A Study On The Mathematics Learning Based On Schema

The dissertation in question is intended to make a theoretical and practical study on the schema. To its knowledge, the author expects the schema theory to be the theoretical prop and the practical guidance to the improvement of the conditions of mathematics teaching and learning in China, and tries to make an experimental attempt at the practice in terms of the aforesaid theory.The research consists of three parts. The first part focuses on the mechanism of schema, the schema theory, the schematic construction in the mathematics learning as well as the connections between the schema and mathematical problem solving; The second part is an intermediary ring which lays a foundation upon the practical research in the light of the first part; The third part centers on the tentative practice under the guidance of the theory. The methods of both the quantitative and the qualitative analysis will be adopted in this paper.A. Presentation on the case study on construction of the proportional reasoning schemaThe development of the proportional reasoning schema, which is influenced by the learners' understanding of the following concepts, will be much interrelated and interacted with the one of such concepts as division, multiplication, fraction and decimals. In the meantime, to experience the solution to the problems of proportion can provide the contexts for the learners to further understand those concepts.To provide the variety of mathematical activities for the learners should be the foundation of school curriculum and mathematics instruction. But most importantly, the learners shall require more opportunities to experience the mathematics problems which will provide rich contexts for them to develop the number concept and theiroperations.B. The following views proved by the findings of the research on the schema and the mathematical problem-solving performance:The successful problem-solving performance is closely related with the better organized and more extended knowledge base. In other words, the better organized schema will contribute to effectively solving the mathematics problems. In the course of the mathematics problem-solving, the highly organized schema will enable the individual problem exploring ability to the extent of expansion, intensify the directiveness and improve the effectiveness of probing into the right problem solution.While in the process of mathematics learning, it is vital to assist the learners with constructing the knowledge chains or improving the connectedness with various kinds of knowledge they had made, particularly for the part of the less effective problem solvers, it is no doubt an effective learning way to instruct them how to shape the conditional schema.Given that the mathematics learning is an unending process of schematic construction, a certain time should be spared to display or discuss the development of a definite topic's schema in the classroom instruction.C. The analysis on the "schema" within the mathematics knowledge shown below:The "schema" can build the different parts which have seemingly loose connections with each other into the closely related body, laying emphasis upon the system of mathematics knowledge. The acquirement of the simple and structured knowledge through the formation of "schema" leads itself to the systematic master of the knowledge and the development of the connected and reticulated structure by processing knowledge, so that the schema can be constructed and developed, thethinking integrity and agility be well trained, and the thinking modes be updated or optimized in the mind of learners.The "schema" is conductive to the improvement of the efficiency and efficacy of the mathematics teaching and learning. The "schema" provides the integrated perspectives highlighting the construction of the mathematical schema for the teaching and the learning, enabling the learners to integratedly grasp the mathematics knowledge, methods and ideas, and effectively eradicate the segment of the mathematical knowledge from the methods. The "schema" helps to overcome...