本文選題：長(zhǎng)方形的面積計(jì)算 + 教材比較��； 參考：《杭州師范大學(xué)》2015年碩士論文

【摘要】：“長(zhǎng)方形的面積計(jì)算”是小學(xué)數(shù)學(xué)的經(jīng)典教學(xué)內(nèi)容,無(wú)論是近代第一部幾何教科書(shū)《形學(xué)備旨》中,還是新中國(guó)的第一本教科書(shū)《(初)高級(jí)小學(xué)算術(shù)課本》內(nèi),都把它列入其中。長(zhǎng)方形面積公式看似簡(jiǎn)單,實(shí)則對(duì)小學(xué)階段所有平面圖形的計(jì)算都起著重要的奠基作用,是小學(xué)生面積計(jì)算學(xué)習(xí)的第一課。日常教學(xué)中教師往往將會(huì)用公式計(jì)算作為教學(xué)目標(biāo),以機(jī)械記憶、大量練習(xí)作為學(xué)生的學(xué)習(xí)方式,使大批學(xué)生成為解題的機(jī)器,只知其然而不知其所以然。為真實(shí)了解學(xué)生對(duì)這一內(nèi)容的掌握情況,筆者圍繞這一內(nèi)容,以杭州市上城區(qū)三所學(xué)校三年級(jí)學(xué)生為對(duì)象,進(jìn)行了“長(zhǎng)方形的面積計(jì)算”的學(xué)前調(diào)查和學(xué)后作業(yè)分析。通過(guò)調(diào)查與分析,發(fā)現(xiàn)學(xué)生對(duì)這一內(nèi)容的掌握情況不容樂(lè)觀,學(xué)生對(duì)公式的意義理解不足的現(xiàn)象比較普遍。學(xué)生雖然知道長(zhǎng)方形的面積計(jì)算公式,但知其然而不知其所以然。為進(jìn)一步追尋原因,筆者從教材理解、教法比較兩個(gè)角度進(jìn)行了研究。在研究中發(fā)現(xiàn)新課標(biāo)各套實(shí)驗(yàn)教材一改“例題—講解”的呈現(xiàn)方式,往往以情景圖、活動(dòng)圖的形式呈現(xiàn),內(nèi)容豐富形式活潑,但隱含其中的知識(shí)結(jié)構(gòu)、內(nèi)容目標(biāo)、學(xué)習(xí)方式等,需要我們剝離形式細(xì)察理解。另外,不同版本的教材編排結(jié)構(gòu)和內(nèi)容各具特色,如果能互相比照,博采眾長(zhǎng)將有利于我們?cè)O(shè)計(jì)出促進(jìn)學(xué)生對(duì)面積公式意義理解的教學(xué)設(shè)計(jì)。在對(duì)不同教學(xué)設(shè)計(jì)的學(xué)習(xí)理解中,使筆者對(duì)于長(zhǎng)方形面積計(jì)算的目標(biāo)定位、環(huán)節(jié)安排、及其背后的認(rèn)知理論有了更加清晰的認(rèn)識(shí)并觸發(fā)了新的教學(xué)設(shè)計(jì)。在對(duì)現(xiàn)行主要的6套教材和77篇典型教學(xué)設(shè)計(jì)的比較分析基礎(chǔ)上,筆者根據(jù)范·希爾幾何學(xué)習(xí)框架形成了新的教學(xué)設(shè)計(jì)。新的教學(xué)設(shè)計(jì)特色明顯:(1)設(shè)置了“形成表象、操作驗(yàn)證、應(yīng)用理解”三步五階段的學(xué)習(xí)序列,層層遞進(jìn),全程促進(jìn)學(xué)生對(duì)長(zhǎng)方形面積計(jì)算公式的意義理解。(2)安排了“探究發(fā)現(xiàn),操作驗(yàn)證”的學(xué)習(xí)方式,在直觀、想像、實(shí)驗(yàn)中發(fā)現(xiàn)面積公式,促進(jìn)意義理解,使學(xué)生知其更知其所以然。(3)在經(jīng)歷系列研究過(guò)程中積累了“推理”活動(dòng)經(jīng)驗(yàn),體驗(yàn)了數(shù)學(xué)公式發(fā)現(xiàn)的樂(lè)趣。本研究提出的教學(xué)設(shè)計(jì)在城市普通小學(xué)、實(shí)驗(yàn)小學(xué)、山區(qū)鄉(xiāng)村小學(xué)進(jìn)行了多次試教,成效明顯,也被上海教育出版社《小學(xué)數(shù)學(xué)教師》雜志全文刊登。從實(shí)踐來(lái)看,本研究較好地解決了學(xué)生對(duì)面積公式的意義理解不足的教學(xué)困境,可以為一線教師的教學(xué)起到一定的參考作用。
[Abstract]:"calculation of rectangular area" is the classical teaching content of primary school mathematics. It is not only in the first modern geometry textbook, but also in the first textbook of New China. Are included in it. The rectangular area formula seems to be simple, in fact, it plays an important role in laying the foundation for the calculation of all plane figures in primary school, and is the first lesson for elementary school students to study area calculation. In daily teaching, teachers often use formula calculation as the teaching goal, mechanical memory and a large number of exercises as the learning way of students, so that a large number of students become the machine for solving problems. In order to understand the students' grasp of this content, the author takes the third grade students of three schools in Shangcheng District of Hangzhou as the object, carries on the pre-school investigation and the post-school homework analysis of "rectangular area calculation". Through investigation and analysis, it is found that the students' grasp of this content is not optimistic, and the phenomenon of students' insufficient understanding of the meaning of the formula is quite common. Students know the square area formula, but they know it and don't know why. In order to further explore the reasons, the author makes a study from the two angles of teaching material understanding and teaching method comparison. It is found in the study that the presentation of "example-explanation" in each set of experimental textbooks of the new curriculum standard is often presented in the form of scene map and activity diagram, and the contents are rich and lively, but the knowledge structure, content objectives, learning methods and so on are implied. We need to peel off the form of a detailed understanding. In addition, the structure and content of different versions of the textbook have their own characteristics. If they can be compared with each other, it will be helpful for us to design a teaching design to promote students' understanding of the meaning of the area formula. In the learning and understanding of different teaching design, the author has a clearer understanding of the goal orientation, link arrangement, and cognitive theory behind the rectangular area calculation and triggers a new teaching design. On the basis of comparative analysis of six main textbooks and 77 typical teaching designs, the author forms a new teaching design according to Van Hill Geometry Learning Framework. The new teaching design features are obvious: (1) set up "formation of appearance, operational verification, application of understanding" three-step and five-stage learning sequence, layer by layer progression, to promote students' understanding of the meaning of the rectangular area calculation formula. The learning method of "operation verification", finding the area formula in intuition, imagination and experiment, promoting the understanding of meaning, making students know more about what they are doing, has accumulated "reasoning" activity experience in the course of a series of research. Experience the fun of finding mathematical formulas. The teaching design proposed in this study has been tried and taught many times in urban primary schools, experimental primary schools and rural primary schools in mountainous areas. The results are obvious and published in the full text of the Journal of Shanghai Education Publishing House, "Primary School Mathematics Teachers". From the point of view of practice, this study has solved the teaching dilemma of students' insufficient understanding of the meaning of the area formula, and can play a certain reference role in the teaching of front-line teachers.
【學(xué)位授予單位】：杭州師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G623.5

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本文編號(hào)：1957348