Making Sense of Models: Investigating Mechanistic Reasoning as a Bridge for Connecting 6th Grade Mathematics and Science Learning

这个项目解决了以下实践问题：中学科学教师发现他们不得不重新教授数学概念，为学生在科学课堂上使用和分析科学现象的计算机模型做好准备，这占用了大量的教学时间。他们中的一些人发现，学生不知道为什么数学是有用的，以及如何将其应用于科学背景。建模也成为《数学共同核心国家标准》和《下一代科学标准》中日益强调的组成部分。这个项目将通过在适合六年级数学和科学课程的基于代理的建模环境中关注机械推理来解决这些问题。机械论推理包括创建实体和理解产生结束状态或状态变化的交互，并解释某事如何工作或产生现象以及为什么。该项目的研究部分将填补计算思维(CT)集成文献的空白，通过调查编程解决数学问题如何同时强化数学概念并为学生进行科学建模做好准备。此外，该项目将：支持未被充分代表的群体参与数学、计算机科学和科学建模；有助于打破中学内部孤立的学科；通过共同设计跨越数学和科学课堂的多学科课程，加强研究和教育的基础设施；开发课程，为学生未来在STEM和CT的努力做准备。该项目将开发和实施一个多学科CT项目，利用计算机建模活动，形成连接学校日常数学和科学学习的桥梁。三个学区的六年级学生和他们的老师将学习在数学课堂上使用CT和机械推理，然后在科学课堂上应用这些技能来解码和修改科学模型。该项目的研究目标如下：(1)进行基于设计的研究周期，为六年级学生开发数学和科学CT课程；(2)开发、测试和完善为期一年的教师专业发展计划，以支持教师学习和实施综合课程；以及(3)进行混合方法研究，探讨综合课程对学生学习的影响，教师和学生对数学和CT的认知，以及机械推理在CT中的作用。该项目将采用教师和项目团队之间的设计协作，为讲习班、教师专业发展和教师促进模式的发展提供支持。一个准实验研究和案例研究将被用来检验这一假设，即机械推理是一项必要的技能，使学生在创建计算人工制品时能够将抽象和自动化联系起来，并在解码计算模型时进行分析。该项目由STEM计算计划资助，该计划旨在研究在从高中到幼儿教育的STEM学科教与学中计算思维和计算的应用集成。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。

This project addresses the following problem of practice: Middle school science teachers find that they have to reteach mathematics concepts to prepare their students to use and analyze computer models of scientific phenomena in their science classes, which takes some significant time away from instruction. Some of them find that students do not know why mathematics is useful and how it can be applied in science contexts. Modeling has also become an increasingly emphasized component of both the Common Core State Standards in Mathematics and the Next Generation Science Standards. This project will address these concerns by focusing on mechanistic reasoning in an agent-based modeling environment appropriate for 6th grade mathematics and science classes. Mechanistic reasoning involves creating entities and understanding interactions that produce an end state or change of state and explain how and why something works or generates a phenomenon. The research component of the project will fill a gap in computational thinking (CT) integration literature by investigating how programing solutions to mathematical problems can simultaneously reinforce mathematical concepts and prepare students for scientific modeling. Furthermore, the project will: support the participation of underrepresented groups in mathematics, computer science, and scientific modeling; contribute to breaking down of siloed disciplines within middle school; enhance infrastructure for research and education through the co-design of multidisciplinary curriculum spanning math and science classrooms; and develop a curriculum that prepares students for future endeavors in STEM and CT.The project will develop and implement a multidisciplinary CT program that uses computer modeling activities to form a bridge that connects regular school day mathematics and science learning. Sixth grade students and their teachers in three districts will learn to use CT and mechanistic reasoning in mathematics classes and then apply those skills in decoding and modifying scientific models in science classes. The research objectives of the project are as follows: (1) Conduct design-based research cycles to develop a math and science CT curriculum for 6th grade students; (2) Develop, test and refine a year-long teacher professional development program that supports teacher learning and implementation of the integrated curriculum; and (3) Conduct a mixed-methods study on the impact of the integrated curriculum on student learning, teacher and student perception of math and CT, and the role of mechanistic reasoning in CT. The project will employ a design collaborative between teachers and the project team, which will provide support for the workshops, teacher professional development, and the development of a teacher facilitation model. A quasi-experimental study and case studies will be used to test the hypothesis that mechanistic reasoning is a necessary skill that enables students to link abstraction and automation when they create computational artifacts and engage in analysis when they decode computational models.The project is funded by the STEM + Computing Program, which seeks to study the applied integration of computational thinking and computing within disciplinary STEM teaching and learning in early childhood education through high school.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.