Final answer:
Parallel adoption is the project implementation method where the old system continues to operate while the new system is developed and tested.
Step-by-step explanation:
The method that allows the old system to continue operating while the new system is developed and tested is known as parallel adoption. In this approach, both the old and new systems run simultaneously for a period of time. This ensures that business operations are not interrupted and provides a means to compare the performance of both systems. Prototyping refers to the creation of a functional model to test design concepts, whereas direct implementation involves a sudden switchover from the old system to the new system without running both at the same time, and there is no method officially called 'indirect implementation' in common IS terminology.