A Study On The Mathematical Curriculum Of "Practice And Integrated Applications" In Junior Middle School

"Practice and Integrated Applications"is a brand new curriculum offered by the Curriculum Standards for Mathematics in the Full-Time Compulsory Education (Experimental Version) besides Number and Algebra, Space and Shape, Statistics and Probability. Is it necessary to offer this curriculum? How is the current situation of its implementation? Are there any problems in its implementation and what are the causes? What can be done to solve these problems? These are the most concerned hot topics in mathematic curriculum reform of the elementary education and the problems which need to be solved urgently in the curriculum construction of Practice and Integrated Application.By utilizing questionnaire surveys, tests, in-depth interviews, discussions, content and statistics analyses, comparing and analyzing text books of different versions, and conducting comparative researches and tests in different regions, this dissertation offers a comprehensive and through examination of the present implementation situation of the curriculum practice and integrated applications in middle school. Then it goes on to systematically analyze the necessity, significance and value of offering this curriculum and put forward a series of strategies for improving the implementation of this curriculum:Studies show:1. It is necessary to offer the curriculum of practice and integrated applications within the mathematics curriculum of junior middle school.The results show that around 92.9% of the teachers surveyed in junior middle school believe that it is necessary to offer this curriculum. It is widely agreed among the teachers interviewed that this curriculum is effective in enhancing the students'interest in mathematics, enabling them to appreciate the value of mathematics and accumulate the experience of the mathematic activity, and raising their innovative spirit and the consciousness of application.The survey results colleted from the students who have taken this curriculum and those who have not indicate that a systematic study of this curriculum is essential for students to improve their abilities of raising questions, applying mathematical knowledge, and enhancing their abilities in mathematical induction and analogous reasoning. For those school who have paid due attention to the implementation of this curriculum, the goal set by the Curriculum Standards for Mathematics in the Full-Time Compulsory Education (Experimental Version) can be fully achieved.2. The implementation of this curriculum in junior middle school faces many problems. The implemented curriculum is far from the intended curriculum, which is mainly due to the deficiencies of the assessment system, the curriculum resources, the curriculum goals, and the curriculum organization.Teachers and students do not pay enough attention to this curriculum. Teachers'understanding of the goal of this curriculum is superficial and inaccurate. Most teachers only use part of the"project-based mathematic learning", and the portion of this part becomes smaller and smaller from the first grade to the third grade. Only some outstanding teachers can take an active part in tapping curriculum resources, transforming the"project-based mathematic learning"and exploring the appropriate teaching method and thus achieving a satisfactory teaching result. However, what the majority of teachers do is unorganized and random. These teachers do not fully understand the focus of this curriculum and leave little time and space for students to explore independently. The summarizing and evaluating content is sketchy and at a relative low level. Most teachers'performance is dissatisfactory in helping the students to understand the links among mathematical knowledge and in enhancing their ability to raise questions and solve unconventional problems by synthetically using their mathematical knowledge.The content of the Project-based Learning in the textbooks published by People's Education Press, East China Normal University Press, Beijing Normal University Press is close to the students'life and cognitive level. They can help students cultivate mathematic logic, deepen the students'understanding of mathematics, broaden their horizon, and guide them to carefully observe life with a mathematic thinking mode. However, quite a few subjects raised by the Project-based Learning seem to be closed to students'real life, but are actually not. And still others are not only lack of feasibility but also are concerned with less important knowledge, which has little value in mathematic connotation. Subjects in the textbooks are lack of hierarchical arrangement and consistency in the points of the synthetic knowledge, the students'experience of mathematic activity, the mathematic thinking mode and the mathematic thinking way. In terms of the arrangement (no obvious difference between the seventh and ninth grade) of pictures and words, pictures and graphs need to be more selective and the words need to be more concise so that the content can be more attractive and much easier for the students to read and the subjects'value can be more prominent.Comparing the implemented curriculum and intended curriculum, there is a great gap in the aspects of curriculum target, content, teaching form and the teaching result. The major four reasons leading to these problems are: firstly, the assessment system for the entrance examination of junior middle school is inappropriate. It is incapable of evaluating the actual implementation of this curriculum; secondly, a systematic organizing and implementing institution is yet to be established. Most of the schools surveyed are lack of effective regulations and measures for carrying out this curriculum; thirdly, the teachers are short of excellent teaching examples with great reference value to follow. There are not enough good curriculum resources for textbooks editing and compiling. Meanwhile, the experience and knowledge that the teachers and students have obtained are limited. At last, the target in the Curriculum Standards for Mathematics in the Full-Time Compulsory Education (Experimental Version) is difficult to reach or understand and not specific, and the value of the subjects'mathematical connotation is little or unclear; and the subjects in the textbooks have little or prominent value for mathematic research and lack hierarchical arrangement in terms of contents.3. The enlightenment of the study: based on the current implementing situation of the curriculum and its main reasons, this dissertation raises a number of corresponding countermeasures for further improvement in the aspects of evaluation, resource development, the curriculum goal and the curriculum organization. The countermeasures for the implementation of the curriculum of practice and integrated applications are as follows: firstly, the evaluation system for middle school mathematics should be improved and new requirements should be added for this part in the entrance examination; Secondly, curriculum resources should be developed scientifically and books with excellent teaching cases compiled. The excellent teaching cases in the mathematics problem-based learning and the mathematic activities of the junior school mathematics should be collected and refined, and the time-saving and high-efficient teaching cases should act as important curriculum resources to help this curriculum become integrated with other curriculums in the conventional teaching. Thirdly, the curriculum goal should be made more prominent and the selecting standard, organizing elements and plan more fixed in order to increase the feasibility of this curriculum. Only after the check of the actual teaching can the basic curriculum target become feasible. The basic teaching target and the core teaching target should be made more obvious by means of the curriculum edition in the curriculum standard and the textbook. Based on the basic curriculum target, the curriculum's organizing elements and plans are established. The textbook should be revised on the base of this so that the consistency of the curriculum's content can be enhanced. Besides, to guarantee the amount and quality of the curriculum's implementation, the school's organizational administration should be strengthened and the quality of the teachers'training should be improved.Based on investigation, interview and content analysis, this dissertation concludes that the curriculum's core target is to help students accumulate the direct experience of mathematic activity and to cultivate students'mathematic thinking pattern and that the key organizing elements of the curriculum include the subject's background and opening type and extent, the synthetic type of the knowledge, the thinking pattern, the thinking method and students'direct experience of the mathematic activity related with the subject.The research results show that there is an urgent need to revise and improve the full-time compulsory education mathematic curriculum standard (the experimental version) and the practice and integrated applications curriculum in junior middle school. The researching results of this dissertation contribute to improving the curriculum design and implementing theories of the practice and integrated applications in the mathematics for the junior middle school and serve as an important reference.