[J];;年期

相關(guān)重要報紙文章 前2條

1 ;關(guān)于六要素[N];科技日報;2001年

2 本報記者 劉子陽;因認知錯誤致舉報不實不究責[N];法制日報;2014年

相關(guān)碩士學位論文 前1條

1 唐佳;高中生三角函數(shù)學習中認知錯誤及糾正的案例分析[D];天津師范大學;2015年

，

本文編號：2502130