@Anonymous
You mentioned that you have a DropDown with the Distinct student names, but you also mention "blank" - how is it that you are accomplishing that? I'm going to go with the thought that perhaps you don't have that worked out yet and will describe the solution you are looking for.
First, you will need a list of distinct names with some indicator that will uniquely identify "All"...so, we'll use "All"
In your OnVisible (or some other place where you will execute a formula) you will need to build a collection for the DropDown. There is no way (that I know of) to build the collection in the DropDown and add the option we want. So:
OnVisible
ClearCollect(studentNames, {Result:"All"}); Collect(studentNames, Distinct(yourDataSource, studentNameField))
Now, set the Items property of your DropDown to the collection - studentNames
You will now have a dropdown with all the distinct student names in it and there will be (first in the list) "All".
Then, for your Gallery, set the Items property as follows:
Filter(yourDataSource, studentNameField=If(yourDropDown.Selected.Value="All", studentNameField, yourDropDown.Selected.Value))
This will give you the results you are looking for.
Hope this helps get you going.