The main thesis of this article is that Vygotsky’s ‘zone of proximal development’ (ZPD) can be redefined in the form of a nonlinear dynamic model. Following a short introduction to the conceptual components of the model, a mathematical reformulation is presented. The mathematical form is shown to generate a variety of developmental patterns, within numerous domains. The ZPD is thus shown to be definable within the terms of a general developmental model. An interesting property of the model is its capacity to show under which conditions (parameter values) unwanted or unsuccessful developmental paths may occur. Finally, it is illustrated how the mathematical reformulation applies to formal and informal instructional settings and development in play contexts.
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Paul van Geert (2010) studied this question.