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

本研究的主要目的是探讨在何种程度上可以使用诊断认知模型（DCM）的评估工具设置的性能标准。 拟议的路径研究项目是使用一个新兴的心理测量方法，调查不同的方法来建立一个工具的代数准备的性能标准。 拟议的研究将使用TIMSS代数项目，并涉及2003年TIMSS美国8年级数据的二次分析。 这项研究将侧重于代数准备所需的技能和知识。这个研究项目包括定量和定性研究。定性研究为定量研究的结果提供了有力的证据。使用诊断认知模型来指导标准制定是令人兴奋的，因为它提供了一个明确定义的方法，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求。迄今为止，还没有研究探讨使用诊断认知模型（DCM）制定绩效标准的主题。 该研究项目为改进标准制定过程提供了一种有前途的方法，使标准制定过程更少地依赖于专家组成员的难以理解的判断，而更多地依赖于易于测量并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方式，而且还因为它有可能改变标准与教师在课堂上有效干预的能力之间的关系，目标是DCM最能预测代数准备程度的方面。研究项目的结果对教学和政策都有更广泛的影响。 本研究不仅增进了我们对教育测量与数学教育相关议题的了解，也为两大阵营建立了一个交流与合作的模式，以进行增值奋进。

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.