Inversion in mathematical thinking and learning
Inversion in mathematical thinking and learning
复制标题
数学思维与学习的逆向思维
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
B. Greer
中科院分区：
文献类型：
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作者：
B. Greer
反演是一个基本的关系构建块，无论是在数学中作为结构的研究，还是在人们的身体和社会经验中，都与许多其他关键要素，如平衡，不变性，逆转，补偿，对称性和平衡有关。在纯粹的形式算术中，加法和减法之间的逆关系，乘法和除法之间的逆关系，对于灵活和有效的计算以及评估学生的概念理解具有重要意义。有人建议，广泛的研究算术应扩大到考虑到自然数以外的数值域和学生的困难，在扩大的意义上的操作，以更一般的域。当考虑到由算术运算所模拟的情况的范围时，运算之间的逆关系的复杂性以及这些关系所采取的形式的可变性变得更大。最后，一些评论提供了不同的目标和关注的认知心理学家和数学教育家照亮了这方面的研究。
Inversion is a fundamental relational building block both within mathematics as the study of structures and within people’s physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and subtraction, and multiplication and division, have important implications in relation to flexible and efficient computation, and for the assessment of students’ conceptual understanding. It is suggested that the extensive research on arithmetic should be extended to take account of numerical domains beyond the natural numbers and of the difficulties students have in extending the meanings of operations to those of more general domains. When the range of situations modelled by the arithmetical operations is considered, the complexity of inverse relationships between operations, and the variability in the forms that these relationships take, become much greater. Finally, some comments are offered on the divergent goals and preoccupations of cognitive psychologists and mathematics educators as illuminated by research in this area.
DOI：
10.1037/0096-3445.127.4.377
发表时间：
1998-12
期刊：
Journal of experimental psychology. General
影响因子：
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作者：
R. Siegler;Elsbeth Stern
通讯作者：
R. Siegler;Elsbeth Stern