Connected Mathematics: Making Sense of Complex Phenomeana through Building Object-Based Parallel Models

连接数学：通过建立基于对象的并行模型来理解复杂现象该项目的内容领域是学习“复杂性”。 复杂性是对系统的研究，其中现象或全局行为来自于较简单部分的相互作用。 许多日常现象表现出复杂的行为：雪花晶体的生长，枫叶的周边图案，道琼斯指数或四年级教室的动态。 这些都是可以被建模为由许多分布式但相互作用的部分组成的系统。 他们都表现出非线性或紧急的品质，使他们超出了目前的K-12数学课程的范围。该项目的目标是通过使用基于对象的并行建模语言（OBPML），使复杂性的学生访问。 学生从“零开始”建立复杂数学和科学现象的模型，并从“可扩展模型”库中扩展模型。通过这些活动，研究人员寻求：* 了解学习者在构建基于对象的并行模型时如何理解复杂现象 * 设计计算工具和活动，以促进学习者在a）构建复杂现象模型和B）构建复杂性直观概念 * 调查学习者参与这种建模的方式改变了他们对数学和科学事业的信念和态度 * 研究学习者在基于对象的并行建模中开发的各种符号化模式。 OBPMLs提供了一种概率和统计建模方法。 该项目的一个成果是加强和扩大了概率和统计在数学和科学课程中的作用，将其与蒙特卡罗模拟等计算技术相结合，从而开发了一个新的主题领域，也许更好地称为随机。 在这方面和其他方面，我们希望开发新的数学内容领域-生活在基于对象的并行介质的内容领域。

Connected Mathematics: Making Sense of Complex Phenomena through Building Object-based Parallel ModelsThe content area of the project 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 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 beyond the scope of current K-12 mathematics curricula.The project goal is to make complexity accessible to students through the use of object-based parallel modeling languages (OBPML). Students build models of complex mathematical and scientific phenomena from "scratch" as well as extending models they are given from a library of "extensible models".Through these activities, the researchers seek:*To understand how learners make sense of complex phenomena when engaged in buiding object-based parallel models*To design computational tools and activities that foster learner's in a) building models of complex phenomena and b) building intuitive conceptions of complexity*To investigate the ways in which learners engage in this kind of modeling change their beliefs about and attitude towards the mathematical and scientific enterprises*To investigate patterns in the kinds of symbolization developed by learners engaged in object-based parallel modeling. OBPMLs afford a probabilistic and statistical approach to modeling. One outcome of the project is a strengthened and broadened role for probability and statistics in the mathematics and science currucula, combining it with computational techniques such as Monte Carlo simulations -- thus developing a new subject area perhaps better called stochastic. In this respect and others, we expect to develop new mathematical contents areas--content areas which live in an object-based parallel medium.