Making Sense of Complex Phenomena Through Building Computational Models.

该提案旨在制定两个计划：研究和教育计划，旨在为从中学到研究生院的学生提供互联数学体验。研究计划的内容领域是学习“复杂性”。复杂性是对系统的研究，在这些系统中，现象或整体行为是由较简单部分的相互作用产生的。许多日常现象都表现出复杂的行为：雪花晶体的生长，枫叶的周长图案，夏季暴风的来临，道琼斯指数或四年级教室的动态变化。这些系统都可以被建模为由许多分布但相互作用的部分组成。它们都表现出非线性或突发性的特性，这使它们远远超出了当前K-12数学课程的范围。本计划的研究目标是：1)了解学习者如何理解复杂现象；2)设计工具和活动，促进建立直观的复杂性概念。研究假设是：学习者通过使用建模环境建立自己的计算模型，可以建立关于复杂性的直觉，并理解复杂现象。即使是通常被认为不擅长数学和科学的学习者，也可以建立模型，显示出比通常在数学课堂上发现的更高质量水平的数学成就。与流行的观点相反，概率和统计是一个复杂领域的例子，学习者可以在其中发展直觉。这项研究的目标人群主要是高中生，尽管一些研究将对年轻和年长的学生以及职前教师进行。在提出的研究中，将使用几个内容域作为要建模的现象的来源。特别的重点将是使用概率和统计作为工具来理解复杂现象，并在此过程中建立概率工具和复杂现象的直观概念。＊＊＊

9552950 Wilensky This proposal is to develop two plans: research and education plans geared to providing Connected Mathematics experiences for students from middle school through graduate school. The content area of the research plan is learning about "complexity". Complexity is the study of systems in which phenomena or global behaviors arise from the interactions of simpler parts. Many everyday phenomena exhibit complex behavior: the growth of a snowflake crystal, the perimeter pattern of a maple leaf, the advent of a summer squall, the dynamics of the Dow Jones or of a fourth grade classroom. These are all systems which can be modeled as composed of many distributed but interacting parts. They all exhibit non-linear or emergent qualities which place them well beyond the scope of current K-12 mathematics curricula. The research goals of this plan are 1) To understand how learners make sense of complex phenomena; and 2) To design tools and activities that foster the building of intuitive conceptions of complexity. The research hypothesis is that: learners, through building their own computational models using modeling environments, can build intuitions about complexity and make sense of complex phenomena. Even learners not usually considered good at mathematics and science can build models that demonstrate a qualitatively greater level of mathematical achievement than is usually found in mathematics classrooms. In contrast to the prevailing view, probability and statistics is an example of a complex domain in which learners can develop intuitions. The target population for this research is primarily high school students, though some research will be conducted with younger and older students and pre-service teachers as well. Several content domains will be used as the source of phenomena to be modeled in the proposed research. A particular focus will be using probability and statistics as tools to understand complex phenomena, and in so doing Building intuitive conceptions of both the probabilistic tools and the complex phenomena. ***