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A long-term (1995-2016) survey for novae in the nearby Andromeda galaxy (M31) was conducted as part of the Research-Based Science Education initiative. During the course of the survey 180 nights of observation were completed at Kitt Peak, Arizona. A total of 262 novae were either discovered or confirmed, 40 of which have not been previously reported. Of these, 203 novae form a spatially-complete sample detected by the KPNO/WIYN 0.9-m telescope within a $20'\times20'$ field centered on the nucleus of M31. An additional 50 novae are part of a spatially-complete sample detected by the KPNO 4-m telescope within a larger $36'\times36'$ field. Consistent with previous studies, it is found that the spatial distribution of novae in both surveys follows the bulge light of M31 somewhat more closely than the overall background light of the galaxy. After correcting for the limiting magnitude and the spatial and temporal coverage of the surveys, a final nova rate in M31 is found to be $R=40^{+5}_{-4}$ yr$^{-1}$, which is considerably lower than recent estimates. When normalized to the $K$-band luminosity of M31, this value yields a luminosity-specific nova rate, $ν_K = 3.3\pm0.4$ yr$^{-1} [10^{10} L_{\odot,K}]^{-1}$. By scaling the M31 nova rate using the relative infrared luminosities of M31 and our Galaxy, a nova rate of $R_\mathrm{G}=28^{+5}_{-4}$ is found for the Milky Way.