The Migration Theory In Maths Teaching

The proliferation of knowledge in modern society, the rapid development of technologyand the goal of education should be shifted to how to improve the students' learning ability.The value of school education lies in "teaching the students how to fish" not just "givingthem a fish", that is, simply imparting knowledge and skills to the students. The focus ofeducation in the 21st century is to learn how to learn, this can be seen from the suggestion"learn how to learn" put forward by UNESCO. "Learning how to learn" is to equip studentswith a real capacity to transfer and solve various problems in different contexts. Therefore,"students learn for transference and teachers teach for transference" has become theconsensus of them.The transference theory is an important component of contemporary study theory.Supported by a variety of study theory various traditional transference theory had appearedin history, the system of modern transference theory has been improved. The domesticresearchers have a detailed discussion about applying transference theory to teaching.However, there are many limitations due to some unfavorable conditions in there research.Higher vocational education is a new force of higher education. The character ofcultivating objective is to meet the needs of today's society and the students are special too.The basic course "Higher mathematics" can not only impart basic knowledge to thestudents but can cultivate students' math thought and other abilities. So all math teachersin higher vocational college should put emphasis on making the students master highermath knowledge and improve their abilities in teaching process, based on transferencetheory, with appropriate teaching methods and making full use of limited time. With regard to the thinking of the use of transference theory in Mathematics teaching,this thesis is primarily on three issues: (1) an analysis of the content and features of thehigher mathematics. (2) an analysis of the characteristics of the students from the aspectsof age, intelligence, cognitive structure, and thinking etc. (3) an analysis and theconclusion about the factors that influences the students' learning positive transference inmathematics, using the passed experience in this field for references and through a seriesof questionnaires. In the author's opinion, the factors can be divided into two parts: thesubjective ones and the objective ones. The former factors includes: the cognitive structurein mathematics, presentation, summarizing capability of the mathematics objects, the fixedmode in learning and the metacognitive ability. The latter ones include: the similaritybetween teaching environment and the learning materials.Combining the analysis above and the teaching carry-outs, the author now is makingdeeper research on the application of transference theory in the higher mathematicsteaching, where four aspects are included: (1) To improve the teaching strategies ofpositive transference in teaching mathematics. (2) To take steps at using positivetransference theory in teaching the mathematics definitions. (3) To take measures to usethe positive transference theory in the teaching of thinking methods. (4) Thecountermeasures of overcoming negative transference.As to the teaching strategy of improving the positive transference in teachingmathematics, the author puts forward the ways of setting up "the learning point structurechart", fulfill the positive transference of the knowledge by drawing assistance from thedefinition chart. Through the chart the students can form in their brains an intense systemof the learning points in the teaching books so as to strengthen the holding ability andstability of the cognitive structure. Besides, during the teaching, we can facilitatetransference by putting the examples in order and designing teaching contexts throughanalogy, pay attention to intensifying summary and generalization ability practice, studystrategies practice and awareness of transference.Because higher mathematical concepts appear in a motorial aspect and it is a dynamicproduct and more abstract than primary mathematics. Thus in addition to the teachingstrategies above I think we can set off from the following aspects: introducing conceptmodel, emphasizing the generalization and refinement of the emotional materials, settingup the conceptual system, systematizing the organization, facilitating transference centeredby core concepts, introducing concepts through analogy.It is widely recognized that mathematical thinking methods transference ofmathematical study. Combining the features of mathematical thinking the followingmeasures are put forward as to the application of transference in teaching: the transferenceof knowledge, principles and attitude are realized by penetrating the teaching thinking andmethods;penetrating "the thinking of limit";revealing the relationship among knowledge;helping the students understand the abstract theoretical knowledge.Negative transference may appear in mathematical study. So the negative transferencein mathematical teaching is analyzed in this thesis: the common factors existed in new andold knowledge can cause negative transference;generalization may cause negativetransference;the relative steadiness in previous cognitive structure can cause negativetransference;analogy thinking can cause negative transference etc. Based on the analysis, Iput forward the strategies overcoming negative transference.Based on years of practical experience, the author provides some teaching cases instudy of mathematical concepts and propositions.