Determining Algebra Readiness and Cognitive Skills Profiles by Using a Diagnostic Cognitive Model to Set a Performance Standard on a Pre-Algebra Test

这项研究的主要目的是调查可以在多大程度上为使用诊断认知模型(DCM)的评估工具设定绩效标准。拟议的路径研究项目是使用一种新兴的心理测量学方法来调查不同的方法，以建立一个工具的代数准备的表现标准。这项拟议的研究将使用TIMSS代数项目，并涉及对2003年TIMSS美国8年级数据的二次分析。这项研究将集中在代数准备所需的技能和知识上。本研究项目既有定量研究，也有定性研究。定性研究为定量调查的结果提供了强有力的证据。使用诊断认知模型来制定标准是令人兴奋的，因为它不仅提供了一种明确定义的方法，而且还因为它承诺提供关于每个学生的优势和劣势的诊断信息，以便教师可以设计特定的补救措施来满足每个学生的需要。到目前为止，还没有研究探讨使用诊断认知模型(DCM)来制定表现标准的主题。这一研究项目为改进标准制定过程提供了一条有希望的途径，使其减少对专家小组成员难以理解的判断的依赖，而相对更多地依赖于易于测量和与测试结果相关的因素，如DCM。这种方法具有潜在的变革性，不仅因为它有可能改变标准制定的实施方式，还因为它有可能通过瞄准最能预测代数准备情况的DCM的方面，改变标准和教师有效干预课堂能力之间的关系。该研究项目的发现对指导和政策都有更广泛的影响。这一研究项目不仅可以增进我们对教育测量和数学教育相关问题的理解，还可以为两个阵营建立一个交流和合作的模式，为增值研究努力。

The primary purpose of the research is to investigate the extent to which a performance standard can be set for an assessment instrument using a diagnostic cognitive model (DCM). The proposed Pathway research project is to use of an emerging psychometric methodology to investigate different approaches to establish a performance standard on an instrument for algebra readiness. The proposed research will use TIMSS algebra items and involve a secondary analysis of the 2003 TIMSS U.S. Grade 8 data. The research will focus on the skills and knowledge required for algebra readiness. This research project involves both quantitative and qualitative studies. The qualitative study provides strong evidence to support the findings of the quantitative investigations. The use of Diagnostic Cognitive Models to inform standard setting is exciting because it offers both a clearly defined methodology, but also because it promises diagnostic information regarding the strengths and weaknesses of each student so that teachers can design a specific remediation to meet each student's needs.To date there is no research that has examined the topic of setting performance standards using a diagnostic cognitive model (DCM). This research project offers a promising way forward for improving processes of standard setting, such that they rely less on the inscrutable judgments of panel members, and relatively more on factors that can be easily measured and related to test outcomes, such as DCM. The approach is potentially transformative not only for its potential to change how standard setting is conducted, but also for its potential to change the relationship between standards and teachers' ability to intervene effectively in the classroom, by targeting aspects of the DCM that best predict algebra readiness. The findings of the research project have broader implications for both instruction and policy. This research project cannot only advance our understanding of related issues in educational measurement and mathematics education, but also establish a model for two camps to communicate and work together for value-added research endeavor.