Children's made-up mathematics problems — a new perspective on talented mathematicians
Children's made-up mathematics problems — a new perspective on talented mathematicians
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孩子们编造的数学问题——天才数学家的新视角
DOI：
10.1007/bf00305073
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发表时间：
1986
影响因子：
3.2
通讯作者：
N. Ellerton
中科院分区：
文献类型：
--
作者：
N. Ellerton
作为大规模数学学习的一部分，学生们被要求编造一个朋友很难解决的数学问题。他们还被要求自己解决问题。一组11至13岁的儿童在完成研究项目的过程中接受了访谈。报告了这组样本中八名能力较强的儿童和八名能力较差的儿童所编造的问题，以及他们在采访中对各自问题的评论。结果突出了两组儿童编造的问题的特点。一般来说，能力较强的孩子比能力较差的同龄人用更复杂的数字系统和更多的运算来弥补计算难度更大的问题。此外，有证据表明，更有能力的学生计划自己的问题并能够得出答案，而能力较差的同龄人在计划和解决自己的问题方面都存在困难。由于每个孩子编造的问题的内容和风格独特地反映了孩子的数学经验和想法，编造的问题是学习数学天赋儿童的一个特别有用的工具，对于这些孩子来说，日常任务通常会快速而准确地完成。
As part of a large scale mathematics study, students were asked to make up a mathematics problem that would be difficult for a friend to solve. They were also asked to solve the problem themselves. A sub-sample of 11- to 13-year-olds was interviewed while they worked through the items in the study.The problems made up by a group of eight more able and eight less able children from this sub-sample are reported here, together with the comments the children made during the interviews about their respective problems.The results highlight features of the problems made up by the two groups of children. In general, the more able children made up problems of greater computational difficulty, with more complex number systems and with more operations than their less able peers. In addition, there is evidence to suggest that the more able students planned their problems and were able to work out the answer, while their less able peers had difficulty with both the planning and the solution of their own problems.As the substance and style of the problem made up by each child uniquely reflects that child's mathematical experiences and ideas, the made up problem is a particularly useful tool for studying mathematically talented children for whom routine tasks are usually completed quickly and accurately.