Measuring Early Mathematical Reasoning Skills: Developing Tests of Numeric Relational Reasoning and Spatial Reasoning

数字关系推理和空间推理对于后期数学课程的成功至关重要，包括代数1，它是中学后水平成功的把关人，以及其他STEM领域的成功，如化学，地质，生物和工程。考虑到这些技能对以后的成功的重要性，有必要有高质量的筛选工具来识别在这些领域有困难的学生。本研究的主要目的是开发K-2年级四年数学筛选评估工具，以衡量学生在数字关系推理和空间推理方面的能力。研究小组将开发包含数字关系推理测试（T-NRR）和空间推理测试（T-SR）的数学推理技能测试系统。这些措施将被教师和学校系统用来筛选学生，以确定谁有可能在早期数学方面遇到困难，包括残疾学生。这些措施将有助于提供有关特定学生可能需要的支持强度的重要信息。每个年级将为T-NRR和T-SR开发三种表格，并收集相应的效度和信度证据。探索研究K-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具（rmt），显著提高pre -12学生和教师对科学、技术、工程和数学（STEM）的学习和教学。DRK-12计划中的项目建立在STEM教育的基础研究和先前的研究和开发工作的基础上，为拟议的项目提供了理论和实证依据。T-NRR和T-SR措施的制定将遵循一个跨越五个阶段的迭代过程。这些阶段包括(1)细化构造；(2)制定试验规范和项目模型；（三）开发项目；(4)对项目进行现场测试；(5)进行效度研究。在每个阶段收集和评价的证据将有助于全面评价这些措施的可靠性和使用这些措施作出的解释的有效性。项目模型、测试规范和项目开发将根据来自认知访谈、实地测试和数学教育者、困难学生教师、文化和语言多样化人群教师以及技术咨询委员会的评论的数据不断进行评估和改进。在T-NRR和T-SR开发的最后阶段，将评估结果的可靠性，并收集多个效度证据来源，以检验与其他标准测量、分类准确性和对增长的敏感性的并发性和预测性关系。大约4,500名K-2年级学生将参与研究的各个阶段，包括实地测试和认知访谈。数据将使用双参数IRT模型进行分析，以确保项目和测试表格的可比性。

Numeric relational reasoning and spatial reasoning are critical to success in later mathematics coursework, including Algebra 1, a gatekeeper to success at the post-secondary level, and success in additional STEM domains, such as chemistry, geology, biology, and engineering. Given the importance of these skills for later success, it is imperative that there are high-quality screening tools available to identify students at-risk for difficulty in these areas. The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). The measures will be intended for use by teachers and school systems to screen students to determine who is at-risk for difficulty in early mathematics, including students with disabilities. The measures will help provide important information about the intensity of support that may be needed for a given student. Three forms per grade level will be developed for both the T-NRR and T-SR with accompanying validity and reliability evidence collected. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.The development of the T-NRR and T-SR measures will follow an iterative process across five phases. The phases include (1) refining the construct; (2) developing test specifications and item models; (3) developing items; (4) field testing the items; and (5) conducting validity studies. The evidence collected and evaluated during each phase will contribute to the overall evaluation of the reliability of the measures and the validity of the interpretations made using the measures. Item models, test specifications, and item development will be continuously evaluated and refined based on data from cognitive interviews, field tests, and reviews by mathematics educators, teachers of struggling students, teachers of culturally and linguistically diverse populations, and a Technical Advisory Board. In the final phase of development of the T-NRR and T-SR, reliability of the results will be estimated and multiple sources of validity evidence will be collected to examine the concurrent and predictive relation with other criterion measures, classification accuracy, and sensitivity to growth. Approximately 4,500 students in Grades K-2 will be involved in all phases of the research including field tests and cognitive interviews. Data will be analyzed using a two-parameter IRT model to ensure item and test form comparability.