Characterizing mathematical reasoning in the introductory chemistry course: Metamodeling knowledge and its role in students' construction and use of mathematical models

大学化学入门课程是学生在科学、技术、工程和数学（STEM）领域寻求专业和发展进一步理解的关键门户。数学问题的解决是一个关键的挑战，许多化学学生求助于使用数学表达式的算法，很少理解他们使用的方程是如何与分子水平上不可见粒子的化学反应联系起来的。然而，对于科学家和工程师来说，数学模型是重要的预测和解释工具。在化学课程中，帮助学生更好地理解如何建立和使用数学模型是一种很有希望的方法。本项目将设计学习活动，以促进对化学数学模型的理解，并研究学生在大学化学入门课堂中如何运用数学模型进行推理。这项研究的结果有望为提高化学专业学生对数学建模和解决问题的理解，以及他们对其在其他STEM领域应用的理解提供见解。在NSF改善本科STEM教育和EHR核心研究项目的支持下，该项目将设计、实施和调查以数学建模为重点的学习活动整合到爱荷华大学STEM专业普通化学课程中的有效性。合作学习活动将让学生参与开发和测试用于理解化学的数学模型，并将利用科罗拉多大学物理教育技术（PhET）开发的化学模拟等资源，让学生测试和完善他们的模型。学生使用数学模型来帮助解释化学现象的情况将通过半结构化访谈进行评估。访谈还将探讨学生的建模元知识，包括理解模型的经验基础，以及与特定数学模型相关的假设和限制。访谈回答将被分析，以表征学生对本科化学序列中特定模型（如理想气体定律、平衡常数表达式）的理解；2)与这些模型相关的元建模思想；3)基于模型的化学和物理变化解释。学生的解释和推理将在不同的化学主题中进行比较，以检查情境对学生使用模型和建模元知识的影响。这项工作将使研究人员和教师更好地了解学生如何使用核心化学内容知识和对建模的理解来从事科学实践。这些特征还将为开发评估提供基础，使研究人员能够追踪学生在化学课程中基于模型的解释和推理的增长，并最终跨越其他STEM学科。

Introductory college chemistry courses are critical gateways for students seeking to major in and develop further understandings of science, technology, engineering, and mathematics (STEM) fields. Mathematical problem solving is a key challenge, and many chemistry students resort to using mathematical expressions algorithmically, with little understanding of how the equations they use relate to what is happening with the chemistry of invisible particles at the molecular level. Yet mathematical models are important predictive and explanatory tools for scientists and engineers. One promising way to support students' reasoning with mathematics in chemistry courses is to help students better understand how to develop and use mathematical models. This project will design learning activities to promote understanding of mathematical models used in chemistry and study students' reasoning with mathematical models in introductory college chemistry classrooms. Results from this research are expected to provide insights regarding ways to improve chemistry students' understanding of mathematical modeling and problem solving, and their understanding of its applications in other STEM fields.Supported by NSF's Improving Undergraduate STEM Education and EHR Core Research programs, this project will design, implement, and investigate the effectiveness of mathematical modeling-focused learning activities integrated into a general chemistry course for STEM majors at the University of Iowa. The collaborative learning activities will engage students in developing and testing mathematical models used to understand chemistry, and will leverage resources such as chemistry simulations developed by the Physics Education Technology (PhET) at the University of Colorado to allow students to test and refine their models. Students' use of mathematical models to help explain chemical phenomena will be assessed through semi-structured interviews. The interviews will also probe students' meta-knowledge of modeling, which includes understanding the empirical basis of models, and the assumptions and limitations associated with particular mathematical models. Interview responses will be analyzed to characterize students' 1) understandings of specific models in the undergraduate chemistry sequence (e.g., ideal gas law, equilibrium constant expression); 2) metamodeling ideas associated with these models; and 3) model-based explanations of chemical and physical changes. Students' explanations and reasoning will be compared across different chemistry topics to examine the impact of context on students' use of models and meta-knowledge of modeling. This work will provide researchers and instructors with a better understanding of how students use core chemistry content knowledge and understandings of modeling to engage in the practices of science. These characterizations will also provide a basis for developing assessments that will enable researchers to trace growth in students' model-based explanations and reasoning across chemistry courses, and eventually across other STEM disciplines.