论文标题:素质教育下数学思维训练的理论与教学研究
A Study on Theories and Teaching Practice of Training of Mathematical Thinking in Quality-oriented Education
论文作者 秦婧
论文导师 马顺业,论文学位 硕士,论文专业 课程与教学论
论文单位 山东师范大学,点击次数 189,论文页数 59页File Size604k
2005-04-15论文网 http://www.lw23.com/lunwen_98267187/ 素质教育;思维训练;数学思维训练;自我训练;训练步骤
quality-oriented education; training of thinking; training of mathematical thinking (TMT); self-training ; training process;
本文在思维训练已有成果的基础上,从素质教育理念出发,并结合数学学科的特点,对数学思维训练进行了理论与教学两个方面的研究。在理论方面,初步探索了素质教育下数学思维训练的作用、含义与特点以及建构主义、元认知理论、脑科学研究成果对数学思维训练的影响和启示。在教学方面,以理论为基础,对数学思维训练的一般步骤、设计准备阶段的具体操作等问题进行了探索,进而给教师提供了一系列建议。在以知识创新与技术创新为基本要求和内在动力的知识经济时代,素质教育重在培养学生的创新精神和实践能力,而创新与实践的关键在于使学生“学会思维”。数学历来被认为是思维的体操,在思维训练方面具有其他学科无法替代的作用,同时,数学思维作为人类的一种思维方式正发挥着越来越重要的作用。因此,如何有效开展数学思维训练就成为数学教育领域的重要课题之一。本文在结合国内外对数学思维训练的研究的基础上,提出了数学思维训练的具体含义,并从以下五个方面进行了分析。其一,数学思维训练应贯彻科学性原则;其二,数学思维训练作为一种学科思维训练必须突出自身的学科特点;其三,数学思维训练贵在自觉,重在实践;其四,数学思维训练与数学知识教学不是对立的而是相互促进的;其五,数学思维训练具有强大的素质教育功能。关于素质教育下数学思维训练的特点,本文从对比素质教育与单纯的应试教育之间的差异入手,提出了以下特点。第一,训练目的的多维性,即数学思维训练的目的不仅在于提高学生的数学考试成绩,还在于促使学生学会“数学化”,开发学生的大脑潜能,促进学生一般思维素质的发展。第二,训练内容全面性,即训练是全方位、多角度进行的,并在整合的基础上发挥作用。第三,训练对象的全体性,即在尊重学生数学思维个体特征的前提之下,使每个学生的数学思维都能得到有效的训练与提高。第四,训练效果评价的综合性,即评价方式、方法、手段、主体等要力求多元化。由于科学的数学思维训练需要以相关理论为依据,所以本文选取了建构主义理论、元认知理论和脑科学三个角度,研究了它们对数学思维训练的影响与作用,获得了许多有益的启示。建构主义理论一方面揭示了行为主义学习观对数学思维
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 ser
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