There are a number of approaches to language processing.

1. constructivism (Ellis)
2. processability theory (Pienemann)
3. processing instruction (VanPatten)

Constructivist approaches to language acquisition (not to be confused with constructivism as a learning theory) are data-driven or emergentist models.  Theorists like Ellis and MacWhinney claim that language acquisition can be explained by connectionist accounts whereby learners progress through practice and exposure to the language, not by acquiring rules, as UG theorists claim (Chomsky).

Other researchers have developed different models, such as processability theory (Pienemann), which posits a language processor with a more complex structure.

Processability theory contains a hierarchy of processing procedures and routines ordered according to their activation. Pienemann predicts that in the acquisition of language processing procedures, the assembly of the component parts will follow an implicational sequence. Subordinate clause procedures are the last ones to be implemented. Within this theory, then, variability is explained in terms of the constraints imposed on the learning process by the architecture of the language processor. The task of language acquisition is seen as the acquisition of processing skills. Learners cannot acquire what they cannot process.

(Romaine, 2003)

Finally, VanPatten's processing instruction (PI) model asks a teaching question:

If we know something about input processing, can we use this information to structure activities to improve processing?

(VanPatten, 2004)

This somewhat controversial instructional approach aims to speed classroom second language learning by designing classroom activities which focus on form-meaning connections. 

Activity

Read more about processing instruction