Development of Probabilistic Understanding in Fourth Grade
Development of Probabilistic Understanding in Fourth Grade
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DOI：
10.5951/jresematheduc.47.1.0028
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发表时间：
2016-01-01
影响因子：
2.8
通讯作者：
Watson, Jane M.
中科院分区：
文献类型：
--
作者：
English, Lyn D.;Watson, Jane M.
我们分析了四年级学生对从实验结果的相对频率到理论概率的转变的理解的发展，重点放在了基本的统计学概念变异和期望上。我们报告了学生对抛出一枚和两枚硬币的结果的初始和不断变化的预期，他们如何将物理和计算机模拟试验的相对频率与理论概率联系起来，以及他们如何创建和解释理论概率模型。研究结果包括学生从最初预测扔两枚硬币的结果的明显等概率偏差，到代表增加试验数量的结果的进展。在观察到随着样本量的增加，与理论概率之间的差异逐渐减小之后，学生们对结果的相对频率与理论概率之间的关系以及它们与变化和期望之间的关系有了更深入的理解。学生们的最终模型表明，他们的概率理解水平不断提高。
We analyzed the development of 4th-grade students' understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. We report students' initial and changing expectations of the outcomes of tossing one and two coins, how they related the relative frequency from their physical and computer-simulated trials to the theoretical probability, and how they created and interpreted theoretical probability models. Findings include students' progression from an initial apparent equiprobability bias in predicting outcomes of tossing two coins through to representing the outcomes of increasing the number of trials. After observing the decreasing variation from the theoretical probability as the sample size increased, students developed a deeper understanding of the relationship between relative frequency of outcomes and theoretical probability as well as their respective associations with variation and expectation. Students' final models indicated increasing levels of probabilistic understanding.