中小学数学“图形与几何”教材内容衔接分析

发布时间：2018-01-11 19:13

本文关键词：中小学数学“图形与几何”教材内容衔接分析　出处：《海南师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：文中“图形与几何”衔接是从中小学“图形与几何”教材内容角度出发,体现在中小学数学课程标准、中小学数学教材以及教材与学生三方面的衔接。论文中运用质性研究和量化研究相结合的研究方法,以皮亚杰认知发展理论为指导,对《义务教育数学课程标准(2011)》中“图形与几何”的中小学课程目标和课程内容设计进行衔接解读、对中小学数学教材中“图形与几何”的编排体例和课程内容做衔接分析;按照伯格(W.Bueger)和威尼斯(W.Shaughnessy)对范希尔几何思维理论水平划分标准,以改编的“七年级范希尔几何思维水平测试卷”为研究工具,对海口市某中学七年级共计103名学生进行测试,以了解七年级学生的实际几何思维水平。研究得出以下结论:(1)中小学“图形与几何”课程目标呈现小步子化特点,虽然阶段目标会出现重复的现象,但是在目标要求程度上初中是小学的进一步深化与提高,中小学的课程目标设置既考虑了不同时期学生的发展特点也关注了学科自身的结构层次,体现出较好的衔接与过渡。(2)中小学“图形与几何”每个主题的课程内容设计相似、内容相关性强,遵循从直观几何、实验几何到论证几何的转变过程,主题之间表现出递进、互补、交叉等衔接方式。(3)初中“图形与几何”的教材编排体例延续了小学数学教材的模式,两者的共性是栏目设置形式多样、数量多、功能重叠,差异体现在编排呈现方式上。总的来说,中小学“图形与几何”教材编排体例衔接很妥当。(4)初中数学教材“图形与几何”的课程广度较大,中小学课时、课程深度、课程难度随着课程内容的不同而变化。从课程内容上分析,小学教材“图形与几何”内容描述方式单一,语言儿童化、形象化、趣味性强,知识具有生活化的特点,具体思维占主导,结论多是考察记忆和背诵能力;初中教材“图形与几何”内容描述注重规范严谨,语言数学化,概念严谨抽象,逻辑性强,抽象思维占主导,知识具有较强的拓展性和延伸性。(5)七年级学生几何思维水平分布差异性较大,主要集中在水平1,七年级教材“图形与几何”内容几何思维水平要求处于水平2,学生实际的几何思维水平和教材“图形与几何”几何思维水平要求不一致,教材要求高于学生的实际几何思维水平。基于上述研究结果并提出以下建议:一是数学课程标准在中小学课程目标和课程内容要求上再进一步细化和明确化;二是中小学数学教师要全面了解两个阶段数学教与学的情况,寻找知识衔接点自编衔接教材,帮助学生跨越衔接障碍;三是学生的几何思维发展是循序渐进的,因此数学教材内容应符合学生的几何思维水平发展特点,保证学生在最近发展区内得到最大化发展。由于受到个人研究能力的限制,本论文还存在很多不足,例如可借鉴的衔接理论太少、样本分布范围小数量少。
[Abstract]:In this paper, the connection of "figure and geometry" is from the angle of teaching material of "figure and geometry", which is embodied in the mathematics curriculum standard of primary and middle schools. The paper uses qualitative and quantitative research methods, guided by Piaget's cognitive development theory. This paper interprets the curriculum objectives and curriculum content design of "Graphics and Geometry" in "Mathematics Curriculum Standard for compulsory Education" (2011). This paper analyzes the arrangement style and curriculum content of "Graphics and Geometry" in mathematics teaching materials of primary and middle schools. According to W. Bueger and W. Shaughnessys, the criteria for the classification of van hill's geometric thinking level. With the adaptation of the seventh grade van Hill geometric thinking Test Paper as a research tool, a total of 103 students in grade 7 of a middle school in Haikou City were tested. In order to understand the practical level of geometric thinking of the seventh grade students, the following conclusions can be drawn: 1) the curriculum objectives of graphics and geometry in primary and secondary schools are characterized by small steps, although the objectives of the stage will be duplicated. But in the degree of goal requirements, junior middle school is the further deepening and improvement of primary schools. The curriculum objectives of primary and secondary schools not only take into account the characteristics of students' development in different periods, but also pay attention to the structural level of the subject itself. The course design of each subject of "Graphics and Geometry" in primary and middle schools is similar, and the content is highly correlated. It follows the transition process from intuitive geometry, experimental geometry to demonstration geometry. Themes show progressive, complementary, crossover, etc.) junior high school "Graphics and Geometry" textbook arrangement style continuation of the primary school mathematics teaching materials, the common character of the two is a variety of column settings. A large number, overlapping functions, differences reflected in the presentation of arrangements. Overall. "Graphics and Geometry" textbook arrangement in primary and secondary schools is very appropriate. 4) the junior middle school mathematics textbook "Graphics and Geometry" has a wide range of courses, the middle and primary school hours, the depth of the curriculum. The difficulty of the course varies with the content of the curriculum. From the analysis of the content of the curriculum, the primary school textbook "Graphics and Geometry" is characterized by a single way of describing the content, a child language, an image and a strong interest. Knowledge has the characteristics of life, the concrete thinking dominates, and the conclusion is the ability of memory and recitation. Junior high school textbooks "Graphics and Geometry" focus on the content description of rigorous norms, mathematical language, rigorous and abstract concepts, strong logic, abstract thinking dominates. Knowledge has a strong extensibility and extensibility. 5) the distribution of geometric thinking level of seventh grade students is quite different, mainly concentrated in level 1. The level of geometric thinking of the seventh grade textbook "Graphics and Geometry" is at level 2, and the students' actual level of geometric thinking is not consistent with that of the textbook "Graphics and Geometry". The teaching material requirement is higher than the students' actual geometric thinking level. Based on the above research results, the following suggestions are put forward: first, the mathematics curriculum standard further refines and clarifies the curriculum objectives and content requirements of primary and secondary schools; Second, mathematics teachers in primary and secondary schools should fully understand the situation of mathematics teaching and learning in the two stages, and find out the self-compiled cohesive teaching materials at the point of knowledge cohesion to help students overcome the obstacles of cohesion; Third, the development of students' geometric thinking is gradual, so the content of mathematics textbooks should accord with the development characteristics of students' level of geometric thinking. Due to the limitation of individual research ability, there are still many shortcomings in this thesis, such as too few cohesion theories and a small number of samples.
【学位授予单位】：海南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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