A cognitive diagnostic investigation of inequality in mathematics mastery in England

许多教育研究使用学科层面的成绩衡量标准，如比萨或国家级评估的分数。这种方法意味着不利因素对一个主题的所有领域都有同样的影响。然而，细粒度的研究发现，低于学科水平的成就差距。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上表现更好。因此，将科目一级的分数作为数学能力的唯一指标的政策或干预措施会忽视性别之间在具体专题上的差异。大多数现代测试都是基于项目反应理论（IRT）。传统的IRT统计模型假设测试是一维的（即测试测量单一的整体能力），并且问题应该对所有社会人口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，因为它们允许多维性。简而言之，CDM是通过确定成功解决每个测试问题所需的特定技能而设计的。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。然后，可以使用该信息来识别具有相似掌握特征的组。研究表明，与IRT相比，CDM可以产生更好的模型拟合（Ma等人，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，例如发现美国的学生需要额外的支持来从表格和图表中阅读数据（Lee等人，2011). FocusMathematics在英国是一个特别相关的话题，因为政府正在考虑将数学作为16岁以上教育的必修课。英国的重要信息可以通过调查组的数学掌握与CDM发现;例如，确定特定的社会人口群体是否与课程的特定领域斗争。以下问题将指导研究：1。具有类似数学掌握概况的英国学生是否可以被有意义地描述为不同的社会人口群体？2.英国不同数学考试的分组一致吗？3.不同国家的群体是否不同？4.在IRT模型和CDM中，群体是否一致？5. CDM或IRT模型是否提供更好的模型拟合？国际和国内的数学测试可以提供CDM所需的响应水平数据。在国家一级，可以访问KS 2 SAT和GCSE的数据，对于国际测试，将使用比萨和TIMSS。虽然DINA模型最常见，但Yamaguchi & Okada（2018）发现，主效应模型对TIMSS数据（即R-RUM，A-CDM，LLM）的模型拟合更好。此外，CDM已经被开发用于解释属性、多级数据和分层属性的部分掌握（即，掌握一种技能需要掌握较低的技能）。在设计模型时将考虑这些变化。将特别注意政策和实践建议。有人批评大规模的评估提供的可采取行动的信息很少，对清洁发展机制的精细分析可以部分解决这一问题。研究结果可能具有重要的课程意义。如果学生谁不选择继续学习数学后16有不同的掌握概况比那些谁是，那么课程可以开发，以提供更多的支持相对薄弱环节。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，可以深入了解群体不同的数学掌握的原因。

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.