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运用合情推理探索高中数学解题思路摘要近些年来，我国数学课程改革渐渐向纵深处发展，合情推理是培养创新能力的推理过程，广泛的渗透于高中数学各个模块的教学内容中。2003年，我...
运用合情推理探索高中数学解题思路 摘 要 近些年来，我国数学课程改革渐渐向纵深处发展，合情推理是培养创新能力的推理过程，广泛的渗透于高中数学各个模块的教学内容中。2003年，我国教育部颁布的《普通高中数学课程标准(实验)》中第一次把合情推理引入高中数学课程，出现了“推理与证明”专题，明确提出了“发展学生的合情推理能力”。现有研究表明，尽管对数学解题中合情推理的理论基础探讨已日趋完善，但有关运用合情推理探索高中数学解题思路的研究则略欠系统性和科学性。 本文首先对合情推理理论基础进行了回顾、总结，包括基本概念框架和支撑理论，在此基础上，通过定性分析的方法，辨析了数学解题与合情推理之间的内在关联关系：帮助促进数学题目条件的理解和独立解题能力的提高，指出数学解题中归纳、类比、联想等方法的含义及应用。接着，本文对几个具体的案例进行详细分析，阐明如何引导学生合理运用合情推理来探索、找到解题思路，在进一步思考的基础上，对运用合情推理探索解题思路的一般规律进行了总结。最后，针对运用合情推理、开阔学生解题思路，本文提出了若干对策与建议，包括提高老师的合情推理素养、注意学生亲历数学活动的真实过程，等等。
关键词：数学解题，合情推理，思路探索，案例分析
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关键词：数学解题，合情推理，思路探索，案例分析
机器翻译勿扰！ 展开
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Reasoning to explore the use of high school mathematics problem-solving ideas
Abstract : In recent years, China's mathematics curriculum reform gradually in depth at the development of plausible reasoning is to develop innovative capacity of reasoning, extensive penetration of the various modules in the teaching of high school mathematics content. In 2003, China's Ministry of Education promulgated the "high school mathematics curriculum standards (experimental)" Reasoning for the first time the introduction of high school mathematics curriculum, a "reasoning and proof," subject, clearly stated that "the development of sensible reasoning ability of students . " Existing studies have shown that, despite the mathematical problem-solving in the theoretical basis of plausible reasoning has been maturing, but the use of reasonable inference to explore ideas of high school mathematics problem-solving and scientific research is Lueqian system. In this paper, the theoretical basis of plausible reasoning were reviewed, summarized, including the basic conceptual framework and support the theory, on this basis, through qualitative analysis, Analysis of a mathematical problem-solving and Reasoning intrinsic association between: Help promote understanding of the conditions of math problem solving capabilities and independence, that the mathematical problem-solving in induction, analogy, think of the meaning and application of such methods. Then, several specific cases of this detailed analysis to clarify how to guide students to explore the rational use of plausible reasoning, problem-solving ideas found in the further consideration based on the reasonable inference to explore the use of general rules to problem-solving ideas summarized. Finally, for the use of plausible reasoning, broaden their problem-solving ideas, this paper presents a number of countermeasures and suggestions, including raising the literacy teacher's sensible reasoning, attention to the students experience the real process of mathematical activity, etc.
Keywords: mathematical problem-solving, Reasoning, explore ideas, case studies
Abstract : In recent years, China's mathematics curriculum reform gradually in depth at the development of plausible reasoning is to develop innovative capacity of reasoning, extensive penetration of the various modules in the teaching of high school mathematics content. In 2003, China's Ministry of Education promulgated the "high school mathematics curriculum standards (experimental)" Reasoning for the first time the introduction of high school mathematics curriculum, a "reasoning and proof," subject, clearly stated that "the development of sensible reasoning ability of students . " Existing studies have shown that, despite the mathematical problem-solving in the theoretical basis of plausible reasoning has been maturing, but the use of reasonable inference to explore ideas of high school mathematics problem-solving and scientific research is Lueqian system. In this paper, the theoretical basis of plausible reasoning were reviewed, summarized, including the basic conceptual framework and support the theory, on this basis, through qualitative analysis, Analysis of a mathematical problem-solving and Reasoning intrinsic association between: Help promote understanding of the conditions of math problem solving capabilities and independence, that the mathematical problem-solving in induction, analogy, think of the meaning and application of such methods. Then, several specific cases of this detailed analysis to clarify how to guide students to explore the rational use of plausible reasoning, problem-solving ideas found in the further consideration based on the reasonable inference to explore the use of general rules to problem-solving ideas summarized. Finally, for the use of plausible reasoning, broaden their problem-solving ideas, this paper presents a number of countermeasures and suggestions, including raising the literacy teacher's sensible reasoning, attention to the students experience the real process of mathematical activity, etc.
Keywords: mathematical problem-solving, Reasoning, explore ideas, case studies
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Using the ratiocination explore high school mathematics problem-solving ideas in recent years, our country to pick the mathematics curriculum reform is to ZongShenChu development, to develop students' innovative ability ratiocination is the reasoning process, extensive penetration in the high school mathematics each module of the teaching content. In 2003, China's ministry of education issued "ordinary high school mathematics curriculum standard (experiment the first time), into the high school mathematics course ratiocination, appear" reasoning and proof "project, definitely put forward" to develop the students' ability of ratiocination ". Current research shows that, although the mathematics problem-solving in the theoretical foundation of the ratiocination discussion has become increasingly perfect, but about using the ratiocination explore high school mathematics problem-solving ideas for the research is slightly less systematic and scientific. In this paper, first ratiocination theory base
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