本文選題：數(shù)學(xué)程序性知識(shí) + 數(shù)學(xué)理解��； 參考：《山東師范大學(xué)》2016年碩士論文

【摘要】：數(shù)學(xué)程序性知識(shí)是高中生數(shù)學(xué)學(xué)習(xí)的重要組成部分,它不僅能夠影響到學(xué)生的學(xué)習(xí)成績(jī),而且對(duì)學(xué)生學(xué)習(xí)信念和學(xué)習(xí)積極性等各方面都有一定影響。現(xiàn)實(shí)的情況是部分高中生不能夠理解數(shù)學(xué)程序性知識(shí),因此,研究高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解過(guò)程是非常重要的。當(dāng)前關(guān)于數(shù)學(xué)理解的研究多集中在數(shù)學(xué)理解的內(nèi)涵、層次、特點(diǎn)、功能、以及調(diào)查研究等方面,而對(duì)于數(shù)學(xué)認(rèn)知理解的研究比較少,特別是對(duì)理解程序性知識(shí)的心理過(guò)程的研究幾乎沒(méi)有。本人在前人研究的基礎(chǔ)上,結(jié)合當(dāng)前高中生數(shù)學(xué)程序性知識(shí)的學(xué)習(xí)情況,深入研究了高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解心理過(guò)程,并且在研究基礎(chǔ)上提出了相應(yīng)的教學(xué)要求和教學(xué)建議。本文主要采用了文獻(xiàn)分析法、訪(fǎng)談法和口語(yǔ)報(bào)告法等研究方法。本文的研究順序是:第一,閱讀大量與數(shù)學(xué)理解有關(guān)的文獻(xiàn),對(duì)國(guó)內(nèi)外數(shù)學(xué)理解的已有研究進(jìn)行綜述;第二,閱讀大量與程序性知識(shí)和數(shù)學(xué)認(rèn)知理解有關(guān)的文獻(xiàn),并且做相關(guān)的理論分析;第三,制定教師訪(fǎng)談提綱,并通過(guò)訪(fǎng)談初步確定影響高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的因素;第四,制定學(xué)生訪(fǎng)談提綱,并通過(guò)對(duì)學(xué)生的初步訪(fǎng)談最終確定影響高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的因素;第五,對(duì)學(xué)生進(jìn)行訪(fǎng)談,確定影響高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的關(guān)鍵因素是什么;第六,對(duì)學(xué)生進(jìn)行訪(fǎng)談,在影響高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的關(guān)鍵因素的基礎(chǔ)上,總結(jié)出高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的過(guò)程、特點(diǎn)和模型;第七,根據(jù)以上的研究結(jié)果和結(jié)論,提出相應(yīng)的教學(xué)要求和教學(xué)建議。本文研究得出的主要結(jié)論有:一、影響高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的因素主要有六個(gè),分別是新舊知識(shí)之間的聯(lián)系、數(shù)學(xué)程序性知識(shí)相關(guān)歷史、數(shù)學(xué)程序性知識(shí)相關(guān)證明、數(shù)學(xué)程序性知識(shí)相關(guān)應(yīng)用、數(shù)學(xué)程序性知識(shí)相關(guān)原則和數(shù)學(xué)程序性知識(shí)相關(guān)適用范圍;二、影響高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解最關(guān)鍵的因素是新舊知識(shí)之間聯(lián)系;三、高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解過(guò)程具有積極主動(dòng)性、連續(xù)性、順序性、遲緩性、惰性和迅捷性的特點(diǎn);四、高中生數(shù)學(xué)程序性知識(shí)認(rèn)知理解的過(guò)程主要是學(xué)生認(rèn)知結(jié)構(gòu)當(dāng)中產(chǎn)生式系統(tǒng)的不斷完善。具體如下:學(xué)生遇到新的數(shù)學(xué)程序性知識(shí)后積極主動(dòng)的搜索認(rèn)知結(jié)構(gòu)當(dāng)中與之相關(guān)的命題網(wǎng)絡(luò),并經(jīng)過(guò)一定的操作之后形成產(chǎn)生式,通過(guò)篩選組合產(chǎn)生式形成簡(jiǎn)單的產(chǎn)生式系統(tǒng),如果學(xué)生滿(mǎn)足于簡(jiǎn)單的產(chǎn)生式系統(tǒng),那么他將處于假理解狀態(tài),如果不滿(mǎn)足于當(dāng)前狀態(tài)就會(huì)繼續(xù)積極主動(dòng)搜索認(rèn)知結(jié)構(gòu)當(dāng)中的命題網(wǎng)絡(luò),并最終篩選組合成完整的產(chǎn)生式系統(tǒng),達(dá)到實(shí)理解狀態(tài)。最后,根據(jù)以上的研究結(jié)果和結(jié)論,提出的教學(xué)要求為:一、教師要加強(qiáng)自身知識(shí)儲(chǔ)備量;二、根據(jù)具體數(shù)學(xué)程序性知識(shí)制定具體的教學(xué)過(guò)程;三、了解高中生的數(shù)學(xué)程序性知識(shí)認(rèn)知理解水平,關(guān)注學(xué)生的心理機(jī)制;四、認(rèn)識(shí)到教師的主導(dǎo)地位且把這種地位發(fā)揮的正確有效;五、注重學(xué)生的主體地位;六、注重對(duì)學(xué)生學(xué)習(xí)動(dòng)機(jī)和學(xué)習(xí)積極性的激發(fā)。提出的教學(xué)建議為:一、不要給予解題模板,引導(dǎo)學(xué)生真正理解數(shù)學(xué)程序性知識(shí);二、引導(dǎo)學(xué)生反思,促進(jìn)程序性知識(shí)的理解與獲得;三、積極與學(xué)生進(jìn)行交流,對(duì)學(xué)生學(xué)習(xí)情況進(jìn)行及時(shí)評(píng)價(jià);四、制定恰當(dāng)?shù)慕虒W(xué)情境和教學(xué)內(nèi)容;五、引導(dǎo)學(xué)生加強(qiáng)新舊知識(shí)聯(lián)系,促進(jìn)學(xué)生知識(shí)系統(tǒng)化;六、發(fā)現(xiàn)學(xué)生對(duì)數(shù)學(xué)程序性知識(shí)理解力的不同,做到因材施教和個(gè)性化教學(xué);七、更多的教授數(shù)學(xué)程序性知識(shí)的相關(guān)原則、相關(guān)應(yīng)用和相關(guān)歷史等各方面相關(guān)知識(shí);八、利用合適材料促進(jìn)學(xué)生從假理解到實(shí)理解狀態(tài)的轉(zhuǎn)換。
[Abstract]:The mathematical programming knowledge is an important part of the high school students' mathematics learning. It not only affects the students' academic achievements, but also has some influence on the students' learning beliefs and learning enthusiasm. The actual situation is that some high school students can not understand the mathematical programming knowledge. Therefore, the study of high school students' mathematical programming knowledge is studied. The process of understanding cognitive understanding is very important. The current research on mathematical understanding is mainly focused on the connotation, levels, characteristics, functions, and investigation and research of mathematical understanding, and there are few studies on cognitive understanding of mathematics, especially the research on the process of understanding procedural knowledge. On the basis of this, combined with the current high school students' learning of mathematical programming knowledge, this paper deeply studies the cognitive process of cognitive understanding and understanding of high school students' mathematical programming knowledge, and puts forward the corresponding teaching requirements and teaching suggestions on the basis of the study. This paper mainly adopts the methods of literature analysis, interview and oral report method. The following order is: first, reading a large number of literature related to mathematical understanding, summarizing the existing research on mathematical understanding at home and abroad; second, reading a large number of documents related to procedural knowledge and cognitive understanding of mathematics, and making relevant theoretical analysis; third, formulating an outline of teacher interview, and preliminarily determining the number of high school students through interviews. Learn the factors of cognitive understanding of procedural knowledge; fourth, make an outline of student interview, and finally determine the factors that affect the cognitive understanding of the mathematical procedural knowledge of high school students through the preliminary interview to the students; fifth, interview the students to determine the key factors that affect the cognitive understanding of the mathematical procedural knowledge of the high school students; sixth, to the students. In the interview, on the basis of the key factors affecting the cognitive understanding of high school students' mathematical programming knowledge, the process, characteristics and models of the cognitive understanding of high school students' mathematical programming knowledge are summed up. Seventh, according to the results and conclusions above, the corresponding teaching requirements and teaching suggestions are put forward. There are six main factors affecting the cognitive understanding of the high school students' mathematical programming knowledge, which are the links between the old and the new knowledge, the related history of the mathematical programming knowledge, the related proof of the mathematical programming knowledge, the application of the mathematical programming knowledge, the related application of the mathematical procedural knowledge and the mathematical procedural knowledge, and the influence of the two. The most important factor in cognitive understanding of high school students' mathematical programming knowledge is the connection between old and new knowledge. Three, the process of cognitive understanding of mathematical procedural knowledge of high school students has the characteristics of active initiative, continuity, sequence, sluggishness, inertia and rapidity; and four, the process of cognitive understanding of the mathematical procedural knowledge of high school students is mainly the cognition of students. As the students meet new mathematical programming knowledge, the students are actively searching for the related propositional networks in the cognitive structure after encountering new mathematical programming knowledge, and form a production form after a certain operation, and form a simple production system by screening the combination generation, if the students are satisfied with the simple production. In a system of birth, he will be in a state of false understanding. If he is not satisfied with the current state, he will continue to actively search the propositional network in the cognitive structure, and finally filter it into a complete production system to achieve the actual understanding. Finally, according to the results and conclusions of the above research, the teaching requirements are as follows: first, teachers should add Strong self knowledge reserves; two, according to specific mathematical programming knowledge to formulate specific teaching process; three, to understand the level of cognitive understanding of mathematical procedural knowledge of high school students, pay attention to the psychological mechanism of students; four, understand the teacher's dominant position and make the position of this position correct and effective; five, pay attention to the main position of the students; six, pay attention to the right The students' motivation of learning and the motivation of learning enthusiasm are: first, do not give the template to solve the problem, guide students to truly understand the mathematical programming knowledge; two, guide students to reflect, promote the understanding and acquisition of procedural knowledge; three, actively and students to make a timely evaluation of students' learning situation; four, make the appropriate work. The teaching situation and content of teaching; five, guide the students to strengthen the old and new knowledge connection, promote the systematization of students' knowledge; six, find the students' different understanding of the mathematical programming knowledge, to teach students in accordance with their aptitude and individualized teaching; seven, more relevant principles of teaching mathematical programming knowledge, related applications and related history, and so on. Knowledge; eight, use appropriate materials to promote students' conversion from false understanding to real understanding.
【學(xué)位授予單位】：山東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：G633.6

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