本文選題：高一學(xué)生 + 分化點(diǎn)��； 參考：《南京師范大學(xué)》2015年碩士論文

【摘要】：數(shù)學(xué)學(xué)習(xí)上總存在一些知識(shí)點(diǎn),在學(xué)習(xí)過程容易導(dǎo)致學(xué)生產(chǎn)生分化,我們稱之為“分化點(diǎn)”。分化點(diǎn)內(nèi)容的掌握程度,直接影響學(xué)生的學(xué)習(xí)成績(jī),也是導(dǎo)致兩極分化的重要因素。從數(shù)學(xué)實(shí)際教學(xué)過程來看,學(xué)困生的出現(xiàn)都可以追溯到具體某一個(gè)分化點(diǎn)的學(xué)習(xí)上。雖然一部分教師已經(jīng)對(duì)高一數(shù)學(xué)分化點(diǎn)進(jìn)行探索研究,但是大多按具體章節(jié)討論,綜合概括、歸類分析較少；大部分研究集中在分化點(diǎn)的外在表現(xiàn),涉及具體內(nèi)容、成因分析,特別是心理成因分析較少。本文首先采用文獻(xiàn)研究的方法,結(jié)合個(gè)人的理解對(duì)分化點(diǎn)的概念作了界定：在教學(xué)過程中,受知識(shí)本身的特點(diǎn)和學(xué)生心理特征的影響,被教師忽略的教學(xué)內(nèi)容；或者是由于教學(xué)觀念陳舊使得問題解決不徹底而引起學(xué)習(xí)困難的重難點(diǎn)內(nèi)容；又或者是造成數(shù)學(xué)成績(jī)大面積滑坡,影響學(xué)生后續(xù)知識(shí)學(xué)習(xí)和最終高考的知識(shí)點(diǎn),都被稱之為“分化點(diǎn)”。在此基礎(chǔ)上,針對(duì)高一數(shù)學(xué)必修一和必修四的知識(shí)內(nèi)容,對(duì)師生進(jìn)行問卷調(diào)查、教師訪談、學(xué)生平時(shí)作業(yè)和測(cè)試的調(diào)查。通過對(duì)數(shù)據(jù)統(tǒng)計(jì)分析,本文得到高一學(xué)生數(shù)學(xué)學(xué)習(xí)(必修一和必修四)中分化點(diǎn),從分化點(diǎn)自身的特點(diǎn)、學(xué)生的認(rèn)知特征、教師的教學(xué)狀況三方面分析了分化點(diǎn)的成因,并提出突破分化點(diǎn)的一般教學(xué)策略和不同類型分化點(diǎn)的教學(xué)策略。最后選擇兩個(gè)班學(xué)生作為研究樣本,進(jìn)行等組實(shí)驗(yàn)。通過問卷調(diào)查、成因分析、策略研究、等組實(shí)驗(yàn)等途徑,本研究主要獲得了以下幾個(gè)基本結(jié)論：(1)認(rèn)定高一學(xué)生數(shù)學(xué)學(xué)習(xí)(必修一和必修四)分化點(diǎn)通過師生的問卷調(diào)查、學(xué)生平時(shí)作業(yè)與測(cè)試的統(tǒng)計(jì),認(rèn)定高一學(xué)生數(shù)學(xué)學(xué)習(xí)(必修一和必修四)的分化點(diǎn),具體是：子集、全集補(bǔ)集、交集、并集、函數(shù)的概念和圖像、函數(shù)的簡(jiǎn)單性質(zhì)、映射的概念、分?jǐn)?shù)指數(shù)冪、指數(shù)函數(shù)、對(duì)數(shù)函數(shù)函數(shù)的零點(diǎn)、用二分法求方程的近似解、函數(shù)的模型及其應(yīng)用、任意角的三角函數(shù)、同角三角函數(shù)關(guān)系、三角函數(shù)的誘導(dǎo)公式、三角函數(shù)的圖像及性質(zhì)、函數(shù)y=A sin(ωx+φ)的圖像、平面向量的基本定理、向量的數(shù)乘、向量的應(yīng)用、兩角和與差的余弦正弦、二倍角的三角函數(shù)。(2)從分化點(diǎn)本身的特點(diǎn)、學(xué)生的認(rèn)知特征、教師的教學(xué)狀況分析高一學(xué)生數(shù)學(xué)學(xué)習(xí)分化點(diǎn)的成因在本研究中發(fā)現(xiàn),從分化點(diǎn)本身來看,在認(rèn)定的分化點(diǎn)所對(duì)應(yīng)的知識(shí)內(nèi)容分別是集合、函數(shù)、三角函數(shù)和平面向量；從學(xué)生的認(rèn)知特征上看,存在著高一學(xué)生的認(rèn)知結(jié)構(gòu)還不夠完善、學(xué)生的思維發(fā)展與學(xué)科思維之間有矛盾、學(xué)生的情意發(fā)展與認(rèn)知發(fā)展還不夠協(xié)調(diào)、學(xué)生學(xué)習(xí)的自我監(jiān)控能力和自我意識(shí)不夠強(qiáng)的因素；從教師的教學(xué)狀況上分析,存在“角色分化”、“經(jīng)驗(yàn)主義”、重結(jié)果輕過程、重知識(shí)輕方法等弊端。(3)本文按陳述性分化點(diǎn)、程序性分化點(diǎn)、過程性分化點(diǎn)提出突破分化點(diǎn)的教學(xué)策略通過對(duì)高一學(xué)生數(shù)學(xué)學(xué)習(xí)分化點(diǎn)的調(diào)查,結(jié)合成因分析,提出了教學(xué)策略,具體為針對(duì)陳述性分化點(diǎn)建議：促進(jìn)學(xué)生對(duì)陳述性分化點(diǎn)內(nèi)容組織和加工、促進(jìn)學(xué)生“圖式”的形成；針對(duì)程序性分化點(diǎn)提出：促進(jìn)學(xué)生產(chǎn)生式系統(tǒng)的建構(gòu)、促進(jìn)學(xué)生自我監(jiān)控能力的培養(yǎng)；針對(duì)過程性分化點(diǎn),希望教師能為學(xué)生提供適當(dāng)?shù)那榫?使他們親身體驗(yàn)知識(shí)的建構(gòu)過程。(4)結(jié)合“函數(shù)的概念和圖像”分化點(diǎn)的研究給出范例,并就教學(xué)策略的有效性進(jìn)行等組實(shí)驗(yàn)研究通過對(duì)“函數(shù)的概念和圖像”分化點(diǎn)的調(diào)查與分析,提出概念教學(xué)環(huán)節(jié)中的三個(gè)階段：概念習(xí)得階段、概念應(yīng)用階段、反思提升階段。進(jìn)而通過等組實(shí)驗(yàn)研究發(fā)現(xiàn)：如果對(duì)分化點(diǎn)成因分析恰當(dāng),教學(xué)策略得當(dāng),學(xué)生的學(xué)習(xí)興趣和學(xué)習(xí)成績(jī)會(huì)有所提高,對(duì)分化點(diǎn)的突破也有正面影響。
[Abstract]:There are always some knowledge points in the study of mathematics. In the process of learning, it is easy to lead to students' differentiation. We call it "differentiation point". The degree of mastery of the content of the differentiation point directly affects the students' learning achievement. It is also an important factor that leads to the polarization. From the perspective of the practical teaching of mathematics, the emergence of the students of learning difficulties can be traced back to the concrete. Although some teachers have explored the differentiation point of high mathematics, most of them are discussed in specific chapters, comprehensive generalization, and less classification analysis. Most of the studies focus on the external performance of the differentiation point, involving specific content, cause analysis, especially the psychological cause analysis. The concept of the differentiation point is defined by the method of literature research and personal understanding. In the course of teaching, the teaching content is ignored by the teacher, which is influenced by the characteristics of knowledge itself and the psychological characteristics of the students; or the difficult and difficult content of the learning difficulties is caused by the obsolescence of the teaching concept, and the difficulty of learning is caused by the obsolescence of the teaching concept; or On the basis of this, a questionnaire survey for teachers and students, teachers' interviews, and the investigation of students' daily homework and testing are carried out on the basis of the data statistics. This paper analyzes the differentiation points in the students' mathematics learning (compulsory and compulsory four). From the characteristics of the differentiation point, the cognitive characteristics of the students and the teaching situation of the teachers, this paper analyzes the causes of the differentiation points, and puts forward the general teaching strategy and the teaching strategy of different types of differentiation points. Finally, it chooses two classes of students. As the research sample, we carry out the group experiment. Through the questionnaire survey, the genetic analysis, the strategy research, and other groups of experiments, the main conclusions are obtained as follows: (1) it is found that the students' mathematical learning (compulsory and compulsory) is determined by the questionnaire survey by teachers and students, and the students' daily homework and test statistics are found to be higher. The student mathematics learning (compulsory and compulsory four) differentiation point, specifically: subset, complete complete complement, intersection, combined, the concept and image of function, the simple property of function, the concept of mapping, fractional exponentiation, exponential function, logarithmic function zero point, the approximate solution of the equation with the two method, the function model and its application, the three of arbitrary angle. The angular function, the relation of the trigonometric trigonometric function, the induction formula of the trigonometric function, the image and properties of the trigonometric function, the image of the function y=A sin (omega x+ phi), the basic theorem of the plane vector, the number multiplication of the vector, the application of the vector, the cosine sine of the difference and the three angle function of the two fold angle. (2) the characteristics of the differentiation point itself, the cognitive characteristics of the students, and the teaching of the students. From the point of view of the differentiation point, the knowledge content corresponding to the differentiation point is set, function, trigonometric function and plane vector from the point of differentiation itself. From the cognitive characteristics of the students, the cognitive structure of the students in the high one is not perfect. There is a contradiction between the development of students' thinking and the thinking of the subject. The students' emotional development and cognitive development are not well coordinated, the self-monitoring ability and self consciousness of the students are not strong enough. From the teaching situation of the teachers, there are some disadvantages such as "role differentiation", "empiricism", heavy result light process, and heavy knowledge and light method. (3) In this paper, the teaching strategy is put forward through the investigation of the differentiation point of high school students and the analysis of the reasons for the differentiation point of the process differentiation point according to the point of the declarative differentiation, the procedural differentiation point and the process differentiation point. The formation of "schema" for students; to the point of procedural differentiation: to promote the construction of students' generation system and to promote the cultivation of students' self-monitoring ability. In the light of the process differentiation point, we hope that teachers can provide students with appropriate situations to experience the construction process of knowledge. (4) combining the "concept of function and image". The study of the point is given an example, and the experimental research on the effectiveness of the teaching strategy is carried out by the investigation and analysis of the differentiation point of "the concept and image of the function". The three stages of the concept teaching link are put forward: the phase of concept acquisition, the phase of concept application, and the reflection of the ascending order. The analysis of the causes of differentiation is appropriate. If the teaching strategies are appropriate, students' interest in learning and academic performance will be improved, and they will also have a positive impact on breakthroughs in differentiation.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 龐維國(guó);;論學(xué)習(xí)方式[J];課程·教材·教法;2010年05期

2 鄭強(qiáng);;數(shù)學(xué)素養(yǎng)與數(shù)學(xué)教學(xué)[J];山東教育學(xué)院學(xué)報(bào);2006年05期

3 陶興模;學(xué)困生學(xué)習(xí)心理障礙分析及對(duì)策研究[J];數(shù)學(xué)教育學(xué)報(bào);2004年02期

4 胡定喜;;淺談初中數(shù)學(xué)教學(xué)分化點(diǎn)的處理[J];德陽(yáng)教育學(xué)院學(xué)報(bào);2001年S3期

5 喻緯;;初中數(shù)學(xué)教學(xué)分化點(diǎn)再探[J];江蘇教育;1987年08期

6 喻緯;;初中數(shù)學(xué)“教學(xué)分化點(diǎn)”的初步調(diào)查和分析[J];揚(yáng)州師院學(xué)報(bào)(自然科學(xué)版);1984年01期

相關(guān)碩士學(xué)位論文 前3條

1 王連國(guó);高中生概率學(xué)習(xí)認(rèn)知障礙分析及對(duì)策研究[D];山東師范大學(xué);2011年

2 鄭曉偉;初一學(xué)生數(shù)學(xué)學(xué)習(xí)分化點(diǎn)的探討和教學(xué)對(duì)策[D];山東師范大學(xué);2011年

3 李春燕;初中化學(xué)分化點(diǎn)的探討和教學(xué)對(duì)策[D];蘇州大學(xué);2008年

，

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