本文關(guān)鍵詞：基于APOS理論的反比例函數(shù)教學(xué)研究　出處：《上海師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

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【摘要】：“數(shù)學(xué)理解”是現(xiàn)今數(shù)學(xué)教育研究與實(shí)踐的焦點(diǎn)之一,理解數(shù)學(xué)概念是數(shù)學(xué)課堂教學(xué)的關(guān)鍵。函數(shù)是初中代數(shù)的重要內(nèi)容,是刻畫和研究現(xiàn)實(shí)世界變化規(guī)律的重要模型。反比例函數(shù)是最基本的初等函數(shù)之一,是初中學(xué)生理解函數(shù)的重要載體。但是對(duì)于剛學(xué)習(xí)函數(shù)的八年級(jí)學(xué)生而言,在反比例函數(shù)概念形成和理解上存在難度�；谝陨媳尘�,本文試圖研究以下問(wèn)題:1、學(xué)生理解反比例函數(shù)概念的困難所在2、利用APOS理論優(yōu)化反比例函數(shù)的教學(xué),對(duì)學(xué)生是否產(chǎn)生積極的影響3、將APOS理論應(yīng)用于概念教學(xué)應(yīng)注意的問(wèn)題為解決這些問(wèn)題,本文將人教版與上教版反比例函數(shù)教學(xué)內(nèi)容、教學(xué)安排進(jìn)行對(duì)比分析,例析了學(xué)生學(xué)習(xí)反比例函數(shù)的困難所在,闡述應(yīng)用APOS理論在反比例函數(shù)教學(xué)中的可行性與必要性,探索出基于APOS理論的反比例函數(shù)的教學(xué)設(shè)計(jì)。根據(jù)同年級(jí)對(duì)照班和實(shí)驗(yàn)班,采用不同教學(xué)設(shè)計(jì)進(jìn)行同一內(nèi)容的教學(xué),設(shè)計(jì)測(cè)試問(wèn)卷、訪談,基于問(wèn)卷調(diào)查的數(shù)據(jù)進(jìn)行分析,得出學(xué)生在反比例函數(shù)的操作、過(guò)程、對(duì)象、圖示等不同階段的理解情況,通過(guò)反比例函數(shù)概念課的課堂對(duì)話分析、學(xué)生活動(dòng)分析,教學(xué)設(shè)計(jì)評(píng)價(jià)、學(xué)生認(rèn)知評(píng)價(jià),發(fā)現(xiàn)基于APOS理論的教學(xué)確實(shí)可以提高學(xué)生對(duì)反比例函數(shù)的理解水平,探索一些教學(xué)規(guī)律。學(xué)生對(duì)反比例函數(shù)操作階段的知識(shí)總體掌握良好,對(duì)反比例函數(shù)的形式化定義的認(rèn)知不夠全面。絕大多數(shù)學(xué)生對(duì)反比例函數(shù)的理解位于操作、過(guò)程階段,少數(shù)學(xué)生上升到對(duì)象、圖式階段,綜合應(yīng)用的能力較弱。對(duì)于概念課的教學(xué),操作、過(guò)程、對(duì)象、圖式循序漸進(jìn),教師要重視學(xué)生對(duì)概念本質(zhì)的體驗(yàn)和豐富內(nèi)涵的理解,引導(dǎo)學(xué)生經(jīng)歷概念本質(zhì)特征構(gòu)建和形成的過(guò)程。本文總結(jié)了對(duì)反比例教學(xué)的啟示:(1)關(guān)注課與課之間的內(nèi)在聯(lián)系,(2)關(guān)注反比例函數(shù)概念形成的過(guò)程,(3)用問(wèn)題引導(dǎo)學(xué)生學(xué)習(xí),(4)突破難點(diǎn),理解概念本質(zhì)。對(duì)概念教學(xué)的啟示:(1)扎實(shí)做好概念教學(xué),(2)通過(guò)多種形式提高學(xué)生概念理解水平,(3)注重引導(dǎo)反思、歸納提煉。對(duì)數(shù)學(xué)教學(xué)的啟示:(1)關(guān)注過(guò)程,促進(jìn)數(shù)學(xué)理解,(2)提高教學(xué)設(shè)計(jì)的有效性。
[Abstract]:"Mathematical understanding" is one of the focuses of mathematics education research and practice nowadays. Understanding mathematical concepts is the key of mathematics classroom teaching. Function is an important content of junior high school algebra. Inverse proportional function is one of the most basic elementary functions and an important carrier for junior high school students to understand the function. But for the eighth graders who have just learned the function. It is difficult to form and understand the concept of inverse proportional function. Based on the above background, this paper attempts to study the following question: 1, the difficulty for students to understand the concept of inverse proportional function 2. Using APOS theory to optimize the teaching of inverse proportion function has a positive effect on students. 3. The problem that should be paid attention to when applying APOS theory to concept teaching is to solve these problems. In this paper, the teaching contents and teaching arrangements of the inverse proportional function are compared and analyzed, and the difficulties of students in learning the inverse proportion function are analyzed. This paper expounds the feasibility and necessity of applying APOS theory in the teaching of inverse proportional function, and explores the teaching design of inverse proportional function based on APOS theory. Using different teaching design for the same content of teaching, design test questionnaires, interviews, based on the questionnaire data for analysis, the students in the inverse proportion function operation, process, object. Through the analysis of classroom dialogue, student activity analysis, teaching design evaluation, student cognition evaluation. It is found that teaching based on APOS theory can improve students' understanding of inverse proportional function and explore some teaching rules. The understanding of inverse proportional function is not comprehensive enough. Most students' understanding of inverse proportional function lies in operation, process stage, a few students rise to object, schema stage. The ability of comprehensive application is weak. For the teaching, operation, process, object and schema of concept class, teachers should pay attention to students' experience of concept essence and understanding of rich connotation. This paper summarizes the enlightenment to inverse teaching: 1) paying attention to the internal relationship between class and class. 2) paying attention to the process of forming the concept of inverse proportion function. (3) to guide students to study with questions) to break through the difficulties and to understand the essence of concepts. The enlightenment to concept teaching is to do a good job in concept teaching. (2) to improve students' level of conceptual understanding through various forms. The enlightenment to mathematics teaching is to pay attention to the process, to promote mathematics understanding and to improve the effectiveness of teaching design.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6

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