Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks
Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks
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澳大利亚八年级数学课本解释中的推理模式
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Jill Vincent
中科院分区：
文献类型：
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作者：
K. Stacey;Jill Vincent
理解数学是建立在推理的基础上的，而不仅仅是要应用的规则的集合，这是向学生传达的重要信息。在这里，我们研究了九本澳大利亚八年级教科书中七个主题中提出的推理。着眼于引入新的数学规则或关系的解释性文本，我们根据所使用的推理模式对解释进行分类。确定了七种模式，制定了一个分类方案，该方案既完善又扩展了以前的方案。大多数教科书对大多数主题都提供了解释，而不是呈现“没有理由的规则”，但主要目的似乎是规则推导或论证，为练习做准备，而不是将解释作为思考工具。教科书一般不区分演绎推理和其他推理模式的合法性。
Understanding that mathematics is founded on reasoning and is not just a collection of rules to apply is an important message to convey to students. Here we examined the reasoning presented in seven topics in nine Australian eighth-grade textbooks. Focusing on explanatory text that introduced new mathematical rules or relationships, we classified explanations according to the mode of reasoning used. Seven modes were identified, making a classification scheme which both refined and extended previous schemes. Most textbooks provided explanations for most topics rather than presenting “rules without reasons” but the main purpose appeared to be rule derivation or justification in preparation for practise exercises, rather than using explanations as thinking tools. Textbooks generally did not distinguish between the legitimacies of deductive and other modes of reasoning.