To check the status of your student's assessment, go to the Test Queue page of your teacher/parent account. There are two columns that will show tests that have been queued and tests currently in progress.
To see which tests are Queued or In Progress, you can hover your mouse over the number. See below.
If you assigned a student an assessment and it is not showing up under the Test Queued and Tests in Progress section, then your student has completed the assessment. You can check the Scores & Reports page for results.