A Study Of Examining Students' Cognition Development In Mathematics By Writing

In 1991, Professional Standards for Teaching Mathematics designed by NCTM proposed to improve the mathematics teaching by means of Journal Writing. In China, many elementary and secondary schools in different provinces and municipalities directly under the jurisdiction of the Central Government such as Sichuan, Zhejiang, Shanghai, Tianjin etc. began regarding mathematical writing as one of the important teaching and learning approaches at the end of the last century.Mathematical writing is one of the effective ways to enrich teaching and evaluation. It can not only enhance the communication between teachers and students, but also make it easy for teachers to be informed of and diagnose students' 'mathematics reality'. Thus, teachers could adopt the appropriate treatment to meet students' real needs. This study chose the plane analytic geometry as the writing content from the textbook of the second curriculum movement in Shanghai, aiming at making a qualitative research on students' mathematical writing. Those students are the second grade students from one of the key senior middle schools in Shanghai. By instructing, assigning, reading, evaluating what students had written and interviewing some students, the writer needs to find out the possibility of examining students' cognition development in mathematics by writing. This study focused on several questions as follows: (1)Can we examine the cognition of several important concepts by writing? (2)Can writing help to access students' process of mathematical problem solving? (3)Can writing help to solve the similar question? (4)Can writing help to form or improve reflective abstraction? (5)What is the students' attitude towards writing?It is found that writing can expose students' concept image, and make the conflict factors between the concept image and concept definition discovered. Writing can also help to access students' process of mathematical problem solving, from which we can find out whether the students have a good grasp of the basic knowledge and skills in the plane analytic geometry. Besides, writing can help students realize the similarity between problems and make use of the former skills to simplify the problem solving. Writing needs students to make comparison, generalization, readjustment and even build a new cognition or schema. It has proved that writing can not only help to foster the reflective abstract, but also deepen the results of reflective abstract. Most students hold serious and positive attitude towards mathematical writing. At the end of the semester, they are better at writing. They can explain and reason in detail, and express their positive passion on mathematics.Based on the findings of this study, some suggestions for teaching by writing in mathematics in the key middle school and questions to be explored in the future are given at the end of this thesis.