【摘要】：函數(shù)知識(shí)是初高中教學(xué)的重點(diǎn)和難點(diǎn),是高考試題中相關(guān)度最高的一個(gè)考點(diǎn)。所涉及的分類(lèi)討論、數(shù)形結(jié)合、聯(lián)系與轉(zhuǎn)化等數(shù)學(xué)思想方法也能為高等數(shù)學(xué)的深入學(xué)習(xí)奠定良好的基礎(chǔ)。但是,基于當(dāng)前各個(gè)學(xué)校師資配備的小循環(huán)特性,初高中的教學(xué)脫節(jié)現(xiàn)象非常嚴(yán)重,尤其是重要的函數(shù)知識(shí)學(xué)習(xí),初高中教學(xué)的側(cè)重點(diǎn)差異很大。本文利用文獻(xiàn)研究法、問(wèn)卷調(diào)查法、案例分析法,對(duì)初高中教材、初高中函數(shù)概念以及函數(shù)與方程、不等式的關(guān)系等進(jìn)行了深入對(duì)比和研究。發(fā)現(xiàn)初中函數(shù)概念教學(xué)中講解函數(shù)發(fā)展史銜接高中函數(shù)集合論的定義;一次函數(shù)與一次方程、一次不等式的聯(lián)系學(xué)習(xí)加強(qiáng)學(xué)生識(shí)圖、繪圖、說(shuō)圖的能力銜接高中函數(shù)與方程、不等式的關(guān)系及應(yīng)用;重視滲透數(shù)形結(jié)合的數(shù)學(xué)思想銜接高中函數(shù)的綜合應(yīng)用。以初高中函數(shù)概念的調(diào)查研究、函數(shù)與方程關(guān)系的案例研究,形象地闡述了教學(xué)銜接性的要點(diǎn)。指出初中的學(xué)習(xí)重點(diǎn)在于讓學(xué)生感知函數(shù)與方程之間是存在聯(lián)系的,并可以借助函數(shù)圖像,利用數(shù)形結(jié)合的數(shù)學(xué)思想,解決一些方程的問(wèn)題,旨在滲透函數(shù)思想。此外,還可以潛移默化地為高中繼續(xù)學(xué)習(xí)函數(shù)與方程的關(guān)系以及函數(shù)的其它應(yīng)用做了很好的鋪墊,這樣循序漸進(jìn)的過(guò)程,使得高中學(xué)習(xí)函數(shù)與方程不是那么的突兀,學(xué)生容易接受。針對(duì)作者所在城市初高中不同版本的教材,從初高中教材函數(shù)部分的內(nèi)容安排、聯(lián)系與區(qū)別、編寫(xiě)特色、思維差異以及初高中實(shí)踐教學(xué)中的體會(huì)進(jìn)行了分析,介紹了初高中函數(shù)教學(xué)的銜接策略。
[Abstract]:The function knowledge is the key and difficult point of the initial high school teaching, and it is the highest correlation in the high test. The methods of mathematical thinking, such as the discussion of the classification, the number-form combination, the relation and the transformation, can provide a good foundation for the in-depth study of higher mathematics. However, based on the small cycle characteristics of the current school teachers, the disjunction of the teaching in the first high school is very serious, especially the important function knowledge study, and the focus of the initial high school teaching is very different. In this paper, the author makes an in-depth comparison and research on the concept of the initial high school teaching material, the concept of the initial high school function, the function and the equation and the inequality by using the literature research method, the questionnaire method and the case analysis method. It is found that the development of the function of the teaching in the concept of the junior high school function is the definition of the set theory of the high school function. The relationship between the function of the elementary function and the basic equation and the one-time inequality enhances the student's identification, drawing, and the ability to connect the high-and high-school function with the equation and the inequality. In this paper, we attach importance to the integrated application of the mathematical idea of the combination of the penetration number and the high-school function. Based on the investigation of the concept of the initial high school function, the case study of the relation between the function and the equation, the main points of the teaching cohesion are set forth. It is pointed out that the main point of the study in junior middle school lies in that the student's perception function and the equation are related, and the problem of some equations can be solved by means of the function image, using the mathematical idea of the number-form combination, and the aim is to penetrate the function thought. In addition, the relationship between the continuing learning function of high school and the equation and the other applications of the function can be well paved, so that the high school learning function and the equation are not so abrupt, and the students are easy to accept. In view of the different versions of the teaching materials in the first high school of the author's city, the paper analyzes the content arrangement, the relation and the difference, the writing characteristic, the thinking difference and the experience in the practice teaching of the junior high school from the first high school teaching material function part, and introduces the connection strategy of the initial high school function teaching.
【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】：2017
【分類(lèi)號(hào)】：G633.6

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