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. ***
