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来的数学课程的成功至关重要，包括代数1，这是在大专水平上取得成功的看门人，以及在其他STEM领域的成功，如化学、地质、生物和工程学。鉴于这些技能对以后成功的重要性，有必要有高质量的筛查工具来识别在这些领域有困难的风险学生。本研究的主要目的是在四年的时间里开发出K-2年级的数学筛选评估工具，以测量学生在数字关系推理和空间推理方面的能力。研究小组将开发数学推理技能体系的测量，其中将包括数字关系推理测试(T-NRR)和空间推理测试(T-SR)。这些措施将被教师和学校系统用来筛选学生，以确定谁有早期数学困难的风险，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。将为T-NRR和T-SR制定每个年级的三个表格，并收集相关的效度和可靠性证据。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)，显著提高K-12学龄前学生和教师在科学、技术、工程和数学(STEM)方面的学习和教学。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，这些研究和开发工作为拟议的项目提供了理论和经验证明。T-NRR和T-SR措施的制定将遵循五个阶段的迭代过程。该阶段包括(1)细化结构；(2)制定测试规范和项目模型；(3)开发项目；(4)实地测试项目；以及(5)进行效度研究。在每个阶段收集和评估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所作解释的有效性。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、有困难学生的教师、文化和语言不同人群的教师以及技术咨询委员会的数据进行持续评估和改进。在T-NRR和T-SR开发的最后阶段，将评估结果的可靠性，并收集多个效度证据来源，以检查与其他标准测量、分类准确性和对增长的敏感性的并发和预测关系。大约4500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。数据将使用双参数IRT模型进行分析，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.