In the forthcoming era of high-precision cosmology, understanding how systematic uncertainties effect the use of Type Ia Supernovae (SNe Ia) as cosmological distance indicators is vital for improving measurements of cosmological parameters. Currently there exists evidence for a correlation between Hubble residuals and specific star formation rates of SNe Ia host galaxies, as well as correlations between SNe Ia brightness and star formation history. In this talk we will present ongoing work into the measurement of correlations between host galaxy star formation history, SNe Ia properties and Hubble residuals, and discuss how this will help us better understand underlying systematic errors in SNe Ia cosmology.