Understanding and Overcoming Barriers to Using Mathematics in Science

这个探索性项目解决了一个影响STEM本科生成功的重大国家挑战，即学生学习数学和学生能够有效地使用数学之间的差异。这一领域以前的大部分工作都集中在确定学生的困难上。这个项目将致力于理解这些困难背后的机制。使用数学建模物理系统是所有STEM学科成功的关键组成部分。这个项目将研究那些在大学水平的微积分上取得成功的本科生，因为他们参加了生命科学物理学入门课程。从研究学生理解和不理解以及如何使用数学来建模系统的原因和方式开始，该项目将编织一个与数学建模相关的线索，包括：一套连贯的阅读材料、测验和点击题、家庭作业问题和考试问题，旨在培养学生在各种背景下的建模技能。这将有助于学生理解符号推理的结构及其对他们所选择的职业的价值。这一数学建模思路将在IPLS课程中实施，并评估其对学生在生物学中使用数学能力的影响。该项目的目标是确定学生在生物学背景下应用数学的困难背后的机制，并制作可以帮助他们作为科学家学习有效地使用数学的材料。该研究将结合定性研究（解决问题的访谈和焦点小组解决问题）和定量研究学生对数学建模问题的反应。本研究的主要背景是马里兰大学帕克分校（UMD-CP）开发的NEXUS/物理IPLS课程。它为不同的人群提供服务，其中包括许多在微积分方面取得成功但在科学中使用数学有困难的学生。UMD-CP（一所大型州立赠地机构）的学生将是主要研究对象。另外两个使用NEXUS/物理材料的机构的学生也将被研究：蒙哥马利学院（两年制机构）和斯沃斯莫尔学院（四年制私立机构）。该项目将使用资源框架作为其核心分析结构，部分是在NSF的支持下开发的，以创建高级思维模型。该框架采用动态的知识碎片方法，考虑概念、认识论和情感资源，以及它们如何相互作用，以及如何与学生对其社会文化环境的感知相互作用。它允许一个动态的，细粒度的方法来学生的思维，为理解在科学中使用数学的障碍和指导材料和测试问题的结构提供了具体的工具。它也提供了洞察建模的认知元素和过程，学习在科学中使用数学的复杂主题。这个项目的智力价值在于让学生更深入地了解STEM学生在学习将数学应用于科学时所面临的障碍。这个探索性项目的更广泛的影响是，从研究中学到的东西和项目开发的材料都可以在许多学院和大学的许多STEM课程中使用。

This exploratory project addresses a significant national challenge impacting the success of STEM undergraduates, the difference between students learning mathematics and students being able to use it productively. Much of the previous work in this area has focused on identifying student difficulties. This project will work to understand the mechanisms that underlie these difficulties. Modeling physical systems using mathematics is a critical component of success in all STEM disciplines. This project will study undergraduates who have been successful in college level calculus as they take an Introductory Physics for Life Sciences (IPLS) course. From studying why and how students do and do not understand and use mathematics to model systems, the project will weave a thread related to mathematical modeling to include: a coherent set of readings, quiz and clicker questions, homework problems, and exam questions intended to build students' modeling skills throughout the class in a variety of contexts. This will help students both understand the structure of symbolic reasoning and its value for their chosen careers. This mathematical modeling thread will then be implemented in the IPLS course, and the effect on students' ability to use mathematics in biology will be assessed.The goal of this project is both to identify the mechanisms underlying students' difficulties in applying mathematics in biological contexts and to produce materials that can help them learn to use mathematics productively as scientists. The study will combine qualitative research (problem-solving interviews and focus-group problem-solving) with quantitative studies of student responses to issues in mathematical modeling. The primary context for the study is the NEXUS/Physics IPLS course developed at the University of Maryland College Park (UMD-CP). It serves a diverse population containing many students who have been successful in calculus but have difficulty using mathematics in science. Students at the UMD-CP (a large state land-grant institution) will be the primary subjects. Students at two additional institutions using NEXUS/Physics materials will also be studied: Montgomery College (a two-year institution) and Swarthmore College (a four-year private institution). The project will use as its core analytic structure the Resources Framework, developed in part with prior NSF support, to create models of high-level thinking. This Framework takes a dynamic knowledge-in-pieces approach that considers conceptual, epistemological, and affective resources and how they interact with each other and with the student's perception of their socio-cultural environment. It permits a dynamic, fine-grained approach to student thinking that provides specific tools for understanding the barriers to the use of mathematics in science and for guiding construction of materials and test questions. It also gives insight into modeling the cognitive elements and processes of learning the complex subject of using mathematics in science. The Intellectual Merit of this project is in developing a deeper understanding of the barriers STEM students face in learning to use mathematics in science. The Broader Impact of this exploratory project is that both what is learned by the research and the materials the project develops could be used in many STEM classes in many colleges and universities.