本文選題：函數(shù)　切入點：課程發(fā)展主線　出處：《華東師范大學(xué)》2017年碩士論文

【摘要】：世界各國在進(jìn)入21世紀(jì)后都加緊了課程改革的腳步,我國的全國課程標(biāo)準(zhǔn)和上海市課程標(biāo)準(zhǔn)也在修訂之中.本文是上海市2015年教育科學(xué)研究重大項目:中小學(xué)數(shù)學(xué)教材的有效設(shè)計(項目編號D1508)的子課題1中小學(xué)數(shù)學(xué)課程內(nèi)容發(fā)展主線的頂層設(shè)計的階段性研究成果.由于函數(shù)在中小學(xué)尤其是中學(xué)階段占有非常重要的地位,因此本文將研究"函數(shù)"的內(nèi)容發(fā)展主線.本文總體上的研究問題是函數(shù)內(nèi)容在中小學(xué)教育階段是如何發(fā)生、發(fā)展的?具體說來有兩個研究問題:(1)學(xué)校數(shù)學(xué)中函數(shù)的核心內(nèi)容有哪些?(2)函數(shù)的核心內(nèi)容是怎樣在學(xué)校數(shù)學(xué)的課程中展開的?本文的研究方法是定性研究,包含了文本分析、比較和訪談.文本包括美國、英國、新加坡、澳大利亞、我國全國高中及義務(wù)教育課程標(biāo)準(zhǔn)和上海市中小學(xué)數(shù)學(xué)課程標(biāo)準(zhǔn)共6個課程標(biāo)準(zhǔn).訪談對象包括11名專家,分別涵蓋了大學(xué)數(shù)學(xué)系的數(shù)學(xué)教授(分析、代數(shù)、幾何方向)、大學(xué)數(shù)學(xué)教育研究者、教材編寫者和高中數(shù)學(xué)教研員.訪談采用半結(jié)構(gòu)式,問題主要用來對函數(shù)內(nèi)容的擬發(fā)展主線進(jìn)行修正.本文的發(fā)展主線的構(gòu)建是建立在學(xué)生認(rèn)知、課程論、數(shù)學(xué)的邏輯與實證研究之上的,它還可以不斷地進(jìn)行改進(jìn).本研究得到的結(jié)果為:問題(1)中小學(xué)階段函數(shù)的核心內(nèi)容有:函數(shù)的概念、函數(shù)的性質(zhì)、函數(shù)的應(yīng)用(與建模),并由6類基本初等函數(shù)作為載體來展開.對問題(2)的回答闡述如下:綜合數(shù)學(xué)中函數(shù)內(nèi)容的邏輯安排與學(xué)生的認(rèn)知特點,以及訪談專家的意見,得到,函數(shù)在中小學(xué)階段是按照"函數(shù)的鋪墊→函數(shù)的'變量說'概念→具體函數(shù)(1)→性質(zhì)→應(yīng)用→具體函數(shù)(2)→性質(zhì)→應(yīng)用→……→函數(shù)的'對應(yīng)說'概念→抽象性質(zhì)→具體函數(shù)(3)→性質(zhì)→應(yīng)用→具體函數(shù)(4)→性質(zhì)→應(yīng)用→……"展開,并以"基本初等函數(shù)→性質(zhì)→應(yīng)用"為單元展開.詳見本文圖19中小學(xué)函數(shù)內(nèi)容的發(fā)展主線圖,圖中從左至右、從下到上的函數(shù)內(nèi)容發(fā)展變化表示了隨著時間的推移,函數(shù)的內(nèi)容從簡單到復(fù)雜的發(fā)展過程.同時本研究還探討了學(xué)習(xí)函數(shù)內(nèi)容前所需要的鋪墊及函數(shù)內(nèi)容所體現(xiàn)的數(shù)學(xué)能力和思想方法.本研究理清了函數(shù)內(nèi)容在中小學(xué)階段的發(fā)展主線,為中小學(xué)數(shù)學(xué)課程標(biāo)準(zhǔn)和教材編寫提供設(shè)計思路,同時有助于教師站在較高的角度把握教材編寫脈絡(luò)、找準(zhǔn)函數(shù)的重點并合理安排函數(shù)內(nèi)容.
[Abstract]:After entering the 21st century, every country in the world has stepped up the pace of curriculum reform, and the national curriculum standards of our country and the curriculum standards of Shanghai are in the process of being revised.This paper is the achievement of the stage research on the top-level design of mathematics curriculum content development of primary and middle schools in Shanghai in 2015: the effective Design of Mathematics textbooks for Primary and Middle Schools (Project No. D1508).Since function plays a very important role in middle school, especially in middle school, this paper will study the main line of content development of "function".The overall research problem in this paper is how the function content occurs and develops in the primary and secondary education stage.Specifically, there are two research questions: 1) what is the core content of function in school mathematics? how does the core content of function develop in the curriculum of school mathematics?The research method of this paper is qualitative research, including text analysis, comparison and interview.The text includes six curriculum standards, including the United States, Britain, Singapore, Australia, China National High School and compulsory Education Curriculum Standard and Shanghai Primary and Middle School Mathematics Curriculum Standard.The subjects included 11 experts, including mathematics professors in the department of mathematics (analysis, algebra, geometry orientation, university mathematics education researchers, textbook writers and senior high school mathematics teachers).The interview is semi-structured, and the problem is mainly used to modify the main line of function content.The main development of this paper is based on student cognition, curriculum theory, mathematics logic and empirical research, it can also be continuously improved.The results of this study are as follows: question 1) the core contents of the function in primary and secondary schools are: the concept of function, the nature of function, the application of function (and modeling), and is carried out by six basic elementary functions as the carrier.The answer to question No. 2 is as follows: the logical arrangement of functional content and the cognitive characteristics of students in comprehensive mathematics, as well as the opinions of the experts, are obtained.In the primary and middle school stage, the function is applied according to the 'variable theory' concept of the function's bedding function and the application of the concrete function's property."Expansion, and the "basic elementary function properties of the application" as the unit expansion.In figure 19, the development of function content is shown in figure 19. The development of function content from left to right and from bottom to top shows that the content of function develops from simple to complex over time.At the same time, this study also discusses the need of learning function content and the mathematical ability and thought method of function content.This study clarifies the main line of development of function content in primary and secondary schools, provides design ideas for mathematics curriculum standards and textbook compilation in primary and secondary schools, and helps teachers to grasp the writing context of textbooks from a higher perspective.Find out the key points of the function and arrange the content of the function reasonably.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G633.6

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