Why and how is it efficient to process sorted arrays than unsorted arrays? It is well accepted that processing sorted arrays is easier and efficient. What would be the pedagogical approach to explain how and why it is more efficient to process sorted collections than unsorted collections.
First, it is not "well accepted" that processing sorted array is more efficient. It depends on what you do. If you spend your time inserting, for instance, then sorted arrays are not necessarily a good choice. You are better off inserting at the end (say if you have resizable arrays such as Vector&lt;X&gt; or ArrayList&lt;X&gt; in Java), and then sort afterwards (you'll pay $O(N*log(N))$ instead of $O(N²)$).

It is true that if you don't have insertions (or very few insertions with respect to searching or other operations for instance) then it is more efficient.
If you want to find an element in a sorted array, you can use binary search which is $O(log(N))$ while if your array is not sorted you have to scan the whole thing which is $O(N)$.

Likewise if you want to perform set operations on two sorted arrays (intersection, union, difference), then doing so on sorted Arrays is linear. If they are not sorted you will be either quadratic (naive algorithm) or have to use an auxiliary data structure (such as a hash table).

Sorted arrays have the same complexity for these operations than the more involved tree structures (AVL or red-black trees) and they have a very compact and simple representation. But you pay the price that insertion is more expensive, since it has to maintain the order of elements.