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，理解图形表示对学生在STEM领域取得成功至关重要。然而，研究表明，许多学生努力发展图形表示的理解。我们认为，学生对坐标系的理解，需要构建和解释图形的理解，是他们理解图形表示的斗争的基础，而且，为发展这种理解奠定了必要的基础。在这个项目中，我们先考察中学生对坐标系和参照系的理解，然后再考察他们的图形构造和解释。这一重点使我们能够设计教学材料，可以支持学生的图形理解的方式，避免或减轻如何持久的挑战，在学生的图形理解中确定的研究文献。本项目的总体目标是推进知识的中学生发展的图形理解“从地面上”注意基础坐标系和包括坐标系的参考系。三个研究问题指导该项目：（一）是什么样的思维方式，通过这些学生个人创建和解释参考框架，坐标系和图形？(ii)学生们是如何发展这些思维方式的？(iii)什么样的教学任务序列支持和建立在学生的各种思维方式在他们的发展图形的理解？该项目通过利用基于设计的方法来解决这些问题，在这种方法中，我们将参与干预和修改的周期，以开发，测试和完善认知模型，建设性的行程和教学任务。通过临床访谈和小规模教学实验的几次迭代，我们打算产生一个理论，解释学生的发展图形的理解，并占他们不同的思维方式。通过这个过程，我们将迭代设计教学任务和任务序列，支持学生在广泛使用和免费提供的Desmos平台中发展对参考框架，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。

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.