I guess they're an EXEMPTION not a deduction. I suppose that matters.
"In 2015, you can claim a $4,000 exemption for each qualifying child, which may include your child or stepchild, foster child, sibling or step-sibling, or descendants of any of these, such as your grandchild. To qualify for the exemption, the child must live with you more than half of the year and be under 19 at the end of the year, or under 24 and a full-time student for the year (defined as attending school for at least part of five calendar months during the year)."