A cognitive diagnostic investigation of inequality in mathematics mastery in England

许多教育研究使用学科水平的成绩测量，如PISA或国家级评估的分数。这种方法意味着劣势平等地影响一个学科的所有领域。然而，细致的研究发现，成绩差距低于学科水平。例如，在数学方面，研究发现女孩在计算问题上表现更好，而男孩在代数和几何问题上表现更好。因此，使用学科水平分数作为数学能力的唯一指标的政策或干预措施将忽视性别在特定主题上的差异。技能而不是主题大多数现代测试是基于项目反应理论（IRT）。传统的IRT统计模型假设测试是单维的（即测试衡量单一的整体能力），并且问题应该对所有社会人口统计学学生群体起相同的作用。认知诊断模型（CDM）绕过了IRT的这些假设，因为它们允许多维度。简单地说，CDM是通过确定成功解决每个测试问题所需的特定技能来设计的。该模型估计每个学生对技能的掌握程度和每项技能的难度。这些信息可以用来识别具有相似掌握特征的群体。研究表明，与IRT相比，CDM可以产生更好的模型拟合（Ma et al., 2020; Yamaguchi & Okada, 2018）。此外，为了实现认知诊断的目标，CDM已被用于识别课程弱点，例如发现美国学生在阅读表格和图表数据时需要额外的支持（Lee et al., 2011）。考虑到英国政府正在考虑将数学作为16岁后教育的必修课，focusmaths在英国是一个特别相关的话题。利用CDM研究小组的数学掌握情况，可以发现英国的重要信息；例如，确定特定的社会人口群体是否在课程的特定领域中挣扎。以下问题将指导研究：1。具有相似数学掌握概况的英语学生是否可以被有意义地描述为不同的社会人口统计学群体？在英国不同的数学测试中，分组是否一致？不同国家的群体不同吗？组在IRT模型和CDM之间是否一致？CDM或IRT模型是否提供更好的模型拟合？方法国际和国家数学测试可提供清洁发展机制所需的反应级数据。在国家一级，可以访问KS2 sat和普通中等教育证书的数据，而对于国际考试，将使用PISA和TIMSS。存在着基于不同假设的各种清洁发展机制方法。虽然DINA模型是最常见的，但Yamaguchi和Okada（2018）发现，主效应模型对TIMSS数据（即R-RUM， A-CDM， LLM）的模型拟合效果更好。此外，CDM已被开发用于解释对属性、多层数据和分层属性的部分掌握（例如，掌握一项技能需要掌握较低的技能）。在设计模型时将考虑这些变化。影响将特别关注政策和实践建议。大规模评估因提供的可操作信息很少而受到批评，而清洁发展机制的细粒度分析可能是这个问题的部分解决方案。这些发现可能对课程设置产生重要影响。如果16岁以后没有选择继续学习数学的学生与那些选择继续学习数学的学生有不同的掌握概况，那么课程可能会被开发为为相对薄弱的部分提供更多的支持。教学策略和干预措施将被审查的数学技能的结果不同。此外，一些人声称评估研究可能经常忽视学习理论。回顾学习科学的发展可以深入了解不同群体对数学掌握程度不同的原因。

Many education studies use subject-level measurements for achievement, such as scores from PISA or national-level assessments. This approach implies disadvantage affects all areas of a subject equally. However, fine-grained studies have found achievement gaps below the subject level. For example, in mathematics, studies have found girls performed better on calculation questions, while boys performed better on algebra and geometry. As a result, policies or interventions using subject-level score as the sole indicator of mathematics ability would overlook differences between genders on specific topics. Skills rather than topicsMost modern testing is based on Item Response Theory (IRT). Traditional IRT statistical models assume that a test is unidimensional (i.e. the test measures a single, overall ability) and that questions should function the same for all sociodemographic student groups. Cognitive diagnostic models (CDM) bypass these assumptions of IRT since they allow multidimensionality. Simply put, CDM are designed by identifying specific skills required to successfully solve each test question. The model estimates each student's mastery of the skills and the difficulty of each skill. The information can then be used to identify groups with similar mastery characteristics. Studies show that CDM can produce better model-fit compared with IRT (Ma et al., 2020; Yamaguchi & Okada, 2018). Also, true to the goal of cognitive diagnosis, CDM have been used to identify curriculum weaknesses, such as finding that students in the USA need extra support for reading data from tables and graphs (Lee et al., 2011).FocusMathematics is an especially pertinent topic in England considering the government is considering making maths compulsory in post-16 education. Important information for England can be found by investigating groups' mathematics mastery with CDM; for example, identifying whether particular sociodemographic groups struggle with a specific area of the curriculum. The following questions will guide the research:1. Can English pupils with similar mathematics mastery profiles be meaningfully described as different sociodemographic groups?2. Are groups consistent across different mathematics tests for England?3. Are groups different in different countries?4. Are groups consistent across IRT models and CDM?5. Do CDM or IRT models provide better model-fit?MethodologyInternational and national mathematics tests can provide the response-level data that is required for CDM. At national level, data from KS2 SATs and GCSEs may be accessed, and for international tests, PISA and TIMSS will be used.A variety of CDM approaches exist, based on different assumptions. While the DINA model is most common, Yamaguchi & Okada (2018) found that main effects models gave better model fit for TIMSS data (i.e. R-RUM, A-CDM, LLM). Furthermore, CDM have been developed to account for partial mastery of attributes, multilevel data, and hierarchical attributes (i.e. mastery of one skill requires mastery of lower skills). These variations will be considered when designing the model. ImplicationsSpecial attention will be given to policy and practice recommendations. Large-scale assessments have been criticised for providing little actionable information, and the fined-grained analysis of CDM could be a partial solution to this. The findings can have important curriculum implications. If students who are not choosing to continue studying mathematics post-16 have different mastery profiles than those who are, then the curriculum may be developed to provide more support for the relative weaknesses. Teaching strategies and interventions will be reviewed for the maths skills where outcomes differ. Furthermore, some claim that assessment research might often ignore learning theory. Reviewing developments in learning sciences could provide insight into the causes of groups' different mathematics mastery.