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

化学入门课程中数学推理的特征：元建模知识及其在学生构建和使用数学模型中的作用

• 批准号: 1611622
• 负责人: Nicole Becker
• 金额: $ 29.97万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1611622&HistoricalAwards=false
• 关键词: Characterizing; mathematical; reasoning; introductory; chemistry

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.

介绍性大学化学课程是学生寻求主修和发展科学，技术，工程和数学（STEM）领域的进一步理解的关键门户。解决数学问题是一个关键的挑战，许多化学专业的学生诉诸于使用数学表达式的算法，很少了解他们使用的方程如何与分子水平上的不可见粒子的化学反应有关。然而，数学模型是科学家和工程师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支持学生进行数学推理的一个很有前途的方法。本研究将设计学习活动，以促进学生对化学中使用的数学模型的理解，并在大学化学入门课堂上研究学生使用数学模型的推理。本研究的结果有望为提高化学专业学生对数学建模和问题解决的理解，以及对数学建模和问题解决在其他STEM领域应用的理解提供见解。在NSF的改善本科STEM教育和EHR核心研究计划的支持下，本项目将设计，实施，并调查了爱荷华州大学STEM专业的普通化学课程中融入以数学建模为重点的学习活动的有效性。协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将通过半结构化面试进行评估。访谈还将探讨学生的建模元知识，其中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。面试回答将被分析，以表征学生的1）在本科化学序列的特定模型的理解（例如，理想气体定律，平衡常数表达式）; 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进行比较，以检查上下文对学生使用模型和建模元知识的影响。这项工作将为研究人员和教师提供更好地了解学生如何使用核心化学内容知识和建模的理解，从事科学实践。这些特征也将为开发评估提供基础，使研究人员能够跟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。

项目成果

Supporting Engagement in Metamodeling Ideas in General Chemistry: Development and Validation of Activities Designed Using Process Oriented Guided Inquiry Learning Criteria

支持参与普通化学中的元建模思想：使用面向过程的引导探究学习标准设计的活动的开发和验证

• DOI: 10.1021/acs.jchemed.0c00321
• 发表时间: 2020
• 期刊: Journal of Chemical Education
• 影响因子: 3
• 作者: Rodriguez, Jon-Marc G.;Lazenby, Katherine;Scharlott, Leah J.;Hunter, Kevin H.;Becker, Nicole M.
• 通讯作者: Becker, Nicole M.

Mapping undergraduate chemistry students' epistemic ideas about models and modeling

绘制本科化学学生关于模型和建模的认知想法

• DOI: 10.1002/tea.21614
• 发表时间: 2019
• 期刊: Journal of Research in Science Teaching
• 影响因子: 4.6
• 作者: Lazenby, Katherine;Stricker, Avery;Brandriet, Alexandra;Rupp, Charlie A.;Mauger‐Sonnek, Kathryn;Becker, Nicole M.
• 通讯作者: Becker, Nicole M.

Undergraduate Chemistry Students’ Epistemic Criteria for Scientific Models

本科化学学生科学模型的认知标准

• DOI: 10.1021/acs.jchemed.9b00505
• 发表时间: 2019
• 期刊: Journal of Chemical Education
• 影响因子: 3
• 作者: Lazenby, Katherine;Stricker, Avery;Brandriet, Alexandra;Rupp, Charlie A.;Becker, Nicole M.
• 通讯作者: Becker, Nicole M.

Undergraduate Chemistry Students’ Conceptualization of Models in General Chemistry

本科化学学生——普通化学模型的概念化

• DOI: 10.1021/acs.jchemed.8b00813
• 发表时间: 2019
• 期刊: Journal of Chemical Education
• 影响因子: 3
• 作者: Lazenby, Katherine;Rupp, Charlie A.;Brandriet, Alexandra;Mauger-Sonnek, Kathryn;Becker, Nicole M.
• 通讯作者: Becker, Nicole M.