The progression of secondary waves emanating from scattering centers within a non-absorbing material in the visible part of the electromagnetic spectrum (wavelength 0.500 µm) is traced using two modeling schemes: the scattering order formulation (SOF) of the discrete dipole approximation (the original SOF) and the SOF with the Twersky approximation, according to which the path of the secondary waves in a successive scattering chain does not loop through the same scattering center more than once (the SOF-Twersky). It is shown that for smaller submicron-sized scatterers (radius 0.100-0.200 µm), the scattering phase function in the backscattering hemisphere converges after a small number of orders of scattering, as does the scattering phase function in the forward scattering hemisphere. For larger submicron-sized to micron-sized scatterers (radius 0.300-0.500 µm), however, the scattering phase function in the backscattering hemisphere deviates significantly from the correct scattering phase function for a small number of orders of scattering, even as the scattering phase function in the forward scattering hemisphere remains at reasonable values. These results point to the particular importance of higher orders of scattering in reducing backscattering by particles composed of non-absorbing materials. Likewise, the results imply that a possible source for the lack of convergence in the original SOF lies in a certain lack of destructive interference of secondary waves propagating in particular into the backscattering hemisphere. The extent to which "downward recursion" can ameliorate this lack of destructive interference of secondary waves propagating into the backscattering hemisphere within the SOF is also examined. In the SOF with downward recursion, looping of secondary scattered waves is allowed, unlike the other versions of the SOF; however, the scattering centers situated the largest distance from one another within a given scatterer interact with one another first, and the interactions proceed to smaller and smaller scattering center separations.