Sorting & Reverse Sorting: How to name options?

Question

We are working on an app that contains a library. this is sortable by different criteria. The user can select the sorting via an action sheet. If a criterion is selected again, the sorting is reverted.
And here the problems start:

Basically we found two options to name the criteria

Either we change the naming

"Last Added"   <-> "First Added"  
"Last Visited" <-> "First Visited"  
"Progress"     <-> "Progress"
"A - Z"        <-> "Z - A"

and indicate the reversing option by adding ⇅.

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Or the title stays the same, something like

Added 
Visited
Progress
A - Z

and indicate ascending and descending sorting by adding ↑ and ↓.

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Personally I feel like the double array ⇅ in option one feels like a dragging control indication. And I find the title Z - A confusing.

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How would we decide for one option?
What are things we should consider?

Thanks!

Answer 1

Imagine that someone picks an option to sort and isn't satisfied with the sorting direction. Would he/she expect to see different options the next time in that menu? I think that people will leave it as it is because they didn't see a better option in the menu last time, why would it be there now?

In the menu, you can just name the data types that can be sorted. People just have to worry about what to sort, not how.

Also use more constructive labels (does "added" mean it has been added or when it was added):

If Sort by looks redundant in the labels use it as a title above the options.

Above the list add an option to change the direction of the list. Now, when a user is unsatisfied with the direction he/she will only have to notice and click this link/button:

[ The list ]

Answer 2

Does the user really need to sort Z–A at all? On iOS, I would expect to see the scrolling list sorted A–Z at all times and have an A–Z picker on the right so that I can jump to an M or a T. That is how I expect to browse a library on iOS.

Instead of showing the user, you are telling the user and then asking them to build a mental model of your app along with you. Personally, I really dislike that on any platform because as a user I have my own things to think about, but it is especially hard on a mobile platform where I could be on an escalator while using your app.