Approximations of practice create valuable opportunities for preservice teachers (PSTs) by engaging them in components of teaching. By reviewing the literature, this study explored PSTs' learning through approximations and the extent approximated practices preserve the complexity -- or authenticity -- of teaching. A review of 25 empirical studies related to approximations of mathematics teaching indicated that mathematics teacher educators are currently exploring an expansion of opportunities through approximations wherein PSTs could experience a higher degree of authenticity. The existing conceptualization of authenticity emphasizes the complexity of practices but overlooks how approximated practices prepare PSTs for their future teaching. An alternative definition is proposed for the emerging conceptualization of authenticity to highlight how PSTs' learning through approximations prepares them for their future teaching. [For the complete proceedings, see ED630060.]