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近年来数学教研界风行“合情推理”之说,客观上遮蔽了归纳推理、类比推理,殊不知这两类推理方法是不能被一言以蔽之的。“合情推理”是一个易使人产生错觉的短语(其中,“合情”二字并无确切含义),却被捧得让人以为比演绎推理还重要。实际上,离开归纳推理、类比推理,“合情推理”毫无意义。归纳与类比是间接认识事物或断定事物属性的思想方法,是人类认识活动须臾不离的思想活动,是学界熟知且各成系统的学问。常言说的经验,主要是通过归纳或类比过程形成的;教科书编写、课堂教学、科学实验、游戏活动都应该遵循归纳或类比的认识规律,绝非“合情推理”所能概括。学生学习过程中的大量直接或间接推理行为中存在着反映认识规律的思维现象,归纳的片面性即为归纳认识过程中的惯常现象,演绎推理可以弥补因归纳片面性而产生的缺失。另外,仅就归纳推理来说,就包括求同法、存异法、同异并用法、剩余法、共变法等,十分丰富,是人人都应掌握的科学方法。“合情推理”之说把这些知识、现象及其精华全遮蔽了,颇有“浮云遮月”的味道,数学营养被大打折扣。阮老师就这个问题写出《例谈小学数学归纳的片面性》这篇好文章,发挥了数学教育的正能量。感谢阮老师!
In recent years, mathematics teaching and research community popular “reasonable reasoning ” theory, objectively obscured inductive reasoning, analogical reasoning, not knowing these two types of inference methods can not be said in a word. “Affirmative reasoning” is a phrase that is easy to make people illusory (where the meaning of “affirmative” has no definite meaning), but it is exalted that people think it is more important than deductive reasoning. In fact, leaving inductive reasoning, analogical reasoning, “sensible reasoning ” is meaningless. Induction and analogy are indirect ways to recognize things or to determine the attributes of things. They are ideological activities that human beings need to understand. They are well-known in the academic world and are systems of learning. The general experience is mainly formed through induction or analogy. Textbook writing, classroom teaching, scientific experiments, and game activities should all follow the generalization or analogy of cognition, rather than the “reasonable inference”. A large number of direct or indirect reasoning behaviors in students’ learning process have the thinking phenomenon reflecting the law of cognition. The one-sidedness of induction is the usual phenomenon in induction process. Deductive reasoning can make up for the lack of induction one-sidedness. In addition, just inductive reasoning, including the law of seeking commonality, the law of difference, the common ground with the use of law, the residual law, covariant and so rich in science, is that everyone should grasp the scientific method. “Affirmative reasoning,” said all of these knowledge, phenomena and their essence completely obscured, quite “cloud cover the moon” flavor, mathematical nutrition is greatly reduced. On this issue, Nguyen teacher wrote a good article “On the One-sidedness of Induction of Elementary Mathematics in Primary Schools” and played a positive role in mathematics education. Thanks to Nguyen teacher!