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数学是思维的数学。本文根据皮亚杰的认知发展理论阐述了数学变式教学与数学思维能力培养的关系。形成数学概念的过程中,利用变式启发学生积极参与观察、分析、发现、感悟、归纳,培养正确概括的思维能力。在理解定理、公式和性质的过程中,利用变式培养学生多向变通的思维能力。在解题教学中,利用变式培养学生联想、转化、推理、归纳、探索的思维能力。进行数学变式教学应注意的问题是变式设计的差异性、变式设计的层次性、变式设计的开阔性、变式训练的灵活性。变式教学可以达到知识和思维能力的双提高,满足学生、学校和社会对学校学科教育的要求。
Mathematics is the mathematical of thinking. Based on Piaget’s theory of cognitive development, this paper expounds the relationship between mathematical variant teaching and mathematical thinking ability cultivation. In the process of forming mathematical concepts, the use of variants to inspire students to actively participate in the observation, analysis, discovery, perception, induction, training correct summary of thinking ability. In understanding the theorem, formula and nature of the process, the use of variants to develop students multi-way flexible thinking ability. In the problem-solving teaching, the use of variant students to associate, transform, reasoning, induction, exploration of thinking ability. The problems that should be paid attention to when teaching math variant are the variability of variant design, the level of variant design, the openness of variant design and the flexibility of variant training. Variant teaching can achieve the double improvement of knowledge and thinking ability to meet the requirements of students, schools and the society for the discipline education in schools.