Leveraging Dynamically Linked Representations in a Semi-Structured Workspace to Cultivate Mathematical Modeling Competencies Among Secondary Students (M2Studio)

数学建模可以帮助人们理解与现实世界现象相关的复杂和关键的未解问题。例如，数学建模可以帮助确定传染病传播的速度，干预措施如何限制传播，以及海平面变化如何影响沿海人口和生态系统。虽然教育工作者和政策制定者认识到数学建模在K-12教育中的重要性，但建模和建模任务的复杂性往往会给课堂实施带来障碍。这样的任务是复杂的，开放式的，并且需要迭代思考和多种数学表示的协调。这个为期三年的设计和开发项目旨在建立一个半结构化的工作场所，以支持学生的数学建模能力，称为M2Studio。该技术将两种现有且广泛使用的技术（CODAP和SageModeler）的各个方面集成到一个工作空间中，该工作空间可以有效地捕获学生的活动、表示、解决问题的序列，以及他们单独或成对地处理数学建模任务时的思考。该项目将在五个设计周期中开发M2Studio的各个方面，研究学生参与和通过平台学习的情况，并从教师那里收集有关M2Studio实施特别有效的条件的数据。该项目建立在数学建模的理论概念化基础上，该模型涉及五个子能力：简化、数学化、数学化、解释和验证。在构建M2Studio和动态连接CODAP和SageModeler的过程中，该系统将提供机会，能够评估学生参与这些子能力的方式。该项目将分为五个设计周期，设计技术和相关课程模块，在学生和教师中部署和测试技术，并评估对学生数学建模能力的影响。前两个设计周期将侧重于技术开发和由4名教师和16名学生进行的简短的现场实验室测试。设计周期3和4将涉及8名教师和400名学生的两次实地测试。第五个设计周期将涉及实施研究，以进一步探索研究问题。学生的学习将通过数学建模次级能力测试进行评估。学生的互动模式将通过对截屏和课堂视频的定性分析来评估。在课堂实施方面，项目是否有效的条件将通过观察、访谈和实施教师的日志来衡量。该平台的最终版本将在各种K-16数学建模社区中托管并广泛提供。探索研究preK-12项目（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学生和教师对科学、技术、工程和数学（STEM）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实证依据。该项目由“面向学生和教师的创新技术体验”（ITEST）项目共同资助，该项目支持有助于提高学生对科学、技术、工程和数学（STEM）以及信息和通信技术（ICT）职业的知识和兴趣的实践、项目要素、背景和过程的理解。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。

Mathematical modeling can support people in making sense of complex and critical unanswered questions related to real-world phenomena. For example, mathematical modeling can help determine the speed at which an infectious disease will spread, how interventions can limit the spread, and how sea level change can impact coastal populations and ecosystems. While educators and policymakers recognize the importance of mathematical modeling in K-12 education, the complexities of modeling and modeling tasks often create barriers for classroom implementation. Such tasks are complex, open-ended, and require iterative thinking and the coordination of multiple mathematical representations. This three-year Design and Development project seeks to build a semi-structured workplace to support students' mathematical modeling competencies called M2Studio. This technology integrates aspects of two existing and widely used technologies (CODAP and SageModeler) into a single workspace that can effectively capture students' activities, representations, problem solving sequences, and thinking as they work individually or in pairs on mathematical modeling tasks. The project will develop aspects of M2Studio across five design cycles, study student engagement and learning via the platform, and collect data from teachers on the conditions under which M2Studio implementation is particularly effective. The project builds on a theoretical conceptualization of mathematical modeling that involves five sub competencies: simplifying, mathematizing, working mathematically, interpreting, and validating. In building the M2Studio and dynamically linking the CODAP and SageModeler, the system will provide opportunities to be able to assess the ways in which students are engaging in these sub competencies. The project will engage in five design cycles to design the technology and associated curricular modules, deploy and test the technologies with students and teachers, and assess the impact on students' mathematical modeling competencies. The first two design cycles will focus on technology development and short in-person lab tests with 4 teachers and 16 students. Design Cycles 3 and 4 will involve two field tests with 8 teachers and 400 students. The fifth design cycle will involve an implementation study to further explore the research questions. Student learning will be assessed via a mathematical modeling sub-competencies test. Student interaction patterns will be evaluated through the qualitative analysis of screencast and classroom videos. The conditions under which the program is more or less effective with respect to classroom implementation will be measured by observations, interviews, and logs from implementing teachers. The final version of the platform will be hosted and made available widely in various K-16 mathematical modeling communities.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 project is co-funded by the Innovative Technology Experiences for Students and Teachers (ITEST) program, which supports projects that build understandings of practices, program elements, contexts and processes contributing to increasing students' knowledge and interest in science, technology, engineering, and mathematics (STEM) and information and communication technology (ICT) careers.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.