【作者】 陆书环；

【导师】 曲安京；

【作者基本信息】 西北大学 ， 科学技术史， 2008， 博士

【摘要】 “问题解决”(Problem Solving)教学思想自1980年代由美国提出后,在国际数学教育界受到普遍重视。并在数学教育哲学、数学学习心理以及数学方法论领域展开深入研究,其教育理念被许多国家引入数学课程中。就数学教育而言,“问题解决”就是在教学中贯彻创造性地应用数学以解决问题的思想,让学生的学习变为学会思维的活动过程。或者说“问题解决”教学是一个发现的过程、探究的过程和创新的过程。从数学史的角度来说,历史上的“问题”与“问题解决”的过程正是数学发现、发明和创造的真实写照。因此历史的“问题解决”是现代“问题解决”教学的不竭动力和源泉。本文以探讨数学史与数学教育结合为目标,以认识论理论为指导,通过深入考察历史的“问题”和“问题解决”渊源,复现数学历史发现过程中问题解决的经典案例,探寻数学发明和创造的踪迹。从而运用现代思维科学、心理学等相关理论探究历史的“问题解决”与现代“问题解决”教学结合的教学策略。为此,本文主要做了以下工作。(1)首先从认识论出发,通过数学进程中若干经典数学问题和重大数学理论的呈现,对数学历史的“问题”产生与发现进行了深入考察与分析,并从整个数学历史发展的角度,阐明数学问题对形成数学概念和推动数学理论发展的重要作用。同时结合我国历史上数学与数学教育相互依存、携手并进的历史发展事实探讨了历史的“问题解决”对于数学教育的有力促进。(2)通过历史上现实问题解决案例和数学理论问题解决过程的探析,再现了数学发现的本原状态,展示数学发现的线索与方法。并从现代“问题解决”教学实际深入分析了可资借鉴的思维因素和问题发现的途径。为数学教学中拓宽教学思维,实现历史的“问题解决”与现代数学“问题解决”教学结合奠定方法论基础。(3)运用思维科学的理论,通过对数学思维分类的探讨指出数学创造思维的特征。进而结合历史的问题解决过程和数学家运用创造性思维,进行数学发现的案例解析,再现了数学家在发现数学结论解决数学疑难,推进数学进展中所显现出的创造思维。从而为现代数学课堂教学培养学生创新思维提供了可供模拟的思路和场境。(4)从科学方法的重要性出发,追寻经典数学方法的源头。对历史问题解决过程中数学思想方法的产生以案例的形式进行再现性分析,给数学学习从数学发现的本原状态中理解方法论的实质,厘清数学思想方法形成的线索,从而为推进数学研究工作和改革数学教学开辟途径。(5)运用现代心理学的迁移原理、思维科学的相似性原理等相关理论,结合现代数学教育中强调人文教育的理念,综合对历史的“问题解决”中数学家面对原始问题进行数学创造方法考察分析,根据学生的认知规律和数学学习的特点,从现代数学课堂教学实际出发,提出了HPM视域下的“问题解决”教学策略。总之本文以历史的观点研究了“问题解决”教学意义和作用,从历史的“问题解决”向现代数学课堂渗透的视角,给出了数学史与数学教育结合的途径。更多还原

【Abstract】 Teaching thought of Problem-Solving that began in America in 1980s was received universal recognition of mathematics education domain in the world. Moreover the deep research was launched in the domain of mathematic education philosophy, mathematics learning psychology as well as mathematics methodology. Its educational idea was introduced into mathematics curriculum in many countries. Speaking of mathematic education, "Problem-Solving" is to implement the thought of applying mathematics to solve the questions in teaching creatively that study will be an active procedure of thought, or the teaching of "Problem-Solving" is a discovery process, inquisition process and innovation process. From the history of mathematics angle, the pross of problems and "Problem-Solving" is accompanied by mathematics discovery, invention and creation.Therefore, to modern "Problem-Solving", historical "Problem-Solving" is drainless power and fountainhead. The aim of this thesis is to discuss uniting the history of mathematics and mathematics education, it is instructed by epistemology theory, through thorough inspecting the historical "problem" and "problem-solving"s origin and finding classical cases about "Problem-Solving" in the process of discoverying mathematics history , inquirying about mathematics invention and the creation trail, Thus teaching strategy about uniting the historical "Problem-Solving" and modern "Problem-Solving" with the help of modern science thought, psychology and correlation theories. Therefore, this article has been mainly done the following work:1. First, the epistemology as starting point, through presenting mathematics advancement in certain classical mathematic problem and significant mathematical theory , the production and discovery to mathematics of historical problem is inspected and analysised, the influential role of mathematics problem which forming mathematics concept and impetus mathematical theory development is exposited. Simultaneously historical "problem-solving" regarded as the mathematics education powerful promotion is discussed by the historical development fact in our country history mathematics and mathematics education depending on each other mutually, and advancing together hand in hand . 2. Searching the realistic case of "Problem-Solving" and the process of mathematical theory solution in history, realistic mathematics discovery is reappeared and the clue and the method of mathematics discovery is demonstrated, then the thought factor and the question discovery way are analyzed from the actual teaching of "Problem-Solving" which lay the methodology foundation for realizing the union of the historical "Problem-Solving" and modern "Problem-Solving".3. Using scientific thought theory, the characteristic of mathematics creative thought is pointed out through discussing the classification of mathematics thought. Then uniting the process of the historical "Problem-Solving "and the mathematician utilizing the creative thought, carriying on the case analysis of mathematics discovery, mathematics creative thought is reappeared in the pross of discoverying mathematic conclusion, solution, and advancing mathematics progress. Thus the simulation of solution and situation are supplied to raise the students’ innovative idea in the modern mathematics teaching.4. To begin with the importance of scientific method, tracking down the source of the classical mathematical method, the production of mathematics thinking method is carried on a reproducibility analysis with the case form in the process of the historical "Problem-Solving", understanding the essence of methodology from the orginal condition in learning mathematics ,and clearing the clue which mathematics thinking method forms, thus the way of advancing mathematics research work and reforming mathematic teaching are opened.5. The article using the migration principle of modern psychology, the similar principle of thought science and so on correlation theories, and uniting humanities education idea that modern mathematics education emphasized, synthesisly analysed mathematics creative method which mathematician facing the primitive question during the historical "Problem-Solving". The teaching strategy of problem-solving is proposed in the HPM according to students’ cognition rule, mathematics learning characteristic and the fact of modern mathematics teaching.In brief, this article has studied the teaching significance and the function of problem-solving with the historical viewpoint. The united way of mathematics history and mathematics education has given in view of the historical "Problem-Solving" seepaging to modern mathematics teaching.更多还原