Children's cognitive representation of the mathematical number line.
Children's cognitive representation of the mathematical number line.
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DOI：
10.1111/desc.12166
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发表时间：
2014-07
影响因子：
3.7
通讯作者：
Geary DC
中科院分区：
文献类型：
--
作者：
Rouder JN;Geary DC
数学数线的学习被假设为依赖于对近似数量的内在感觉。儿童的数字线位置预测符合该系统的基本属性，具体而言，位置被夸大为小数字和压缩为大的。备选假设基于比例推理;具体而言，数字相对于设置的锚点（如线上的端点）放置。传统的测试这些替代品涉及拟合组中位数相应的回归模型，假设同质残差，因此不捕捉有用的信息之间和儿童内的变化，在整个数字线的位置。为了更全面地评估差异预测，我们开发了一套新的分层统计模型，能够同时估计平均水平和性能变化以及发育转变。使用这些技术，我们拟合了224名儿童纵向评估从一年级到五年级（含）的号码线位置。压缩模式在一年级的平均表现中是明显的，但是当对数据的全范围变化进行建模时，只有20%的一年级学生最适合。大多数一年级学生的位置建议使用终点，与比例推理一致。发展转型涉及纳入一个中点锚，符合修改后的比例推理策略。这里介绍的方法，使一个更细致入微的评估儿童的数字线的代表性和学习比以往任何方法，并表明，发展的改善主要是从中点分割的线。
Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children’s number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses are based on proportional reasoning; specifically, numerals are placed relative to set anchors such as end points on the line. Traditional testing of these alternatives involves fitting group medians to corresponding regression models which assumes homogenous residuals and thus does not capture useful information from between- and within-child variation in placements across the number line. To more fully assess differential predictions, we developed a novel set of hierarchical statistical models that enable the simultaneous estimation of mean levels of and variation in performance, as well as developmental transitions. Using these techniques we fitted the number line placements of 224 children longitudinally assessed from first to fifth grade, inclusive. The compression pattern was evident in mean performance in first grade, but was the best fit for only 20% of first graders when the full range of variation in the data are modeled. Most first graders’ placements suggested use of end points, consistent with proportional reasoning. Developmental transition involved incorporation of a mid-point anchor, consistent with a modified proportional reasoning strategy. The methodology introduced here enables a more nuanced assessment of children’s number line representation and learning than any previous approaches and indicates that developmental improvement largely results from midpoint segmentation of the line.
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影响因子：
4
作者：
Geary DC
通讯作者：
Geary DC
影响因子：
4
作者：
Booth, JL;Siegler, RS
通讯作者：
Siegler, RS
影响因子：
4.6
作者：
Geary, David C.;Hoard, Mary K.;Numtee, Chattavee
通讯作者：
Numtee, Chattavee
影响因子：
5.4
作者：
STEVENS, SS
通讯作者：
STEVENS, SS
影响因子：
2.6
作者：
Ashcraft, Mark H.;Moore, Alex M.
通讯作者：
Moore, Alex M.