Patterns, Probabilities, and People: Making Sense of Quantitative Change in Complex Systems
Patterns, Probabilities, and People: Making Sense of Quantitative Change in Complex Systems
复制标题
模式、概率和人：理解复杂系统中的数量变化
DOI：
10.1080/10508406.2014.976647
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发表时间：
2015
影响因子：
3.8
通讯作者：
U. Wilensky
中科院分区：
文献类型：
--
作者：
Michelle Wilkerson;U. Wilensky
学习科学界在理解人们如何思考和学习复杂系统方面取得了重大进展。但人们如何理解通常用于研究这些系统的定量模式和数学形式却知之甚少。在本文中，我们提出了关注和支持复杂系统的行为与定量和数学描述之间的联系的案例。我们引入了一个框架来检查学生如何将复杂系统的行为和定量方面联系起来，并用它来分析对 11 名高中生的采访，因为他们与基于代理的模拟进行交互，该模拟产生了简单的指数式人口增长。尽管学生们能够轻松地描述模拟行为与其生成的定量模式之间的许多联系，但我们发现他们并不能轻易地描述个体行为与变化模式之间的联系。案例研究表明，这些缺失的联系导致那些从事有意义的有意义构建模式的学生在解释模拟中的定量模式时仍然犯了错误。这些困难可以通过吸引学生注意模拟环境中的数量变化图以及生成它的基本规则来解决。我们讨论了对学习环境设计、复杂系统定量推理研究以及数学推理在复杂系统流畅性中的作用的影响。
The learning sciences community has made significant progress in understanding how people think and learn about complex systems. But less is known about how people make sense of the quantitative patterns and mathematical formalisms often used to study these systems. In this article, we make a case for attending to and supporting connections between the behavior of complex systems, and the quantitative and mathematical descriptions. We introduce a framework to examine how students connect the behavioral and quantitative aspects of complex systems and use it to analyze interviews with 11 high school students as they interacted with an agent-based simulation that produces simple exponential-like population growth. Although the students were comfortable describing many connections between the simulation’s behavior and the quantitative patterns it generated, we found that they did not readily describe connections between individual behaviors and patterns of change. Case studies suggest that these missed connections led students who engaged in productive patterns of sense-making to nonetheless make errors interpreting quantitative patterns in the simulation. These difficulties could be resolved by drawing students’ attention to the graph of quantitative change featured in the simulation environment and the underlying rules that generated it. We discuss implications for the design of learning environments, for the study of quantitative reasoning about complex systems, and for the role of mathematical reasoning in complex systems fluency.