No, you can't claim school tuition or other expenses for your children.
Generally, you can claim the tuition and fees deduction if all three of the following requirements are met.
You pay qualified education expenses of higher education.
You pay the education expenses for an eligible student.
The eligible student is yourself, your spouse, or your dependent for whom you claim an exemption on your tax return.
The tuition and fees deduction is based on qualified education expenses you pay for yourself, your spouse, or a dependent for whom you claim an exemption on your tax return. Generally, the deduction is allowed for qualified education expenses paid in 2013 in connection with enrollment at an institution of higher education during 2013 or for an academic period beginning in 2013 or in the first 3 months of 2014.
Eligible educational institution. An eligible educational institution is any college, university, vocational school, or other postsecondary educational institution eligible to participate in a student aid program administered by the U.S. Department of Education. It includes virtually all accredited public, nonprofit, and proprietary (privately owned profit-making) postsecondary institutions. The educational institution should be able to tell you if it is an eligible educational institution.
Answers are correct to the best of my ability but do not constitute legal or tax advice.
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