Project Mission and Goals
The overall goal of this 4-5 year project is to create tools that will help learners (at all levels) make greater sense of complex phenomena and to study how learners come to understand 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. Complexity is a theme that cuts across traditional discipline boundaries. Yet it is rarely found as an explicit theme in K-16 curricula. Indeed, many studies have shown that, in both the public at large and in science classrooms, "good thinking" about systems of interacting agents is not easily found.

This is a time that is seeing a ground swell of interest in the sciences of complexity. It is also a time of increasing globalization of economies and increasing awareness of the interconnectedness of both natural and human systems. This has resulted in a strong need, in both the public at large and in the scientific community, for increased abilities in systems (or ecological) thinking .

This project grows out of and responds to that need. The concrete goals of the project are to:

  • Create (and enhance existing) so-called "object-based parallel modeling languages" (OBPML) (sometimes also known as agent-based modeling languages) that can be used by learners to create rich and detailed models of large systems of interacting agents and objects. The languages should strive to obey the maxim "low threshold, no ceiling" -- that is, they should be simple enough that middle schoolers can use them to create models, yet powerful enough that research scientists can do their research using these languages.

  • Create a library of so-called "extensible models" (i.e., domain specific models created using these toolkits) for learners to explore and extend. Since complexity is a theme which cuts across traditional content domains, the models developed will include content material from across the natural and social sciences as well as from the discipline of mathematics .

  • Characterize the developmental path of learning to think about complex systems. How does "complex" thinking develop and mature? How do learners shift from thinking in terms of hierarchical and deterministic control to probabilistic and decentralized approaches? The data for this developmental theory will be gathered through conducting in-depth learning interviews with users of the OBPML and the extensible models.
All of these goals will be pursued with the framework of "Connected Mathematics". Traditional mathematics education has proceeded from a view that mathematics is "given" rather than constructed and is to be transmitted to learners primarily through formalism. As a result, mathematics is usually taught in isolation from other domains and the role of technology in mathematics education has primarily been to better inculcate or animate the existing formalisms. In contrast, the theory of Connected Mathematics sees the fundamental activity of mathematics as that of making and designing new mathematical representations and connecting these representations to each other and to other domains. The vision of mathematics as being made and not simply received leads naturally to a role for technology. Technology is not there simply to animate received truth, it is an expressive medium a medium for the making of new mathematics. It follows that we can make better use of computational technologies than simply running black-box simulations we can make mathematics by constructing computational embodiments of mathematical models. The true power of the computer will be seen not only in better teaching of the old topics but in transforming ideas about what can be learned.

As the project unfolds, we expect to develop:

  • New modeling environments which move beyond current OBPML -- that integrate multiple levels and modes of representation

  • A library of extensible models - a valuable resource shared through publication on the world wide web

  • A body of case studies of learners building computational models of complex phenomena

  • A cognitive science theory of how learners come to make sense of complex phenomena and of the role of modeling in facilitating that sense-making.

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