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以服务于高质量教学的过程中，参与课程推理。目前，对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。在这个研究项目中，团队开发并验证了中学教师数学课程推理的两种测量方法。第一项措施是从教师的角度看待课程推理，第二项措施关注数学教育研究界的观点。本研究将教师自我评估与专业观察者（如教练、学校领导和研究人员）的自我评估进行比较，并与之保持一致，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数，支持提高课程推理分数的可解释性和实用性，以改善课堂实践。研究人员仔细研究了四个研究问题：b[1]效度证据在多大程度上支持使用课程推理自我评估调查套件来衡量中学数学教师自己的课程推理？效度证据在多大程度上支持使用课程推理观察评估来衡量中学数学教师的课程推理？用新的课程推理工具来衡量中学数学教师的课程推理是否存在显著的关系？[4]在这两项测试中，哪些基准定义了不同的课程推理水平？研究小组以美国心理学会、美国教育测量委员会、美国教育研究协会的共同标准为基础，收集了有效性数据。本研究通过这两项措施的发展促进了我们对教师课程推理的认识。研究人员利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，从而将研究与实践联系起来。该团队使用Rasch心理测量工具来制定标准，以提高课堂使用措施的可用性。探索研究preK-12项目（DRK-12）旨在通过研究和开发创新资源、模型和工具，显著提高preK-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。 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知识价值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.