We performed a time-resolved spectral analysis of 53 bright gamma-ray bursts (GRBs) observed by Fermi/GBM. Our sample consists of 1117 individual spectra extracted from the finest time slices in each GRB. We fitted them with the synchrotron radiation model by considering the electron distributions in five different cases: monoenergetic, single power law, Maxwellian, traditional fast cooling, and broken power law. Our results were further qualified through the Bayesian information criterion (BIC) by comparing with the fit by empirical models, namely, the so-called Band function and cutoff power-law models. Our study showed that the synchrotron models, except for the fast-cooling case, can successfully fit most observed spectra, with the single power-law case being the most preferred. We also found that the electron distribution indices for the single power-law synchrotron fit in more than half of our spectra exhibit flux-tracking behavior, i.e., the index increases/decreases with the flux increasing/decreasing, implying that the distribution of the radiating electrons is increasingly narrower with time before the flux peaks and becomes more spreading afterward. Our results indicate that the synchrotron radiation is still feasible as a radiation mechanism of the GRB prompt emission phase.