Who should claim the education credit — parent or student?

It depends. A parent who pays qualified higher-education costs for a dependent is entitled to the credit. But if the parent's income is too high to qualify for the credit, don't waste the credit-let the student take it. Best strategy: Simply waive the dependency exemption for the child and let the student take the education credit on his/her return, as long as the student has sufficient income to generate a tax bill that can be offset by the credit.