Supporting Teachers to Teach Mathematics Through Problem Posing

这个项目旨在支持教师让他们的学生参与数学问题提出(基于问题的学习，或P-PBL)。P-PBL是一种强有力的数学教与学方法，为学生提供了从事真实数学实践的机会。例如，数学中的猜想是问题提出的一种形式，在解决复杂问题时往往起着重要的作用，而问题提出是数学建模的重要组成部分。然而，尽管P-PBL很重要，但被广泛使用的课程教材并没有以实质性和一致性的方式纳入P-PBL，使得教师几乎没有资源来实施这一过程。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，不仅将支持教师发展P-PBL是什么样子以及如何在他们自己的课堂上实施，而且还将作为专业发展(PD)提供者的丰富资源。该项目将为地区行政人员、数学教师、教育工作者和研究人员以及课程开发人员和政策制定者提供关于使用问题提出进行教学的有价值的发现。该小组将开发和试点一套20个−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获得的“经验教训”。该项目承诺对数学教育领域产生更广泛的影响，因为第一个目标是通过让学生参与提出数学问题来支持教师教授数学。通过引导学生构建和探究自己的问题，P-PBL既有助于创造数学学习机会，又有助于培养学生的数学中介能力和积极的数学认同。一个由教师和研究人员组成的网络改进社区将问题提出整合到日常数学教学中，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来教授数学的新的和重要的见解做出了贡献。这将通过第二个项目目标实现，即纵向调查支持教师使用P-PBL教学的承诺，以加强教师的教学实践和学生的学习。准实验设计结合基于设计的研究方法和改进科学将被用来理解P-PBL在实践中如何、何时和为什么有效。具体地说，我们计划对来自六所中学的36名教师及其大约3600名学生进行多年的跟踪调查，以纵向探讨P-PBL在发展教师关于问题提出的信念、他们关于P-PBL的信念以及他们的实际教学实践方面的前景。我们还将调查学生的学习，通过提出问题的表现、解决问题的表现和数学倾向来衡量。该项目的结果不仅将增加总部外对支持教师将P-PBL纳入其数学教学的承诺的理解，而且也将增加对教师在参与一个侧重于通过整合P-PBL改进任务和课程的网络改进社区时所面临的挑战的理解。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，显著提高Pre-K-12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，为拟议的项目提供了理论和经验上的证明。该奖项反映了NSF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。

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.