You've starred your words, closed InferCabulary, and reopened your Dashboard and your starred words are not showing.
This happens because when InferCabulary opens you are seeing all of the words in the system, not just the words you have starred.
To see Starred or Previously Starred words click on Starred, make your selection and click Apply. You can choose to Unstar words already starred by selecting Unstar All.
After applying one or more filters, star individual words by clicking on the boxes next to the words or select the Star All box. InferCabulary let's you star up to 50 words at a time.
As your student plays through the game, words that are Learned (seen in Basecamp and correctly answered in 2 Climbs) will be unstarred and seen again, but not as often as other words he is learning or progressing on.