This paper presents a model of how children generate concrete concepts from perception through processes of differentiation and integration. The model informs the design of a novel methodology ("evolutionary maps" or "emaps"), whose implementation on certain domains unfolds the web of itineraries that children may follow in the construction of concrete conceptual knowledge and pinpoints, for each conception, the architecture of the conceptual change that leads to the scientific concept. Remarkably, the generative character of its syntax yields conceptions that, if unknown, amount to predictions that can be tested experimentally. Its application to the diurnal cycle (including the sun's trajectory in the sky) indicates that the model is correct and the methodology works (in some domains). Specifically, said emap predicts a number of exotic trajectories of the sun in the sky that, in the experimental work, were drawn spontaneously both on paper and a dome. Additionally, the application of the emaps theoretical framework in clinical interviews has provided new insight into other cognitive processes. The field of validity of the methodology and its possible applications to science education are discussed.