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是成功的关键在以后的数学课程，包括代数1，一个看门人在中学后水平的成功，并在其他STEM领域的成功，如化学，地质学，生物学和工程。鉴于这些技能对以后成功的重要性，必须有高质量的筛选工具，以确定学生在这些领域的困难风险。本研究的主要目的是开发数学筛选评估工具，在四年的过程中，测量学生的能力，在数字关系推理和空间推理的K-2年级。研究团队将开发数学推理技能测量系统，其中包括数字关系推理测试（T-NRR）和空间推理测试（T-SR）。这些措施将供教师和学校系统使用，以筛查学生，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关于特定学生可能需要的支助强度的重要信息。将为T-NRR和T-SR制定每个年级的三种表格，并收集相应的有效性和可靠性证据。探索研究K-12计划（DRK-12）旨在通过研究和开发创新资源，模型和工具（RMT），显着提高学前班学生和教师的科学，技术，工程和数学（STEM）的学习和教学。DRK-12项目中的项目建立在STEM教育的基础研究以及为拟议项目提供理论和经验依据的先前研究和开发工作的基础上。T-NRR和T-SR措施的开发将遵循五个阶段的迭代过程。这些阶段包括（1）完善结构;（2）开发测试规格和项目模型;（3）开发项目;（4）现场测试项目;（5）进行有效性研究。在每个阶段收集和评价的证据将有助于全面评价计量的可靠性和使用计量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认知访谈，实地测试和数学教育工作者，努力学习的学生的教师，文化和语言多样性人群的教师以及技术咨询委员会的评论数据进行持续评估和改进。在T-NRR和T-SR开发的最后阶段，将估计结果的可靠性，并收集多个来源的有效性证据，以检查与其他标准措施的并发和预测关系，分类准确性和对生长的敏感性。 大约4,500名K-2年级的学生将参与研究的所有阶段，包括实地测试和认知访谈。将使用双参数IRT模型分析数据，以确保项目和测试表的可比性。

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.