小学数学“长方形面积计算”的教学研究

发布时间：2018-05-30 23:38

本文选题：长方形的面积计算 + 教材比较　；参考：《杭州师范大学》2015年硕士论文

【摘要】：“长方形的面积计算”是小学数学的经典教学内容,无论是近代第一部几何教科书《形学备旨》中,还是新中国的第一本教科书《(初)高级小学算术课本》内,都把它列入其中。长方形面积公式看似简单,实则对小学阶段所有平面图形的计算都起着重要的奠基作用,是小学生面积计算学习的第一课。日常教学中教师往往将会用公式计算作为教学目标,以机械记忆、大量练习作为学生的学习方式,使大批学生成为解题的机器,只知其然而不知其所以然。为真实了解学生对这一内容的掌握情况,笔者围绕这一内容,以杭州市上城区三所学校三年级学生为对象,进行了“长方形的面积计算”的学前调查和学后作业分析。通过调查与分析,发现学生对这一内容的掌握情况不容乐观,学生对公式的意义理解不足的现象比较普遍。学生虽然知道长方形的面积计算公式,但知其然而不知其所以然。为进一步追寻原因,笔者从教材理解、教法比较两个角度进行了研究。在研究中发现新课标各套实验教材一改“例题—讲解”的呈现方式,往往以情景图、活动图的形式呈现,内容丰富形式活泼,但隐含其中的知识结构、内容目标、学习方式等,需要我们剥离形式细察理解。另外,不同版本的教材编排结构和内容各具特色,如果能互相比照,博采众长将有利于我们设计出促进学生对面积公式意义理解的教学设计。在对不同教学设计的学习理解中,使笔者对于长方形面积计算的目标定位、环节安排、及其背后的认知理论有了更加清晰的认识并触发了新的教学设计。在对现行主要的6套教材和77篇典型教学设计的比较分析基础上,笔者根据范·希尔几何学习框架形成了新的教学设计。新的教学设计特色明显:(1)设置了“形成表象、操作验证、应用理解”三步五阶段的学习序列,层层递进,全程促进学生对长方形面积计算公式的意义理解。(2)安排了“探究发现,操作验证”的学习方式,在直观、想像、实验中发现面积公式,促进意义理解,使学生知其更知其所以然。(3)在经历系列研究过程中积累了“推理”活动经验,体验了数学公式发现的乐趣。本研究提出的教学设计在城市普通小学、实验小学、山区乡村小学进行了多次试教,成效明显,也被上海教育出版社《小学数学教师》杂志全文刊登。从实践来看,本研究较好地解决了学生对面积公式的意义理解不足的教学困境,可以为一线教师的教学起到一定的参考作用。
[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.
【学位授予单位】：杭州师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G623.5

【参考文献】