Fostering Equitable Groupwork to Promote Conceptual Mathematics Learning

当学生以小组形式工作时，它可以促进丰富的学习机会，并教会他们以对生活和未来工作重要的方式进行合作。然而，让学生以小组形式工作，也会为一些学生创造机会，使他们以隐性和显性的方式被边缘化。关于教师有意识地处理地位问题的公平小组活动的研究表明，这种工作可以对学生的学习机会产生积极影响(广义上定义为学习内容，但也包括学生对了解/做数学意味着什么的积极的数学认同和观点)。大多数关于数学教育中公平小组合作的工作都已经预先确定了合作的含义。这项探索性研究涉及首席调查员(PI)和一名中学教师及其学生之间的长期合作伙伴关系。这项研究的两个主要目标是描述学生如何随着时间的推移学会相互合作，以理解数学，以及学生和他们的老师如何谈判什么是公平合作，并优先考虑非裔美国学生的观点。通过这种方式，它通过以下方式增加了这一文献：a)从一开始就优先考虑非裔美国学生对合作的看法；b)纵向描述学生如何学习合作；c)在小组背景下记录学生的数学学习；d)为教师教育工作者、教师和学生开发一套专注于公平小组工作的资源。本项目的PI将使用话语心理学和话语分析的理论和方法，与一位中等年级的数学教师合作检查公平小组工作。这所规模较小的私立学校招收的大部分是来自低收入社区的非裔美国学生。PI借鉴了与复杂教学相关的研究，以及关于公平小组合作和富有成效的学生互动的实证研究。制定公平协作定义的基础包括从学生那里收集关于他们重视的各种关系和互动的信息，以及从数学教育和教育文献中借鉴基于资产和人性化的与非裔美国学生有关的研究。这些信息将用于为伙伴关系工作提供信息，并用于分析将收集的数据。这项工作有许多新的方面，包括，例如，学生如何互动与“公平参与”的发展理念和可能支持这种参与的做法之间的持续互动。该提案包括与合作教师一起阅读、计划、反思和观看视频和研究周期的三个阶段。在三个阶段中，将制定分组任务，教师将使用这些任务和其他复杂教学的重要方面来制定任务，并将收集专注于这些法规的数据。这项工作将从六年级开始，然后扩展到更多的年级。数据来源将在与实践教师的工作中收集(例如，计划和反思课程的录音)，在课堂上设定有小组价值的任务(例如，视频、音频、现场笔记、书面作业)，以及在课堂教学时间之外(例如，与学生的访谈)。学习数学包括了解学生谈论数学的方式发生的变化，以及他们如何随着时间的推移进行合作。PI将使用特殊的语篇分析方法，包括系统功能语言学的主位分析。这样的策略有助于关注讨论的内容，以及随着时间的推移，人们如何将不同的想法相互联系起来。PI将分析小组互动以开发12个小插曲，这些小插曲可用于对学生进行焦点小组访谈，并在以后用于教师教育。这些小插曲将包括，例如，公平合作的插图和出现的问题的变化(例如，可能使互动变得不富有成效的“错失的机会”)。这一奖项反映了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。

When students work in small groups it can promote rich learning opportunities and teach them to collaborate in ways that are important for life and future work. Having students work in small groups, however, can also create opportunities for some students to be marginalized in implicit and explicit ways. Research on using equitable groupwork in which issues of status are consciously addressed by the teacher has shown that such work can have a positive impact on students’ opportunities to learn (broadly defined as learning content but also students’ developing positive mathematical identities and perspectives on what it means to know/do mathematics). Most of the work on equitable groupwork in mathematics education have had pre-determined definitions of what it means to collaborate. This exploratory study involves a long-term partnership between the principal investigator (PI) and a middle school teacher and her students. Two major goals of the study are to describe how students learn to collaborate with one another over time to make sense of mathematics, and how students and their teacher negotiate what constitutes equitable collaboration, with African American students’ perspectives being prioritized. In this way, it adds to this body of literature by: a) prioritizing African American students’ perspectives on collaboration from the outset; b) describing, longitudinally, how students learn to collaborate; c) documenting students’ mathematics learning within the context of small groups; and d) developing a set of resources for teacher educators, teachers, and students that focus on equitable groupwork.Using theories and methods from discursive psychology and discourse analysis, the PI of this project will collaborate with a middle grades mathematics teacher to examine equitable groupwork. The small private school enrolls mostly African American students from low income neighborhoods. The PI draws on research related to complex instruction and empirical studies on equitable groupwork and productive student interactions. The basis for the developing definition of equitable collaboration involves gathering information from students about the kinds of relationships and interactions they value, as well as drawing on asset-based and humanizing research related to African American students from mathematics education and education literatures. This information will be used to inform the partnership work as well as be used to analyze the data that will be collected. There are many novel aspects of the work, including, for example, a continual interaction between how students are interacting and the developing idea of “equitable participation” and practices that might support that kind of participation. The proposal includes three phases of work with the collaborating teacher to read, plan, reflect, and view videos and research cycles. In the three phases, groupworthy tasks will be developed, the teacher will use these tasks and other important aspects of complex instruction to enact the tasks, and data will be collected focused on these enactments. The work will begin with the 6th grade, then expand into additional years. The data sources will be gathered in the work with the practicing teacher (e.g., recordings of planning and reflection sessions), in the classroom enactments of the groupworthy tasks (e.g., video, audio, fieldnotes, written work), and outside of the classroom teaching time (e.g., interviews with students). The learning of mathematics involves understanding the changes that take place in how students talk about mathematics and how they collaborate over time. The PI will use particular discourse-analytic methods, including thematic analyses from systemic functional linguistics. Such strategies help to focus on the content of the discussions and how people put various ideas in relationship to one another over time. The PI will analyze the small group interactions to develop 12 vignettes that can be used to do focus group interviews with students and later be used in teacher education. These vignettes will include, for example, illustrations of equitable collaborations and variations of issues that come up (e.g, “missed opportunities” that might keep the interaction from being productive).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.