In this video a recursive strategy called binary search is introduced for finding elements in a sorted list. The approach involves splitting the list into halves and searching for the target value within one of the halves. This method is more efficient than sequential searching, especially for large lists. By repeatedly dividing the list into smaller sub-lists, the algorithm can quickly narrow down the possible locations of the target value. The implementation involves a user-facing method that calls a recursive function to search for the element. The base case is when the begin and end pointers cross, indicating that the element is not in the list. Otherwise, the algorithm applies the binary search strategy to find the target value.