Multidimensional item response theory and the Force Concept Inventory
Multidimensional item response theory and the Force Concept Inventory
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多维项目反应理论和力概念量表
DOI：
10.1103/physrevphyseducres.14.010137
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发表时间：
2018
影响因子：
3.1
通讯作者：
Gay Stewart
中科院分区：
文献类型：
--
作者：
J. Stewart;Cabot Zabriskie;Seth DeVore;Gay Stewart
力概念量表（FCI）测试结构的研究主要采用因子分析、聚类分析等探索性方法。多维项目反应理论 (MIRT) 提供了传统探索性因素分析的替代方案，允许统计测试来确定最佳因素数量。将 MIRT 应用于 $N=4,716$ FCI 后测试样本，确定 9 因素解决方案为最佳解决方案。额外的分析表明，已识别的因素结构的很大一部分来自使用问题块的实践和成对的类似问题。将 MIRT 应用于减少的 FCI 项目集，删除被阻止的项目和重复的项目，产生 6 因素解决方案；然而，这些因素与牛顿力学的一般结构关系不大。 FCI 的理论模型是根据专家解决方案构建的，并通过将 MIRT 参数矩阵约束到理论模型来拟合 FCI。然后探索理论模型的变化以确定最佳模型。最优模型支持牛顿第一定律和第二定律的微分；一维和三维运动学；以及牛顿第二定律的力相加原理。 FCI 作者提出的模型也很适合；最佳 MIRT 模型在统计上更优越。
Research on the test structure of the Force Concept Inventory (FCI) has largely been performed with exploratory methods such as factor analysis and cluster analysis. Multi-Dimensional Item Response Theory (MIRT) provides an alternative to traditional Exploratory Factor Analysis which allows statistical testing to identify the optimal number of factors. Application of MIRT to a sample of $N=4,716$ FCI post-tests identified a 9-factor solution as optimal. Additional analysis showed that a substantial part of the identified factor structure resulted from the practice of using problem blocks and from pairs of similar questions. Applying MIRT to a reduced set of FCI items removing blocked items and repeated items produced a 6-factor solution; however, the factors had little relation the general structure of Newtonian mechanics. A theoretical model of the FCI was constructed from expert solutions and fit to the FCI by constraining the MIRT parameter matrix to the theoretical model. Variations on the theoretical model were then explored to identify an optimal model. The optimal model supported the differentiation of Newton's 1st and 2nd law; of one-dimensional and three-dimensional kinematics; and of the principle of the addition of forces from Newton's 2nd law. The model suggested by the authors of the FCI was also fit; the optimal MIRT model was statistically superior.