Despite the increasing number of experimental mapping showing that human arithmetic cognition is supported by widely spread neural circuits; the theoretical reasoning about these data remains mostly metaphorical and guided by a connectionist approach. Although neurons at distinct areas in the brain are assumed to take charge of different duties in the solution of the experimental task, the results are always discussed by hypothesizing some association between the different areas without questioning any difference of behavior at the level of the neurons at each of these areas. Here, the brain is assumed as Distributed Intelligent Processing System (DIPS) formed by collections of loosely interacting specialized agents (neurons), each agent specializing, for example, in data collection (sensors), problem solving (associative neurons), data communication (interneuronal systems) and in acting upon the surrounding environment (motorneurons). A new technique for EEG brain mapping is proposed and used to study arithmetic cognition in elementary school aged children and adults. Factor analysis showed three distinct patterns of neuronal recruitment for arithmetic calculations in all experimental groups which varied according to the type of calculation, age and sex.