Collaborative Research: Advancing Equity Goals in Secondary Classrooms by Incorporating Mathematical Justification in Teaching

创造和证明数学主张是数学教育的基本学习目标和有价值的结果。为了促进公平的学习结果，教师追求这一目标的方式必须确保每个学生都有机会在课堂上发展和分享理由。这项先导性研究的预期结果是：(1)以实践为基础的基础知识，了解学生参与数学证明如何促进公平结果；(2)设计原则和教学行动的初步框架，使学生参与数学证明以促进公平目标。该项目的基本贡献是将关于数学证明和数学课堂公平学习的研究汇集在一起。学生对数学的投入取决于他们的代理感和接触复杂数学的途径。数学论证的讨论可以为学生提供一个发展中介的语境，也可以为教师提供一个让学生理解数学思想的途径。该项目探索了两个研究问题。首先，数学论证的实践在哪些方面是教师促进可获得性和代理性的一种负担？第二，教师如何让学生在课堂上为自己辩护，从而朝着更公平的教学结果前进？在康涅狄格州和密歇根州的高中有两个研究网站。教师将在学习小组中探索数学合理性和公平性。数据收集包括学习小组会议的录音、访谈和录像观课。数据分析将包括创建一个带注释的时间表，以记录教师关于公平和数学合理性的对话的进展。将开发一个框架来记录教师的动作，以支持学生在数学证明中的访问和代理。该项目得到了NSF的EHR核心研究(ECR)计划的支持。ECR计划强调基础STEM教育研究，以产生该领域的基础知识。在基本、广泛和持久的关键领域进行投资：STEM学习和STEM学习环境，扩大STEM的参与，以及STEM劳动力发展。该计划支持积累强有力的证据，为理解、构建理论以解释并建议干预和创新以应对教育中持续存在的挑战的努力提供信息。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。

Creating and justifying mathematical claims is an essential learning goal and valued outcome of a mathematics education. To advance equitable learning outcomes, it is essential that teachers pursue this goal in ways that ensure every student has opportunities to develop and share justifications in their classrooms. The intended outcomes of this pilot study are: (1) practice-grounded, foundational knowledge about how students’ participation in mathematical justification can advance equity outcomes, and (2) an initial framework for design principles and teaching moves that engage students in mathematical justification to advance equity goals.The fundamental contribution of this project is bringing together research about mathematical justification and equitable learning in mathematics classrooms. Students’ engagement in mathematics depends on their sense of agency and access to complex mathematics. Discussions of mathematical justification can provide a context for students to develop agency and for teachers to provide students with access to understanding mathematical ideas. The project explores two research questions. First, in what ways is the practice of mathematical justification an affordance for teachers to promote access and agency? Second, how do teachers engage students in justification in their classroom to advance toward more equitable instructional outcomes? There are two research sites at high schools in Connecticut and Michigan. Teachers will work in study groups to explore mathematical justification and equity. Data collection includes recordings of study group meetings, interviews, and video-recorded lesson observations. Data analysis will include creating an annotated timeline to document the progress of teachers’ conversations about equity and mathematical justification. A framework will be developed to document teacher moves that support students’ access and agency in mathematical justification. This project is supported by NSF's EHR Core Research (ECR) program. The ECR program emphasizes fundamental STEM education research that generates foundational knowledge in the field. Investments are made in critical areas that are essential, broad and enduring: STEM learning and STEM learning environments, broadening participation in STEM, and STEM workforce development. The program supports the accumulation of robust evidence to inform efforts to understand, build theory to explain, and suggest intervention and innovations to address persistent challenges in education.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.