高中生数学思维障碍的初步研究

【作者】 田珍；

【导师】 傅海伦；

【作者基本信息】 山东师范大学 ， 学科教学， 2003， 硕士

【摘要】 本文认为，研究高中学生数学思维障碍对于增强高中数学教学的针对性和实效性有十分重要的意义。 思维，是人脑对客观事物的一种概括的，间接的反应，是客观事物的本质和规律的反映。数学思维，其界定有很多说法。本文认为，数学思维是针对数学活动而言的，通过对数学问题的提出、分析、解决、应用和推广的一系列工作，以获得对数学对象(空间形式，数量关系，结构模式)的本质和规律的认识过程。这个过程是人脑的意识对数学对象信息的接收、分析、选择、加工与整合。在问题解决中，由于学生不具备良好的思维品质而不能顺利地解决问题，从而在问题解决中造成思维的中断或错位，就是思维障碍。 传统教育由教师为中心而造成思维中的权威定势，以书本为中心造成思维中的唯书本定势，在一定程度上限制了学生的思维，造成思维的障碍。素质教育给数学教学提出了新的要求，不仅要让学生掌握知识，更要注意智力的开发和能力的提高，尤其是思维能力。而学生思维的深化，障碍的克服，关键在于教师的引导，在教师引导下探索出克服产生思维障碍的有效方法和途径。 本文研究数学思维障碍的理论依据是：建构主义的数学学习观，认识论和心理学。数学建构活动就是数学抽象过程，是一个不断发展深化的过程。要不断的“建构和反思”和“反思再建构”，才能使知识建构得准确，掌握得完全。否则就会形成思维障碍。根据布鲁纳的认识发展理论，学习本身是一种认识过程，学生对所学知识认知上的不足，理解上的偏颇，在解决具体问题时就会产生思维障碍，影响学生解题能力的提高。一种学习对另一种学习的作用，在心理学中称作学习的迁移。心理学家根据学习迁移的性质和作用，通常把迁移分为正迁移和负迁移两种情况。充分利用迁移，可以帮助学生克服思维障碍，提高思维能力。 本文从元认知、思维定势、数学活动的过程知识三个方面探讨了数学思维障碍的形成因素。 元认知是对思维与学习的认识与控制，是一个人对自己的认识过程、认知产品或各种与认知有关的事物的理解。简言之，元认知就是对认知的认知，对思维的思维。(美国心理学家弗莱维尔)元认知对于培养学生思维能力有十分重要的意义。元认知参与思维调控的基本原则有三条，即动因原则、审美原则和反思原则。元认知在数学思维中发挥作用的基本形式是反思。元认知的薄弱，将形成数学思维的缺陷，导致数学思维障碍。 本文认为思维障碍的形成的另一个原因是由于思维定势的负效应。学生受己有数学知识和成功经验的影响，对新概念，新知识的本质属性缺乏正确的认识，受习惯化或事物功能固定性以及视觉干扰因素和非智力因素等心理品质的影响，都会产生思维障碍。 本文分析了数学活动的形式方面和直觉方面的两个特征。形式方面主要指通常所说的“数学的思维活动”特征，是以数学符号为载体，通过抽象、概括、演绎、归纳、分析、综合、反省等进行的头脑中的操作活动。直觉是不经过推理的一种认识，这是己有经验、技能和知识的产物，它在认识过程中起着从属的作用。在数学教学过程中，不仅存在着大量的结果知识，而且更多地存在着大量的过程知识。在此基础上，本文认为，由于数学教学的目标导向总是定位在结果知识的获取，而忽略或抑制了过程知识发挥的空间，以致于使学生在数学活动中难以意识和应用隐性的过程知识，一般都是在外部强力的驱使下应用纯粹的逻辑力量和机械训练，来掌握显性的结果知识，这是学生形成思维障碍的症结所在。 根据高中生的思维特点和思维的可训练性，本文提出解决思维障碍的具体措施。】.让学生了解影响自己数学思维的各种因素。2.在教学中注意揭露数学思维的特点。3.培养学生自我评价、自我监控的习惯。4.利用陷阱题，防止错觉定势。5.把形同质异的题目放一块分析、比较，消除思维定势。6.优化知识的储备状态，学会分析、比较，消除思维定势。7.加强变式练习，学会在变式中认识事物的本质属性，消除思维定势。 教师要注意挖掘数学知识的内涵，帮助学生消除思维障碍。 教师要注意数学思想方法的教学，帮助学生消除思维障碍。 教师要注意根据数学知识的特点，创设思维的最近发展区。 教师要注意多角度、多方向的分析问题，帮助学生学会辩证思维、学会转化。 在实验设计中，针对作业布置、分析和反馈，采用多组准实验设计中的不相等实验组与控制组前后测设计。通过对实验班五个月的教学，对实验班和控制班的数学成绩和思维能力进行了测定，并进行了结果分析，得出实验班明显优于控制班的初步结论。这说明通过作业布置，培养学生自我评价、自我监控和反思的习惯，对学生克服思维障碍，提高思维能力产生了积极有效的影响。我们研究思维障碍，探索克服思维障碍的有效途径，对提高数学成绩，培养数学思维能力有重要意义。更多还原

【Abstract】 The study of mathematical thinking obstacles of the senior middle school students is of great significance to enhance actual effect of mathematical teaching.Thought is a general and indirect reaction which brain has on objective things. Furthermore, it is also a reflection of the essence and law of objective things. There are many statements on the boundary of mathematical thought. In the view of the article, mathematical thought is aimed at mathematical activity. It is a process of cognition to acquire the essence and law of mathematical objects (space form, quantity relation, structure mode) by rising analyzing, solving, applying and popularizing mathematical problems. In this process, the consciousness of brain can receive, analyze, and choose. Process and conform the information of mathematical objects. In the problem solving, if students have not fine thought quality, they will hardly solve problems smoothly. Then thought will discontinue or dislocate. This phenomenon is thinking obstacles.Traditional education puts center on teachers and books. This results in the authoritative tendency and the book tendency in thought. The condition limits the thoughts of the students and causes thinking obstacles to a degree. Quality education puts forward a new requisition that not only lets students master knowledge, but also puts attention to mental development and improving ability, especially thinking ability. However, the key of deepening students thought and conquering thought obstacles lies in the guidance of teachers. Under teachers’ guidance, students can explore effective methods and ways of overcoming thinking obstacles.The article has mathematical learning ideas, theory of knowledge and psychology of constructivism as theoretical basis in studying mathematical thinking obstacles. Mathematical constructive activity is a mathematics abstract process and a process if developing and deepening uninterruptedly. Only students "construct and self -examine" and "self-examine and construct" continuously, can they construct knowledge accurately and master knowledge completely. Or they will form thinking obstacles. According to Bmner’s knowledge development theory, learning itself is a process of cognition. When students understand knowledge insufficiency and partially, they will produce thinking obstacles in solving problems. The effect, which a kind of study has, another is called transference, in psychology. According to the nature and effect of transference, psychologists generally divide it into positive transference and negative transference. To make full use of transference may help students overcome thinking obstacles and improve thinking ability.The article probes into the formal factor of mathematical thinking obstacles from three aspects: meta-cognition, thinking tendency, and process knowledge of mathematical activity.Meta-cognition is cognition and control to thought and learning. It is an understanding of self-cognitive process, cognitive product or all kinds of things about cognition. In a word, meta-cognition is the cognition to cognition and the thought to thought. It is very important to cultivate students’ thinking ability. In the process of meta-cognition participating regulate and control of thinking, there are three basicprinciples, that is, agent principle, aesthetic principle and reflective principle. The fundamental form by which meta-cognition gives full scope to mathematical thought is self-examination. The weakness of meta-cognition will form the deficiency of mathematical thought and lead to its obstacles.The other reason of forming thought obstacles is negative effect of thought tendency. Being affected by their former mathematical knowledge and successful experiences, students lack right cognition to the nature attribute of new conception and knowledge. Besides that, they will be affected by some factors. For example, habit, the function fixity of things, visual sense interference, non-intelligence factors and so on. All these will produce thinking obstacles.The art更多还原