Collaborative Research: Quantifying Curricular Reasoning as a Critical Practice in Teaching Mathematics

数学教师在设计和与学生互动、选择课程材料和实施课程标准的过程中进行课程推理，以服务于高质量的教学。目前，中学数学教师课堂决策的课程推理还没有统一的测量方法。在本研究项目中，研究小组开发并验证了中学教师数学课程推理的两个测量标准。第一个措施是从教师的角度来看课程推理，第二个措施是从数学教育研究群体的角度来考虑。本研究将教师自我评价与专业观察者(如教练、学校领导和研究人员)的自我评价进行比较和调整，以确定教师自我报告测量的有效性。本研究建立了中学数学教师课程推理的基准分，研究人员仔细考察了四个研究问题：[1]在多大程度上支持中学数学教师使用课程推理自评量表测量自己的课程推理水平？[2]有效性证据在多大程度上支持使用课程推理观察评估来测量中学数学教师的课程推理？[3]当使用新的课程推理工具测量中学数学教师的课程推理时，中学数学教师的课程推理水平之间是否存在显著的关系？[4]在这两种测量上，哪些基准定义了不同的课程推理水平？研究小组根据美国心理协会、国家教育测量委员会和美国教育研究协会共同持有的标准收集有效性数据。本研究通过这两种测量方法的发展，加深了我们对教师课程推理的理解。这项工作架起了研究和实践的桥梁，研究人员使用自我报告和观察证据来支持和改进教师的课程推理实践。该团队使用Rasch心理测量工具来制定标准，以提高课堂使用测量的可用性。探索研究PRK-12项目(DRK-12)旨在通过研究和开发创新资源、模式和工具，显著提高Pre-K-12学生和教师的科学、技术、工程和数学(STEM)的学习和教学。 -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经验上的证明。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Teachers of mathematics engage in curricular reasoning as they design and interact with their students, choose curricular materials, and implement curriculum standards in the service of high-quality instruction. Currently, there is no shared measure of curricular reasoning of middle school teacher classroom decision making in mathematics. In this research project, the team develops and validates two measures of middle school teachers’ curricular reasoning in mathematics as practiced. The first measure looks at curriculum reasoning from the perspective of the teacher, the second measure attends to the perspectives of the mathematics education research community. The research examines teacher self-assessment compared and aligned with those of professional observers (e.g., coaches, school leaders, and researchers) to establish the validity of the teacher self-report measure. The research establishes benchmark scores of teachers curricular reasoning in middle school mathematics, supporting increased interpretability and utility of the curricular reasoning score to improve classroom practice.The researchers carefully examine four research questions: [1] To what extent does validity evidence support use of the Curricular Reasoning Self-Assessment Survey Suite for middle school mathematics teachers to measure their own curricular reasoning? [2] To what extent does validity evidence support use of the Curricular Reasoning Observation Assessment to measure middle school mathematics teachers’ curricular reasoning? [3] Is there a significant relationship between middle school mathematics teachers’ curricular reasoning when measured by the new curricular reasoning tools? [4] What benchmarks define different curricular reasoning levels on each of the two measures? The research team gathers validity data based on shared standards held by the American Psychological Association, the National Council on Measurement in Education, and the American Educational Research Association. The research advances our understanding of teacher curricular reasoning through the development of the two measures. The work bridges research and practice as the researchers use self-report and observational evidence to support and improve teachers’ practice of curricular reasoning. The team uses Rasch psychometric tools for standard setting to improve the usability of the measures for classroom usage. The Discovery Research preK-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. 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. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.