ABSTRACT

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We randomly assigned fourth and fifth graders to a number line training, an area model training, or a non-numerical control condition. The number line and area model trainings involved both proper and improper fractions and were closely modeled on the training procedures in prior studies. Fraction training with the area model produced improvements in children’s area model estimation of proper and improper fractions. However, contrary to our expectations, training with the number line did not improve number line estimation, and neither training led to improvements in transfer tasks assessing fraction magnitude knowledge. These findings suggest that children can develop the skill to represent improper fractions on area models with brief training. Nevertheless, it is unclear whether this skill enhances a comprehensive understanding of fraction magnitudes.

摘要

数线和面积模型都广泛用于教学分数中。先前的研究发现，与使用面积模型相比，使用数字线进行15分钟的训练后，二年级和三年级的学生对适当分数的量级知识有了更好的了解。当前的研究旨在将这些发现扩展到不正确的分数。我们将四年级和五年级学生随机分配给数字线训练，区域模型训练或非数字控制条件。数量线和面积模型训练涉及适当的分数和不正确的分数，并且在以前的研究中以训练程序为模型进行了紧密建模。使用面积模型进行分数训练可以改善儿童对适当和不正确分数的面积模型的估计。但是，与我们的预期相反，用数字线进行的训练不会改善数字线的估计，并且两种训练都不会导致评估分数幅度知识的传输任务得到改善。这些发现表明，在简短的培训下，儿童可以发展出在区域模型上表示不正确分数的技能。但是，尚不清楚此技能是否可以增强对分数幅度的全面理解。