There are a couple of other factors you ought to consider if you are deciding whether to pay your spring 2019 tuition in 2018 or in 2019. A certain amount of tuition will get you the maximum education credit. For the American Opportunity Credit, $4,000 of tuition will give you the maximum tax credit of $2,500. For the Lifetime Learning Credit, $10,000 of tuition will give you the maximum credit of $2,000. If you pay any more than those amounts in one year, the additional tuition payment will not increase your tax credit for that year.
(It's a little more complicated if you have more than one student on your tax return, but I got the impression that that is not your situation. The maximum for the American Opportunity Credit is per student, but the maximum for the Lifetime Learning Credit is per tax return.)
Also, as you probably know, you can only claim the American Opportunity Credit 4 times for any one student. That might affect whether you want to pay more tuition in one year or split it between two years.
I haven't mentioned the Tuition and Fees Deduction because, as of now, that deduction expired at the end of 2017 and is not available for 2018 or later years. That could change if Congress acts in the next few weeks.
