Understanding Of The Concept Of Children 6-11 Years Of Age Line In Hangzhou City

Understanding is the most important section of mathematics study, and is one of the popular themes in the world mathematics education field. In geometry’s world, line becomes the basic element and composes a study of plane geometry. However, during the teaching process, people could feel finite and difficult when understand the concept of line. Nowadays, there are few researches related to line understanding of children. Children from different ages have different opinions in this theme, so when we could thoroughly understand children’s thoughts about line, more suitable books and teaching methods can be made for children.In this thesis, the understanding of line is set as the key. According to children’s characteristics, we can divide this into two parts:feature and nature. If children can understand these two parts, we consider they gain a good knowledge of line. Based on this point, the key concept of this thesis can be:"understanding of line from6to llaged children in Hangzhou district". In general, we will discover two questions:firstly, whether children have right or wrong knowing of line for children from Hangzhou and its profound meaning; secondly, what kind of level could children from different ages reach.First and foremost, based on our research question, we start to write literature review. According to current situation in the world, we need to set up two key points and make suitable questionnaires. Then, we invite some experts and teachers to guide us in order to get a perfect questionnaire. After that, we choose a number of children do the interview using these questionnaires. Lastly, quantitative and qualitative research methods are used in it. Utilizing quantitative research method aims to code results of those questionnaires, and input to database, then use Excel to analyze these data. If we want to analyze reasons of children’s written answers and after-school interviews, we should use qualitative research method.According to our research, we make these following conclusions:Firstly, misunderstanding of line from children can be:(1) pre-understanding;(2) negative transfer of word understanding;(3) mix understanding of line and other graphs;(4) mechanical comprehension based on image. In another section, some errors can be:(1) pre-understanding;(2) subjective judgment. Secondly, children from different ages get not the same comprehension:children from6to8years old could not understand the concept of line; children at the age of9-year-old have a promote increase; however, children at10to11years old get a steady rise. Through the section of representational transformation, the level of line comprehension goes from low to high. So it can be divided into three levels:oral language and image; image and real situation; and oral language and real situation. In the other aspects, children’s understanding can be divided into four parts: pre-understanding; subjective judgment; intuitive understanding and abstract understanding. Children from6,7years old could reach the level of intuitive understanding; children from8-9year-old can be set to the level between intuitive and abstract understanding; and children at the age of10,11can be reached the level of abstract understanding.The unique point of this thesis should be put children as our case study. Using representational transformation and SOLO evaluation theory to discover the misunderstanding of line from a majority of children can assist us to gain better knowledge of this key point. The meaning of this theory strengthens the comprehension of line for children, and provides some advice for the new curriculum standard, textbooks and teaching methods.