A Study On Theories And Teaching Practice Of Training Of Mathematical Thinking In Quality-oriented Education

Based on the research results already available, the thesis, starting from the basicconcepts of quality-oriented education and in connection with features of mathematicsas a discipline, intends to make analysis of the training of mathematical thinking (TMT)in both theory and practice. In theory, it makes a basic exploration of such problems asconstructivism, meta-cognitive theory, the revelatory effect of cerebral science on TMT,as well as its function, meaning and features in quality-oriented education; while inteaching practice, it studies the general procedures and program design of TMT, and itspractical methods, based on relevant theories, thus providing a series of suggestions tothe teacher.In an era of knowledge economy with scientific and technological innovation asbasic demands and inherent driving force, quality-oriented education places emphasison the training of students'innovative spirit and practical skills, the key of which liesin enabling them to "learn how to think". It has always been regarded that mathematicsis a gymnastics of thinking, which is in this respect irreplaceable by any other subject.Meanwhile, mathematical thinking, as one kind of thinking pattern, is playingincreasingly important role, therefore how to carry out the training of this kind hasbecome a key task in the field of mathematics education.This thesis, in connection with the results of TMT research from both home andabroad, puts forward its concrete meaning, and makes analysis from five perspectives.First, TMT should implement the scientific principle. Second, it must give prominenceto its own characteristics as a disciplinary training of thinking. Third, its value consistsin self-consciousness, and its stress in practice. Fourth, it is mutually promoting withteaching of mathematical knowledge rather than contradictory to it. And finally, TMTpossesses a quite powerful function in quality-oriented education. As to the features of TMT in quality-oriented education, the thesis, proceedingwith the difference between exam-oriented education and its quality-orientedcounterpart, puts forth the following points. First is the multi-dimensionality oftraining purpose. In other words, the target of TMT rests not only in improving thestudents'scores in exam, but also in encouraging them to learn to think"mathematically", developing the potentials of their brain, and promoting the progressof their quality in general thinking. Second is the completeness of the training, that is,the training is carried out in an all-around way from multiple angles, and it shouldbring its role into play on the basis of integration. Third is the wholeness of the training,namely, with adequate respect to the individuality of each student's mathematicalthinking, efforts should be made to exercise and improve this ability. Fourth is thecomprehensiveness of the evaluation of the training effect, i.e., we should strive for theplurality of manner, method, measure, as well as the subject being evaluated. Since scientific TMT requires relevant theories as its foundation, this thesisselects three angles—constructivist theory, meta-cognitive theory, and cerebral science,to study their influence and effect on TMT, and have already obtained a lot ofprofitable inspiration. Constructivist theory reveals the negative effects of behavioristicoutlook on TMT; besides, it sets the direction for its teaching practice. The researchshows that meta-cognitive theory is an important way to enhance the quality ofstudents'mathematical thinking, helpful both to the transfer of mathematical thinkingstrategy in different contexts, and to the increase of their self-consciousness. It is thusadvisable that we apply the meta-cognitive training as a breakthrough for TMT, andlead students from training in teacher's charge to that on their own. Cerebral scienceprovides the physiological basis to the feasibility of TMT; in addition, it indicates thatTMT has to be a cerebral exercise in accordance with proper degree and timing. The actual operation of TMT and the study of program design serve as a bridgelinking theory and teaching practice, in which there are significant values for research.