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H ave you ever asked your students the following questions: Why do we need oxygen? How does it get into our cells? How do ecosystems maintain their balance? What are the roles of different organ-isms? All of these questions focus on systems thinking and are useful in helping to push students to think below the surface. Systems thinking is so important that(More)
This paper introduces a novel approach towards balancing of nonlinear systems. It differs from other approaches in two key ideas: The first is the observation that linear time-invariant systems have a single equilibrium point (the origin), and that the balanced realization for the class of a linear time-invariant systems essentially relates to this(More)
Fragile X syndrome, the most common form of inherited mental retardation in males, arises when the normally stable 5 to 50 CGG repeats in the 5' untranslated region of the fragile X mental retardation protein 1 (FMR1) gene expand to over 200, leading to DNA methylation and silencing of the FMR1 promoter. Although the events that trigger local CGG expansion(More)
!! Understanding complex systems is a difficult but important component of scientific literacy (Sabelli, 2006). !! SBF is a conceptual representation for reasoning about multiple complex systems. !! Two lenses for studying transfer-Actor-oriented approach: traces trajectories adopted by the learner to see similarities between two situations (Lobato, 2006).(More)
To reason about complex natural systems, learners need opportunities to develop and represent their ideas about how these systems operate. In our work, we use an explicit conceptual representation – the Structure-Behavior-Function (SBF) ontology (Goel et al., 1996; Hmelo-Silver et al., 2007; Goel et al. 2009) – to help middle school students model and(More)
In this paper we develop a set of sufficient conditions in terms of controllability and observability functions under which a given state space realization of a formal power series is minimal. Specifically, it will be shown that positivity of these functions, plus a few technical conditions, implies minimality. In doing so, connections are established(More)
Learning about ecosystems is challenging because, like any complex system, they are simultaneously multidimensional and dynamic. Often, learners engage only with the visible components of an ecosystem and draw either single or linear causal connections between components. In this study, we explored how using a Structure-Behavior-Function framework supported(More)