91,755 research outputs found
Exploring the mathematics of motion through construction and collaboration
In this paper we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models – in the form of programs – to formalise and thus extend their existing knowledge. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position-time and velocity-time graphs. They shared their findings on a specially-designed web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online communities
Wisdom of groups promotes cooperation in evolutionary social dilemmas
Whether or not to change strategy depends not only on the personal success of
each individual, but also on the success of others. Using this as motivation,
we study the evolution of cooperation in games that describe social dilemmas,
where the propensity to adopt a different strategy depends both on individual
fitness as well as on the strategies of neighbors. Regardless of whether the
evolutionary process is governed by pairwise or group interactions, we show
that plugging into the "wisdom of groups" strongly promotes cooperative
behavior. The more the wider knowledge is taken into account the more the
evolution of defectors is impaired. We explain this by revealing a dynamically
decelerated invasion process, by means of which interfaces separating different
domains remain smooth and defectors therefore become unable to efficiently
invade cooperators. This in turn invigorates spatial reciprocity and
establishes decentralized decision making as very beneficial for resolving
social dilemmas.Comment: 8 two-column pages, 7 figures; accepted for publication in Scientific
Report
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