Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA.
The Siegler Center for Innovative Learning (SCIL), Advanced Technology Center, Beijing Normal University, China.
Dev Sci. 2018 Jul;21(4):e12601. doi: 10.1111/desc.12601. Epub 2017 Sep 12.
Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining fourth to eighth graders' estimates of fraction sums. We found that roughly half of estimates of sums were smaller than the same child's estimate of one of the two addends in the problem. Moreover, children's estimates of fraction sums were no more accurate than if they had estimated each sum as the average of the smallest and largest possible response. This weak performance could not be attributed to poor mastery of arithmetic procedures, poor knowledge of individual fraction magnitudes, or general inability to estimate sums. These results suggest that a major source of difficulty in this domain is that many children's learning of fraction arithmetic procedures develops unconstrained by conceptual understanding of the procedures. Implications for education are discussed.
许多儿童即使经过多年的教学也未能掌握分数算术。最近的一项分数算术理论（Braithwaite、Pyke 和 Siegler，2017）假设，这种分数算术程序学习不良反映了对它们的概念理解不佳。为了检验这一假设，我们进行了三项实验，考察了四至八年级学生对分数和的估计。我们发现，大约一半的和的估计值小于问题中两个加数之一的同一儿童的估计值。此外，儿童对分数和的估计值并不比他们将每个和估计为最小和最大可能响应的平均值更准确。这种较差的表现不能归因于算术程序掌握不佳、对个别分数大小的知识了解不佳或一般无法估计和。这些结果表明，该领域的一个主要困难来源是，许多儿童对分数算术程序的学习不受对程序的概念理解的限制。讨论了对教育的影响。
