Using Rule Space and Poset-based Adaptive Testing Methodologies to Identify Ability Patterns in Early Mathematics and Create a Comprehensive Mathematics Ability Test

目前正在为3-7岁儿童制定一项新的评估，为教师提供关于儿童在计数、排序、加减法和测量等10个领域的数学能力发展的诊断信息。正在利用创新的心理测量模型开发基于研究的综合数学评估（克雷马），以揭示儿童在10个领域中每个领域的具体属性方面的信息。克雷马将通过使用计算机自适应测试，在相对较短的时间内根据精心制定的学习轨迹提供信息。该项目由两个目标指导：1）产生认知诊断自适应评估，这将产生比以前更有用和详细的关于学生数学知识的信息，以及2）使用尖端的心理测量方法对发展进程进行密切的认知诊断。正在开发一个约350个项目的项目库，可用于确定3-7岁儿童对10个领域的理解水平，这些领域已被确定为进一步学习数学的基础。布法罗大学的道格拉斯·克莱门茨（Douglas Clements）博士领导的研究小组在凯斯西储大学的统计学家柯蒂斯·龙冈（Curtis Tatsuoka）博士的协助下进行开发工作。克雷马使用基于Q矩阵理论、规则状态模型和偏序集的前沿心理测量模型进行开发。初始项目池包括来自REMA的项目，REMA是一种基于一维IRT模型的先前开发的工具。新的项目正在至少200名学生中进行试点，这些学生来自一个由800名学生组成的小组，平均分布在学前班到二年级。然后，成功的项目用于创建新的克雷马。新的评估正在对300名学前至二年级的儿童进行实地测试。随机抽取50名学生（每个年级至少10名），在他们完成这些项目时进行录像。目前正在使用具体的趋同标准来反馈具体项目的执行情况，以满足所需的规格。一名外部评估员正在对这一过程进行审计，并对项目编码和其他分析进行抽查，主要产品将是广泛提供的克雷马。这套采用电脑自适应测验的仪器，可为教师提供有关幼儿对重要数学概念的理解的现成资料。新的心理测量模型将被用来处理来自单个项目的多个属性，并将为推动幼儿数学评估领域的发展做出巨大努力。出版商表示有兴趣广泛提供评估，增加评估对幼儿数学学习产生重大影响的可能性。

A new assessment for children ages 3-7 is being developed to provide teachers with diagnostic information on a child's development of mathematics facility on ten domains such as counting, sequencing, adding/subtracting, and measurement. The Comprehensive Research-based Mathematics Assessment (CREMA) is being developed using innovative psychometric models to reveal information about children on specific attributes for each of the 10 domains. The CREMA will produce information based on carefully developed learning trajectories in a relative short period of time by using computer adaptive testing. The project is guided by two goals: 1) to produce a cognitively diagnostic adaptive assessment that will yield more useful and detailed information about students' knowledge of mathematics than previously possible, and 2) subject the developmental progressions to close cognitive diagnosis using cutting-edge psychometric approaches. An item pool of about 350 items is being developed that can be used to identify the level of understanding children ages 3-7 have on the 10 domains that have been identified as foundational to further learning in mathematics. A research team headed by Dr. Douglas Clements at the University of Buffalo is conducting the development work while being assisted by Dr. Curtis Tatsuoka, a statistician at Case Western Reserve University.The CREMA is being developed using leading-edge psychometric models based on Q-Matrix theory, rule-state models, and posets. The initial item pool includes items from the REMA, a previously developed instrument based on unidemensional IRT models. New items are being piloted with at least 200 students from a group of a total of 800 students evenly distributed among pre-K to grade 2. The successful items then are used to create the new CREMA. The new assessment is being field tested with 300 children, pre-K to grade 2. A random sample of 50 students (at least 10 from each grade) is being video taped as they work the items. Specific criteria of convergence are being used for feedback on how specific items are performing to meet the required specifications. An external evaluator is auditing the process and is doing spot checks of item codings and other analyses performed.The main product will be the CREMA that will be made widely available. This instrument using computer adaptive testing will provide teachers with ready information on young children's understanding of critical mathematical ideas. The new psychometric models that will be used and developed to process multiple attributes from individual items will make large strives to move forward the field of mathematics assessment of young children. A publisher has expressed interest to make the assessment widely available that increases the likelihood the assessment will have large impact on early childhood mathematics learning.