If they are only using box 2, they are only telling what they billed you.
(some schools only report one of the two boxes)
If the first year (2015?) they billed you for classes, but you did not pay for the classes,
you could have used that amount for the next year.
If they billed you for 2,000 but you only paid 1,500, you can use 1,500 in tuition fees paid
So, YES, if I understand you correctly, the amounts on the 1098-T are not split or carried over by the school, (only you can do that) so what they report is what was billed. If they split it, you can add it together.
If 2015 says Sept 15 and Jan 16, add it together for what was billed in 2015
The 2016 1098-T should NOT include the amount billed for JAN 2016, because it was reported in 2015
