ABSTRACT
We explain key mathematical concepts used in dynamical systems theorizing. Our explanations focus on the identified deterministic nature of dynamical systems and how these views define and delimit what chaos and dynamism mean. We build on these insights to demonstrate that dynamical systems are often predictable and that explanation remains a legitimate and possible objective for SLA research, including in studies that continue the established tradition of engagement with learner variation. We discuss selected examples of the application of dynamic approaches to SLA to illustrate tensions in and potentially misleading conclusions derived from research that foregrounds metaphorical rather than mathematical interpretations of dynamics and chaos. We use these illustrative examples to indicate the thoughtful engagement with mathematics that will be needed to substantiate explanations of dynamical perspectives on SLA.
