A major challenge to the standard Λ-CDM cosmology today is the ‘Sub-Structure Problem’. Numbers of dwarf galaxies as predicted by simulations are often larger than those observed. This may not be a fault of the standard cosmology, however: Many galaxy surveys suffer from biases leading to a preferential detection of higher surface brightness (and usually, more massive) objects, leading to an incorrect galaxy stellar mass function (GSMF). I will introduce a galaxy sample selection method using core-collapse supernovae (CCSNe). Using a complete sample of ~900 z < 0.2 CCSNe, identified from the SDSS-II Supernova Survey, as pointers towards their host galaxies, we find 140 new low surface brightness galaxies whilst identifying the hosts. Selecting star-forming galaxies using CCSNe leads to the removal of surface brightness and mass biases. I will demonstrate how CCSN-rates as a function of galaxy stellar mass can be used to trace both star-formation rates and the form of the star-forming galaxy stellar mass function. Resultant number densities are well-constrained deep into the dwarf galaxy mass regime and are found to increase following a power-law with decreasing mass down to the low mass limit of 106.4 solar masses, and are well-represented by a single Schechter function. This lack of downturn to galaxy number densities down to the low mass limit implies that down to these dwarf galaxy masses there is no obvious truncation to star formation in dwarf galaxies. I will draw comparisons between these observational results and those of sophisticated simulations, and discuss prospects for developing our observational studies in the era of LSST.