Mathematical Modeling Cycles as a Task Design Heuristic
Mathematical Modeling Cycles as a Task Design Heuristic
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作为任务设计启发式的数学建模周期
DOI：
10.54870/1551-3440.1391
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
J. Czocher
中科院分区：
文献类型：
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作者：
J. Czocher
由于有许多关于建模的理论观点（Srilliant，Kaiser，& Blomhoj，2006）-并且对于数学建模的定义没有共识（Cai等人，2014）-数学建模的评估往往是临时的或基于经验，而不是理论上的基础（Frejd，2013）。因此，本研究试图利用建模任务设计原则，以生成能唤起学生数学建模过程的任务。通常在研究报告中，尽管所有数据、结果、解释和结论都来自仪器，因此取决于仪器的起源，但仪器开发的空间最小。本文试图使透明的考虑和决定，目前在一个研究人员的日志，但通常是从结果的传播削减。然后我用这些想法来反思特定领域的建模周期理论和用于设计任务的方法。理论观点设置任务设计项目基兰，多尔曼，大谷（2015）回顾了数学教育研究中的任务设计原则。审查围绕两个方面进行。第一个维度是理论的范围，告知研究目标（大的，中间的，或特定领域），第二个是设计是否可以被描述为设计作为实施或设计作为意图。设计即实施研究关注的是“一个设计的序列被整合到课堂环境中并随后逐步完善的过程”（Kieran等人，2015年，第28页）。这与如何理解设计研究项目是一致的（Cobb，Confrey，DiSessa，Lehrer，& Schauble，2003）。相比之下，设计作为意图的研究“解决了设计的初始表述”，并使用了完善的理论框架，以提供意图的清晰度和连贯性（Kieran等人，2015年，第28页）。大的理论框架一般解释学习（例如，认知建构主义或社会建构主义理论）。中级框架可以应用于许多数学领域和领域（例如，教学情境理论）。最后，领域特定框架指定推理过程（例如，建模或建模）或内容（例如，使用Kieren et al.的维度，我可以使用特定领域的理论将这个任务设计项目描述为设计即意图。该研究计划的目标是从数学建模范式中研究数学思维。参加者是修读微分方程课程的工程系本科生。这个项目的一个子目标是创建一个观察性的规则，可以用来系统地观察学生的建模活动，因为它展开。因此，采用了与数学建模过程相关的特定领域理论。在一对一的面试环境中，通过对学生建模任务的微观分析来指导该规则的创建。这需要一种设计研究能够处理的“自举”方法（DiSessa，Cobb，& Disessa，2004，p. 85）。任务和题目是通过基于学生数学建模的迭代设计过程开发的。通过对学生在任务上的工作进行定性分析来开发标题的方法在其他地方介绍（Czocher，2016）。设计的任务需要满足特定的意图，即唤起学生的建模过程，以便这些过程可以系统地记录下来。设计任务的目的不是为了直接衡量学生的能力，也不是为了教授建模。相反，这是一种尝试，以研究和更详细地解释组成部分的数学建模确定的文献作为中央的数学建模过程或困难的学生。…
Since there are many theoretical perspectives on modeling (Sriraman, Kaiser, & Blomhoj, 2006) - and no consensus as to a definition of mathematical modeling (Cai et al., 2014) -assessments of mathematical modeling tend to be ad hoc or based on experience rather than theoretically grounded (Frejd, 2013). Therefore, the research presented here sought to take advantage of modeling task design principles in order to generate tasks that would evoke students' mathematical modeling processes. Typically in research reports, the smallest amount of space is accorded to instrument development despite the fact that all data, results, interpretations, and conclusions are derived from the instrument and therefore dependent upon its genesis. This paper attempts to make transparent the considerations and decisions that are present in a researcher's logs but that typically are cut from the dissemination of results. I then use these ideas to reflect on the domain-specific theory of modeling cycles and the methods used to design the tasks.Theoretical PerspectivesSituating the Task Design ProjectKieran, Doorman, and Ohtani (2015) reviewed of sets of principles for task design in mathematics education studies. The review was organized around two dimensions. The first dimension was the scope of the theory informing the research objectives (grand, intermediate, or domain-specific) and the second was whether the design could be characterized as design as implementation or design as intention. Design as implementation studies focus attention on "the process by which a designed sequence is integrated into the classroom environment and subsequently is progressively refined" (Kieran et al., 2015, p. 28). This is consistent with how design research projects are understood(Cobb, Confrey, DiSessa, Lehrer, & Schauble, 2003). In contrast, design as intention studies "address the initial formulation of the design" and use well developed theoretical frames in order to provide clarity and coherence to the intention (Kieran et al., 2015, p. 28). Grand theoretical frames explain learning in general (e.g., cognitive constructivist or social constructivist theories). Intermediate-level frames can be applied across many mathematical areas and domains (e.g., theory of didactical situations). Finally, domain-specific frames specify reasoning processes (e.g., conjecturing or modeling) or content (e.g., place value, geometry).Using Kieren et al.'s dimensions, I can situate this task design project as design as intention using a domain-specific theory. The objective of the research program was to study mathematical thinking from within a mathematical modeling paradigm. The participants were to be undergraduate engineering students in a course on differential equations. One sub goal of this project was to create an observational rubric that could be used to systematically observe students' modeling activity as it unfolded. Thus, domain-specific theories related to mathematical modeling processes were adopted. The creation of the rubric was to be guided by microanalysis of students' work on modeling tasks within a one-on-one interview setting. This required a "bootstrapping" approach that design studies are able to handle (DiSessa, Cobb, & Disessa,2004, p. 85). The tasks and the rubric were developed through an iterative design process grounded in the students' mathematical modeling. The development of the rubric through qualitative analysis of the students' work on the tasks is presented elsewhere (Czocher, 2016).The tasks designed needed to satisfy a particular intention, namely, evoking students' modeling processes so that those processes could be documented systematically. The goal in designing the tasks was not to create a direct measure of students' competencies nor to teach modeling. Instead, it was an attempt to study and explain in greater detail components of mathematical modeling identified by the literature as central to the mathematical modeling process or as difficult for students. …
将事物理解为模型或建模（Lesh, R. & Doerr, H. M.，eds.，Beyond Constructivism）
DOI：
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发表时间：
2018
期刊：
教育科学 数学教育，明治図書
影响因子：
--
作者：
Takashi Kawakami;Akihiko Saeki;& Masafumi Kaneko;川上 貴
通讯作者：
川上 貴