Collaborative Research: Middle School Students Graphing From the Ground Up

图形表示在STEM领域中很常见，用于建模、交流和分析现象，理解图形表示对于学生在STEM领域的成功至关重要。然而，研究表明，许多学生努力发展对图形表示的理解。我们认为，学生对坐标系的理解，即构建和解释图形所需的理解，是他们理解图形表示法的努力的基础，而且，也为发展这种理解奠定了必要的基础。在这个项目中，我们考察了中学生对坐标系和参照系的理解，然后考察了他们的图表结构和解释。这一重点允许我们设计教学材料，以避免或缓解研究文献中确定的学生在图形理解方面的持续挑战，从而支持学生的图形理解。本项目的总体目标是通过关注组成坐标系的基本坐标系和参照系，促进中学生对图形的理解。三个研究问题指导这个项目：(I)个人学生创建和解释参照系、坐标系和图表的思维方式是什么？(Ii)学生发展这些思维方式的一般过程是什么？(Iii)在学生发展图形理解的过程中，什么顺序的教学任务支持和建立了学生的不同思维方式？该项目通过利用基于设计的方法来解决这些问题，在该方法中，我们将参与干预和修改的循环，以开发、测试和改进认知模型、建设性的行程和教学任务。通过几次反复的临床访谈和小规模教学实验，我们打算提出一种理论来解释学生对图形的理解能力的发展，并解释他们不同的思维方式。通过这个过程，我们将反复设计教学任务和任务序列，以支持学生在广泛使用和免费提供的Desmos平台上发展对参照系、坐标系和图形的理解。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PreK-12学生和教师的科学、技术、工程和数学(STEM)的学习和教学。 -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。该奖项反映了美国国家科学基金会的法定使命，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。

Graphical representations are common in STEM fields for modeling, communicating, and analyzing phenomena, and understanding graphical representations is critical to student success in STEM fields. Yet, research indicates that many students struggle to develop an understanding of graphical representations. We contend that students’ understanding of coordinate systems, an understanding required to construct and interpret graphs, underlies their struggles to understand graphical representations and, moreover, lays the foundation necessary for developing that understanding. In this project, we examine middle-school students’ understandings of coordinate systems and frames of reference prior to examining their graph construction and interpretation. This focus allows us to design instructional materials that can support students’ graphing understandings in ways that avoid or mitigate how persistent challenges in students’ graphing understandings identified in the research literature.The overarching goals of this project are to advance knowledge of middle school students’ developing understandings of graphs “from the ground up” with attention to underlying coordinate systems and frames of reference that comprise the coordinate systems. Three research questions guide the project: (i) What are the ways of thinking through which individual students create and interpret frames of reference, coordinate systems, and graphs? (ii) In what general progressions do students develop these ways of thinking? (iii) What sequence of instructional tasks support and build on students’ varied ways of thinking in their development of graphing understandings? The project addresses these questions by leveraging a design-based methodology in which we will engage in cycles of intervention and revision to develop, test, and refine cognitive models, constructive itineraries, and instructional tasks. Through several iterations of clinical interviews and small-scale teaching experiments, we intend to produce a theory that explains students’ developing graphing understandings and accounts for their varied ways of thinking. Through this process, we will iteratively design instructional tasks and task sequences that support students developing understandings for frames of reference, coordinate systems, and graphs in the widely used and freely available Desmos platform.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.