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

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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.