Relatively recent development in the so called midisuperspace approach to loop quantum
gravity/cosmology, involving in particular the abelianization of the constraint algebra,
has given high hopes for probing the genuine quantum dynamics at least in some scenarios in
(nonlinear inhomogeneous) cosmology and black holes/matter collapse. Focusing on the application
of this procedure to the cosmological model of a Gowdy universe with local rotational symmetry
I am going to discuss the method's strengths and weaknesses. In particular I will focus on the
issue of reproducing the General Relativity as the low energy limit of this model.