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The evolution of an assignment: how a Writing-to-Learn assignment's design shapes organic chemistry students’ elaborations on reaction mechanisms 作业的演变:"从写作到学习 "作业的设计如何影响有机化学学生对反应机理的阐述
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-11-08 DOI: 10.1039/D3RP00197K
Ina Zaimi, Amber J. Dood and Ginger V. Shultz

Asking students to explain why phenomena occur at a molecular level is vital to increasing their understanding of chemistry concepts. One way to elicit students’ mechanistic reasoning and guide construction of knowledge is through Writing-to-Learn (WTL), which is a promising approach for students in organic chemistry courses. In the design of WTL assignments, rhetorical aspects provide an authentic context by designating a role, genre, and audience for students. This context can support students’ learning, but, if the rhetorical aspects misalign with the learning objectives of the assignment, they can hinder students’ ability to achieve these objectives. In this project, we designed a WTL assignment about a base-free Wittig reaction, which we implemented in an organic chemistry laboratory course. Here, we explore how changes in the rhetorical aspects of this assignment can influence the way students explain two different comparisons of reaction mechanisms. We consider how students use explicit and implicit properties and how the use of these features compares within the context of the reaction. Results indicate that, when the rhetorical aspects align with the learning objectives of the assignment, students provide more productive elaborations that use both explicit and implicit properties. This is supported by both the analysis of students’ writing and students’ feedback about the assignments.

要求学生解释为什么会出现分子水平的现象,对提高他们对化学概念的理解至关重 要。激发学生的机械推理并指导知识建构的一种方法是写作学习(WTL),这对有机化学课程的学生来说是一种很有前途的方法。在 WTL 作业的设计中,修辞学方面通过为学生指定角色、体裁和受众来提供真实的情境。这种情境可以支持学生的学习,但是,如果修辞方面与作业的学习目标不一致,就会妨碍学生实现这些目标。在本项目中,我们设计了一个关于无碱维蒂希反应的 WTL 作业,并在有机化学实验课程中实施。在此,我们探讨了这一作业的修辞方面的变化如何影响学生解释两种不同反应机理的方式。我们考虑了学生如何使用显性和隐性特征,以及这些特征在反应上下文中的使用比较。结果表明,当修辞方面与作业的学习目标一致时,学生使用显性和隐性特征进行的阐述更有成效。对学生写作的分析和学生对作业的反馈都证明了这一点。
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引用次数: 0
Use of machine learning to analyze chemistry card sort tasks 利用机器学习分析化学卡片分类任务
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-11-07 DOI: 10.1039/D2RP00029F
Logan Sizemore, Brian Hutchinson and Emily Borda

Education researchers are deeply interested in understanding the way students organize their knowledge. Card sort tasks, which require students to group concepts, are one mechanism to infer a student's organizational strategy. However, the limited resolution of card sort tasks means they necessarily miss some of the nuance in a student's strategy. In this work, we propose new machine learning strategies that leverage a potentially richer source of student thinking: free-form written language justifications associated with student sorts. Using data from a university chemistry card sort task, we use vectorized representations of language and unsupervised learning techniques to generate qualitatively interpretable clusters, which can provide unique insight in how students organize their knowledge. We compared these to machine learning analysis of the students’ sorts themselves. Machine learning-generated clusters revealed different organizational strategies than those built into the task; for example, sorts by difficulty or even discipline. There were also many more categories generated by machine learning for what we would identify as more novice-like sorts and justifications than originally built into the task, suggesting students’ organizational strategies converge when they become more expert-like. Finally, we learned that categories generated by machine learning for students’ justifications did not always match the categories for their sorts, and these cases highlight the need for future research on students’ organizational strategies, both manually and aided by machine learning. In sum, the use of machine learning to analyze results from a card sort task has helped us gain a more nuanced understanding of students’ expertise, and demonstrates a promising tool to add to existing analytic methods for card sorts.

教育研究人员对了解学生组织知识的方式深感兴趣。卡片分类任务要求学生对概念进行分组,是推断学生组织策略的一种机制。然而,卡片分类任务的分辨率有限,这意味着它们必然会忽略学生策略中的一些细微差别。在这项工作中,我们提出了新的机器学习策略,利用潜在的更丰富的学生思维来源:与学生分类相关的自由形式书面语言理由。利用大学化学卡片分类任务的数据,我们使用语言的矢量化表示和无监督学习技术来生成可定性解释的聚类,这可以为学生如何组织知识提供独特的见解。我们将这些聚类与对学生分类本身的机器学习分析进行了比较。机器学习生成的聚类显示了与任务中内置的聚类不同的组织策略;例如,按难度甚至学科分类。此外,机器学习生成的类别中,我们认为新手类的分类和理由比任务中原有的类别要多得多,这表明当学生变得更像专家时,他们的组织策略就会趋于一致。最后,我们还了解到,机器学习为学生的理由所生成的类别并不总是与他们的排序类别相匹配,这些情况凸显了未来研究学生组织策略的必要性,包括人工研究和机器学习辅助研究。总之,使用机器学习来分析卡片分类任务的结果,有助于我们更细致地了解学生的专业知识,并为现有的卡片分类分析方法提供了一个很有前途的工具。
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引用次数: 0
Impact of fill-in-the-nodes concept maps on low prior-knowledge students learning chemistry: a study on the learning achievements and attitude toward concept maps† 填写节点概念图对低先验知识学生学习化学的影响:关于学习成绩和对概念图的态度的研究†
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-11-01 DOI: 10.1039/D3RP00238A
Quan-Thanh Huynh and Yu-Chuan Yang

Numerous studies have proven the learning benefits of concept maps in science subjects, particularly for students with low prior knowledge. There is a scarcity of research dedicated to the examination of chemistry courses at the university level, and the findings pertaining to academic performance in that subject exhibit a lack of consistency. This study examined the impact of concept maps on students of a General Chemistry course who had low prior knowledge. The study applied a quasi-experimental design to collect data on two topics: uncertainties of measurements (Topic 1) and acid–base (Topic 2). Fill-in-the-nodes concept maps were developed and served as learning materials. ANCOVA and Johnson–Neyman techniques were used to analyze the scores of concept tests of Topic 1 and Topic 2, respectively. In both Topics 1 and 2, the results showed that the treatment group outperformed the control group. However, the aforementioned finding was limited to the subset of students whose pre-test scores were below 30.7 out of a total of 47. From the analysis of the attitude questionnaire, the authors concluded that the students appreciated the usefulness of concept maps. However, they might hesitate to engage in using this new learning tool. The study's findings strengthen the evidence of the learning benefits of concept mapping. Moreover, using concept maps in teaching is feasible because of their low cost and minimally invasive modification to instructional design. The practices for implication of concept mapping are also discussed.

许多研究已经证明了概念图对理科学习的益处,尤其是对已有知识较少的学生。但专门针对大学化学课程的研究却很少,而且有关该学科学习成绩的研究结果也缺乏一致性。本研究探讨了概念图对原有知识水平较低的普通化学课程学生的影响。研究采用准实验设计,收集了两个主题的数据:测量的不确定性(主题 1)和酸碱(主题 2)。研究人员绘制了 "填写节点 "概念图,并将其作为学习材料。采用方差分析和约翰逊-奈曼技术分别分析了课题 1 和课题 2 的概念测试得分。结果显示,在课题 1 和课题 2 中,治疗组的成绩均优于对照组。不过,上述结果仅限于 47 名学生中前测得分低于 30.7 分的那部分学生。通过对态度问卷的分析,作者得出结论:学生们赞赏概念图的实用性。但是,他们在使用这种新的学习工具时可能会犹豫不决。研究结果进一步证明了概念图对学习的益处。此外,在教学中使用概念图是可行的,因为概念图成本低,对教学设计的修改微创。研究还讨论了概念图的应用实践。
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引用次数: 0
Chemistry graduate teaching assistants’ teacher noticing 化学研究生助教的教师注意事项
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-30 DOI: 10.1039/D3RP00003F
Eleni K. Geragosian, Diana Zhu, Marc Skriloff and Ginger V. Shultz

Chemistry graduate teaching assistants (GTAs) have substantial facetime with undergraduate students at large research institutions where they lead discussion and lab sessions. Emerging research describes GTAs’ content and teaching knowledge for introductory chemistry classes, but we need to know more about how GTAs manage their classes in the moment and how they assess student learning during class time. We conducted classroom observations and post-observation interviews with six chemistry GTAs with various years of teaching experience and who were teaching a variety of classes (e.g., general chemistry discussion, biochemistry discussion, organic chemistry lab, computational chemistry lab, and more). These GTAs were each observed and interviewed multiple times over the course of a semester. Through qualitative analysis guided by the teacher noticing framework, we describe what chemistry GTAs notice, or pay attention to, regarding student learning in their teaching sessions and how they interpret what they notice. We found that chemistry GTAs often paid attention to the types of questions that students asked but relied on their students to take initiative to ask questions in order to assess their learning. Also, GTAs often focused on superficial features of their class sessions to assess learning, like whether students finished their tasks and left their session early. However, some GTAs noticed more sophisticated evidence of student understanding, such as when students connected content covered across multiple class sessions. The results from this study contribute to our understanding of how chemistry GTAs lead their sessions and evaluate student learning during their sessions. Results serve to inform potential training designs that can support chemistry GTAs’ teacher learning through learning to notice—and to create opportunities to notice—significant features of their classrooms.

在大型研究机构中,化学研究生助教(GTAs)与本科生有大量的接触时间,他们主持讨论和实验课。新近的研究描述了研究生助教在化学入门课程中的教学内容和教学知识,但我们需要更多了解研究生助教如何在课堂上管理课堂,以及他们如何在课堂上评估学生的学习情况。我们对六位有不同年限教学经验、教授不同课程(如普通化学讨论、生物化学讨论、有机化学实验、计算化学实验等)的化学GTA进行了课堂观察和观察后访谈。在一个学期中,我们对这些 GTA 进行了多次观察和访谈。通过以教师注意框架为指导的定性分析,我们描述了化学高级教师在教学过程中对学生学习的注意点或关注点,以及他们如何解释自己的注意点。我们发现,化学高级教师通常会关注学生提出的问题类型,但依赖学生主动提问来评估他们的学习情况。此外,一般教师往往关注课堂教学的表面特征来评估学生的学习情况,如学生是否完成任务和提前离场。然而,一些一般教师注意到了学生理解能力的更复杂的证据,比如学生将多节课所涉及的内容联系起来。本研究的结果有助于我们了解化学高级教师如何引导他们的课程并在课程中评估学生的学习情况。研究结果为潜在的培训设计提供了参考,这些设计可以支持化学高级教师通过学习注意到--以及创造机会注意到--课堂的重要特征来进行教师学习。
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引用次数: 0
Investigating evidence in support of validity and reliability for data collected with the meaningful learning in the laboratory instrument (MLLI)† 调查使用实验室有意义学习工具(MLLI)收集的数据的有效性和可靠性证据†。
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-27 DOI: 10.1039/D3RP00121K
Elizabeth B. Vaughan, A. Montoya-Cowan and Jack Barbera

The Meaningful Learning in the Laboratory Instrument (MLLI) was designed to measure students’ expectations before and after their laboratory courses and experiences. Although the MLLI has been used in various studies and laboratory environments to investigate students’ cognitive and affective laboratory expectations, the authors of the instrument reported a discrepancy between the intended factor structure of the MLLI and the factor structure suggested by the data collected in preliminary studies. Therefore, the aim of this study was to investigate the validity and reliability evidence related to data collected with the MLLI, especially that related to structural validity. Evidence to support structural validity would provide greater meaning for the reporting and interpretation of MLLI scores. In this study, two possible a priori models for the factor structure of data collected from multiple institutions with the MLLI were investigated using confirmatory factory analysis (CFA). This initial investigation found poor data-model fit for each of the two tested models. Cognitive interviews and free response items were then used to inform modifications to the two a priori structures, and a third alternative structure, which included a negative method factor, was also investigated. Once a best fitting model was identified, further model revisions were informed by a combination of modification indices and qualitative data. Evidence of adequate-to-good data model fit was found for the final revised version of the MLLI, deemed the MLLIv2. Additionally, evidence of both internal structure validity and single administration reliability were found for each of the MLLIv2 factors. The structure of the data from these items leads to scale scores that likely represent student expectations that contribute to meaningful learning and student expectations that detract from meaningful learning. As the results of this study provide the first psychometrically supported scales for MLLI data, they have implications on the future reporting and analyses of MLLI scores.

实验室有意义学习工具(MLLI)旨在测量学生在实验课程和实验经历前后的期望。尽管 "实验室有意义学习量表 "已被用于各种研究和实验室环境,以调查学生的认知和情感实验室期望,但该量表的作者报告说,"实验室有意义学习量表 "的预期因子结构与初步研究中收集的数据所显示的因子结构之间存在差异。因此,本研究的目的是调查通过 MLLI 收集到的数据的有效性和可靠性证据,特别是与结构有效性相关的证据。支持结构效度的证据将为 MLLI 分数的报告和解释提供更大的意义。在本研究中,我们使用确证工厂分析法(CFA)研究了从多个机构收集的 MLLI 数据的两个可能的先验因素结构模型。初步调查发现,两个测试模型的数据模型拟合度较差。随后,我们利用认知访谈和自由回答项目对这两个先验结构进行了修改,并研究了第三个替代结构,其中包括一个负方法因子。一旦确定了最佳拟合模型,就会结合修正指数和定性数据对模型进行进一步修正。有证据表明,最终修订版的 MLLI(MLLIv2)的数据模型拟合度足够好。此外,MLLIv2 的每个因子都有内部结构有效性和单次施测可靠性的证据。从这些项目的数据结构中得出的量表分数很可能代表了有助于有意义学习的学生期望和有损于有意义学习的学生期望。由于本研究的结果为 MLLI 数据提供了第一个心理测量学支持的量表,它们对未来 MLLI 分数的报告和分析具有重要意义。
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引用次数: 0
A design-based research approach to improving pedagogy in the teaching laboratory 采用基于设计的研究方法改进实验室教学法
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-18 DOI: 10.1039/D3RP00134B
Christine E. Mundy, Marietjie Potgieter and Michael K. Seery

The laboratory is a complex environment where the three levels of the chemistry triplet coincide. As the laboratory environment places a large demand on the working memory of students, cognitive load theory can address overload which causes barriers to learning. Breaking down barriers requires iterative phases of analysis/exploration, design/construction and evaluation/reflection over multiple cycles which are the hallmarks of design-based research. In a complex setting, managing change and redressing teaching approaches can be difficult to navigate. Design-based research incorporates iterative phases in which theory informs decision making. This paper uses the context of a laboratory exercise of emission spectra to illustrate how the cognitive load theory can be used in tandem with design-based research to support student learning in the exercise. Using this approach, it was possible to show how barriers to student understanding, including task demands and conceptual demands were supported through proposed approaches focusing on extraneous, intrinsic and ultimately germane cognitive load.

实验室是一个复杂的环境,化学三要素的三个层次在这里同时出现。由于实验室环境对学生的工作记忆要求很高,认知负荷理论可以解决造成学习障碍的超负荷问题。要打破障碍,就需要在多个周期内反复进行分析/探索、设计/构建和评估/反思,这也是以设计为基础的研究的特点。在复杂的环境中,管理变革和纠正教学方法可能难以驾驭。基于设计的研究包含迭代阶段,在这些阶段中,理论为决策提供依据。本文以发射光谱的实验室练习为背景,说明认知负荷理论如何与基于设计的研究相结合,以支持学生在练习中的学习。利用这种方法,可以说明如何通过建议的方法支持学生的理解障碍,包括任务要求和概念要求,这些方法的重点是外在的、内在的以及最终与之相关的认知负荷。
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引用次数: 0
Making sense of chemical equilibrium: productive teacher–student dialogues as a balancing act between sensemaking and managing tension† 化学平衡的意义:师生对话是感性认识和管理紧张关系之间的平衡之举†。
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-17 DOI: 10.1039/D3RP00249G
Ylva Hamnell-Pamment

Navigating the observational, symbolic, and theoretical knowledge domains of chemistry is crucial for chemistry sensemaking. However, this has been shown to be particularly challenging for students of chemistry. In order to reach government standards for sensemaking in the chemistry subject, it is important to investigate how chemistry teachers can sustain sensemaking practices in their classrooms. In this study, conversation analysis was used to study videotaped teacher–student dialogues at upper secondary school practical lessons in chemical equilibrium. Common patterns in how sensemaking was produced in interaction were found in four experienced chemistry teachers’ sensemaking dialogues with students. The data show how the teachers use coordinated actions in conversations to create a balance between (1) managing sensemaking dialogues in the laboratory classroom on a moment-to-moment basis through connecting theory and experience, and (2) managing the tension between exposing students’ knowledge gaps and presenting the students as competent as part of the interaction. The results of the study indicate that resolving tension in interaction is an important part of teacher–student sensemaking in chemistry, and also identify the chemical equation as a possible tool for sensemaking progression. The detailed examples of teacher–student sensemaking can be used as models for chemistry teachers interested in how sensemaking can be achieved practically.

浏览化学的观察、符号和理论知识领域对于化学感性认识至关重要。然而,这对学习化学的学生来说尤其具有挑战性。为了达到政府对化学学科感性认识的标准,研究化学教师如何在课堂上维持感性认识的实践是非常重要的。本研究采用对话分析法,研究高中化学平衡实践课上师生对话的录像。在四位经验丰富的化学教师与学生的感性认识对话中,发现了在互动中如何产生感性认识的共同模式。数据显示了教师如何在对话中使用协调行动,在以下两个方面取得平衡:(1) 通过将理论与经验联系起来,在实验课堂上时刻管理感性认识对话;(2) 在互动过程中,管理暴露学生知识差距与展示学生能力之间的矛盾。研究结果表明,化解互动中的紧张关系是师生化学感性认识的重要组成部分,同时也确定了化学方程式是感性认识进展的可能工具。师生建立感性认识的详细实例可作为化学教师的范例,供有兴趣了解如何切实建立感性认识的化学教师参考。
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引用次数: 0
Progression from Chinese High School onto a TransNational Chinese-UK University joint BSc degree in chemistry; an international study focussing on laboratory practical skills 从中国高中升入跨国中英大学化学联合理学士学位;侧重于实验室实践技能的国际研究
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-16 DOI: 10.1039/D3RP00099K
Julie Hyde, James S. Wright and Andi Xie

An investigation was carried out into laboratory practical skills development and students’ specific challenges in transition from laboratory chemistry at Chinese High School (HS) to a fully English style university laboratory course. To the best of our knowledge this is the first study of its type investigating practical laboratory skills for a TransNational Education (TNE) Chemistry BSc (3 + 1) degree programme between the United Kingdom (UK) and the People's Republic of China (PRC). Internationalization of such courses have become popular in recent years. The two universities in this study are Nanjing Tech University (NJTech) and the University of Sheffield (UoS). Our study is exploratory with the aim to determine the level of practical laboratory skills the NJTech students gained from High School and the challenges they encountered as they joined a UK degree laboratory programme delivered in English. For this international study, a mixed-methods approach was followed using qualitative inductive and deductive methodologies. Using open-ended questions it was found that particular challenges in the transition were around the lack of prior laboratory experience and the development of many new skills, laboratory notebook documentation, laboratory safety, and studying laboratory chemistry in a second language. Students welcomed these challenges and felt they were developing into professional chemists. Specific recommendations are made for international TNE degrees with laboratory programmes, particularly for those students who progress from Chinese High School through the Chinese GaoKao system into a western university chemistry laboratory programme. The scaffolded/structured curriculum design allowed for total and successful integration of the NJTech with the Sheffield home students during the final year of their BSc in Chemistry. After graduation, having gained high class degrees and becoming fluent in English many of the students progressed into Industry, and onto Masters or PhD programmes in the UK and throughout the world, suggesting internationalisation of students on our TNE programme was successful.

在从中国高中化学实验课程过渡到全英文的大学实验课程的过程中,我们对实验实践技能的培养和学生所面临的具体挑战进行了调查。据我们所知,这是首次在英国(UK)和中华人民共和国(PRC)之间开展的跨国教育(TNE)化学学士(3 + 1)学位课程的实验室实践技能调查研究。近年来,此类课程的国际化已成为一种流行趋势。本研究中的两所大学是南京理工大学(NJTech)和谢菲尔德大学(UoS)。我们的研究是探索性的,旨在确定南京理工大学的学生从高中获得的实际实验技能水平,以及他们在参加以英语授课的英国学位实验课程时遇到的挑战。在这项国际研究中,我们采用了一种混合方法,即定性归纳法和演绎法。通过开放式提问,我们发现学生在过渡时期所面临的特殊挑战主要集中在缺乏实验经验、许多新技能的开发、实验笔记本的记录、实验室安全以及用第二语言学习实验化学等方面。学生们对这些挑战表示欢迎,并认为他们正在成长为专业化学家。本报告对开设实验课程的国际 TNE 学位提出了具体建议,特别是针对那些从中国高中通过中国高考制度升入西方大学化学实验课程的学生。通过支架式/结构化的课程设计,南京理工大学的学生在化学学士学位的最后一年成功地与谢菲尔德的本土学生完全融合。毕业后,许多学生获得了高级学位,并能说一口流利的英语,进入了英国和世界各地的工业界、硕士或博士课程,这表明我们的 TNE 课程成功地实现了学生的国际化。
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引用次数: 0
Exploring relationships that college instructors seek to build with intention in chemistry classrooms 探究大学教师在化学课堂上努力建立的意向关系
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-13 DOI: 10.1039/D3RP00198A
Patricia Moreira and Vicente Talanquer

Teaching is a complex activity that demands paying attention to diverse components and relationships that affect the learning process, and acting with intentionality to build and nurture those connections. In this qualitative research study, we proposed and used an intentional–relational framework to explore differences in the relationships that four general chemistry instructors sought and acted to build with intention in their classes. Our goal was not to evaluate the quality of instruction but rather to characterize instructors’ practices to gain insight into educational relationships that may affect student performance. All instructors in our sample manifested a strong interest in helping students succeed in their studies and relied on a variety of resources designed and integrated into their courses to support student learning. They mostly differed in the extent to which they attended and responded to contextual issues, intentionally seeking to make content relevant to students, helping them build connections between their interests and the discipline, and adapting resources to create more inclusive learning environments. These differences seem to affect student performance in common exams. Our study highlights the importance of analyzing the relationships that instructors build with intention to support professional development and teacher reflection, and better understand the impact of instructors’ decisions on student performance.

教学是一项复杂的活动,需要关注影响学习过程的各种因素和关系,并有意识地建立和培养这些联系。在这项定性研究中,我们提出并使用了一个 "意向-关系 "框架,以探索四位普通化学教师在课堂上有意识地寻求和建立的关系的差异。我们的目标不是评估教学质量,而是描述教师的做法,以深入了解可能影响学生成绩的教育关系。在我们的样本中,所有教师都表现出了帮助学生学业成功的强烈兴趣,并依靠设计和整合到课程中的各种资源来支持学生的学习。他们在关注和应对情境问题、有意识地使教学内容与学生相关、帮助学生建立兴趣与学科之间的联系以及调整资源以创造更具包容性的学习环境等方面的程度大多有所不同。这些差异似乎会影响学生在统一考试中的成绩。我们的研究强调了分析教师与学生之间建立的关系的重要性,以支持教师的专业发展和反思,并更好地了解教师的决定对学生成绩的影响。
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引用次数: 0
How much is just maths? Investigating problem solving in chemical kinetics at the interface of chemistry and mathematics through the development of an extended mathematical modelling cycle 有多少只是数学?通过开发一个扩展的数学建模循环,在化学与数学的交界处研究化学动力学的问题解决方法
IF 3 2区 教育学 Q1 Social Sciences Pub Date : 2023-10-10 DOI: 10.1039/D3RP00168G
Sofie Ye, Maja Elmgren, Magnus Jacobsson and Felix M. Ho

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

化学动力学问题的解决给大学生带来了巨大的挑战,因为它往往需要大量使用数学作 为工具和语言,而且化学现象和数学表征之间的转换和过渡也极具挑战性。在本文中,我们将介绍一项研究的主要发现,该研究调查了化学专业学生围绕稳态近似解 决任务的情况。在数学建模循环(MMC)的基础上,通过对使用 "思考-大声说 "协议收集到的数据进行定性分析,我们开发出了扩展的数学建模循环。这个根据经验得出的扩展数学建模周期对化学现象的数学建模过程进行了更详细的说明,突出了在整个建模周期中出现的审议和评估等方面,以及在解决问题过程中数学外资源的不同特点、激活点和作用。我们进一步引入并使用问题解决轨迹作为工具,对学生在尝试解决问题的过程中所使用的复杂多样的方法进行可视化分析。总之,扩展的多变量模型为学生的认知和元认知活动提供了一个更精细的模型,为研究和实践提供了更多的启示。
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