【作者】 宁锐；

【导师】 邓安邦； 许清华；

【作者基本信息】 四川师范大学 ， 课程与教学论， 2001， 硕士

【摘要】 “在数学问题解决活动中，创造性思维具有怎样的活动规律”，这是本文要解决的核心问题。 首先对创造性思维和数学问题解决的教育理论进行了综述，提出了探讨数学问题解决过程中创造性思维活动的理论框架其中认为：信息客体与主体的认知结构相互作用形成开放思维系统，创造性思维是开放思维系统完成信息加工的自组织过程。数学问题解决是创造性地进行解决数学问题的数学认知活动。 在上述框架下，从三类数学问题解决活动出发，探讨创造性思维在数学问题解决中的作用，得出： 在数学习题类的数学问题解决活动中，学生的问题空间中调动了较多的数学知识和先前解题经验，形成了复杂的问题图式这些图式是思维系统自组织活动的要素，图式的转移（转换）使问题获解，创造性思维的作用表现为促进图式的转移（转换）更简约、概括和迅速地完成。 数学开放题的开放问题情景引起思维系统的开放，形成了创造性思维积极活动的机制，创造性思维的作用表现为不仅引导思路发散，而且促进思维在更高层次对问题结构进行概括。 数学建模问题解决中，创造性思维的作用表现为促进主体更简约和全面地对问题结构进行理解，促进对问题对象向数学对象转换，因此它引导抽象、简化和归纳等数学思维积极活动。 最后，我们提出了一些教学些启示：1、营造“问题解决“情境，诱发创造需要；2、建构良好认知结构，打好创造基础；3、优化数学思维结构，激发创造内因；4、增强协同合作精神，挖掘创造潜能。更多还原

【Abstract】 In this paper the core problem to solve is that how creative thinking wutks in Mathematical Problem Solving (NIPS). At first, make a general statement on the theory of creative thinking arM] MPS and put forward theoretical framework of creative thinking action in MPS. It is regarded that creative thinking is self-organized procecku in which the open thinking system is established through the interaction between cognitive structure of the information object and the information subject and finishes information processing. MPS is mathematical recognizing action to solve creatively mathematical problem. In the mentioned above framework, analyze the function of creative thinking in MPS from the perspective of three types of NIPS, and get to the follow conclusion: In the NIPS of mathematical exercise, in the sttxlents?problem space there are more mathematical knowledge and acquired experience in solving mathematical exercise, and complicated problem scheta is formed. These scheta are the factors of self-organized action, and it’s interchange of scheta enables problem to solve. The function of creative thinking is to promote the finish of interchange of scheta in a more brief, generalized and quick manner. The problem scene of mathematical open problem results in the open thinking system, and forms the mechanism of positive action of creative thinking. The function of creative thinking is to lead the ways of thinking to problem scene, also to generalize problem structure on higher leveL In the problem solving of mathematical modeling, function of creative thinking is to promote the object getting a more brief and comprehensive understanding of problem structure and the interchange from problem object to mathematical object, so it leads the positive development of mathematical thinking such as abstracting and simplifying and generalizing. At last, we provide some ad ices for teaching: (1) construct the scene of“problern solving”and bring out the need of creation; (2) construct good cognition structure and build the base of creation, (3) optimize mathematical thinking structure and engine the internal cause of creation; (4)strengthen the spirit of cooperation and tap the creative potentials.更多还原