Decompression theory and the way you manage decompression are two entirely different things. Mark Powell wrote an entire book (two editions) on decompression theory, and he never once mentioned how to use tables. With scuba instruction, a student should receive thorough instruction on decompression theory, after which he or she should be taught how to manage it, be it with tables or a computer.
As I have written many times before, if you did a a multi-level dive before your computer conked out, the tables will be pretty much useless to you as a backup, because your dive will likely have exceeded the limits.