Supporting Teachers to Teach Mathematics Through Problem Posing

本项目旨在支持教师让学生参与数学问题提出（基于问题提出的学习，简称P-PBL）。P-PBL是一种强有力的数学教与学的方法，为学生提供了参与真实数学实践的机会。例如，数学中的命题，即问题提出的一种形式，往往在解决复杂问题中起着重要作用，而问题提出是数学建模的重要组成部分。然而，尽管它的重要性，广泛使用的课程材料未能纳入P-PBL在实质性和一致的方式，离开教师很少的资源来制定这一进程。该项目将开发提出问题的课程和教师实施P-PBL的说明性案例，不仅支持教师发展P-PBL的愿景以及如何在自己的课堂上实施，而且还将作为专业发展（PD）提供者的丰富资源。这个项目将产生有价值的发现，教学使用问题提出的地区行政人员，数学教师，教育工作者和研究人员以及课程开发者和政策制定者。该团队将开发和试点一套20 - 30个基于研究的P-PBL案例，为P-PBL的实施提供关键细节，并揭示从开发过程中吸取的“经验教训”。该项目有望对数学教育领域产生更广泛的影响，因为第一个目标是支持教师通过让学生参与数学问题提出来教授数学。P-PBL通过引导学生建构和探究自己的问题，既创造了数学学习的机会，又培养了学生的数学能动性和积极的数学认同感。一个由教师和研究人员组成的网络化改进社区将把问题提出融入日常数学教学，并通过迭代任务和课程设计不断提高P-PBL的质量。这个项目的智力价值在于它对通过提出问题进行数学教学的新的重要见解的贡献。这将通过第二个项目目标来实现，即纵向调查支持教师使用P-PBL教学的承诺，以促进教师的教学实践和学生的学习。一个准实验设计加上设计为基础的研究方法和改进科学将被用来了解如何，何时，以及为什么P-PBL工程在实践中。具体来说，我们计划跟踪样本的36名教师和他们的约3,600名学生从六所中学多年来纵向探索P-PBL的承诺，发展教师的信念提出问题，他们的信念P-PBL，他们的实际教学实践。我们还将通过提出问题的表现、解决问题的表现和数学倾向来调查学生的学习情况。该项目的调查结果将增加不仅支持教师将P-PBL融入他们的数学教学的承诺领域的理解，但也了解教师在从事网络化的改善社区，专注于改善任务和经验教训时所面临的挑战，通过整合P-PBL。 探索研究preK-12计划（DRK-12）旨在通过研究和开发创新资源，模型和工具，显着提高preK-12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。该奖项反映了NSF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。

This project aims to support teachers to engage their students in mathematical problem posing (problem-posing-based learning, or P-PBL). P-PBL is a powerful approach to the teaching and learning of mathematics, and provides students with opportunities to engage in authentic mathematical practices. For example, conjecturing in mathematics, a form of problem posing, often plays an important role in solving complex problems, and problem posing is an important component of mathematical modeling. Yet despite its importance, widely used curriculum materials fail to incorporate P-PBL in substantial and consistent ways, leaving teachers with few resources to enact this process. This project will develop problem-posing lessons and illustrative cases of teachers implementing P-PBL that will not only support teachers to develop a vision of what P-PBL looks like and how to implement it in their own classrooms, but will also serve as rich resources for professional development (PD) providers. This project will generate valuable findings about teaching using problem posing for district administrators, mathematics teachers, educators, and researchers as well as curriculum developers and policy makers. The team will develop and pilot a set of 20−30 research-based P-PBL cases that provide critical details for the implementation of P-PBL and reveal “lessons learned” from the development process. The project promises broader impact on the field of mathematics education as the first goal is to support teachers to teach mathematics through engaging their students in mathematical problem posing. By guiding students to construct and investigate their own problems, P-PBL both helps to create mathematical learning opportunities and develops students’ mathematical agency and positive mathematical identities. A networked improvement community of teachers and researchers will integrate problem posing into daily mathematics instruction and continuously improve the quality of P-PBL through iterative task and lesson design. The intellectual merit of this project is its contribution of new and important insights about teaching mathematics through problem posing. This will be realized through the second project goal which is to longitudinally investigate the promise of supporting teachers to teach with P-PBL for enhancing teachers’ instructional practice and students’ learning. A quasi-experimental design coupled with design-based research methodology and improvement science will be used to understand how, when, and why P-PBL works in practice. Specifically, we plan to follow a sample of 36 teachers and their approximately 3,600 students from six middle schools for multiple years to longitudinally explore the promise of P-PBL for developing teachers’ beliefs about problem posing, their beliefs about P-PBL, and their actual instructional practice. We will also investigate students’ learning as measured by problem-posing performance, problem-solving performance, and mathematics disposition. The findings of the project will add not only to the field’s understanding of the promise of supporting teachers to integrate P-PBL into their mathematics instruction, but also to its understanding of the challenges that teachers face when engaging in a networked improvement community that is focused on improving tasks and lessons by integrating P-PBL. 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.