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The first step is to go to the assignment itself.
From there, you will need to click on the "Student Activity" option on the navigation bar.
This sits right under the name of the assignment. Once you are in student activity, you can scroll down the page to view any of your students.
Once you have found the student that you are investigating, you will see a blue horizontal bar to the right of their name. This blue bar with have various vertical lines running across the bar. If you hover the mouse cursor over the different bars, Blackboard will tell you when the student started and finished the assignment, as well as the different times the Blackboard saved the student's work.