"She withdrew $12,027 from the coverdell" .... "Room and board based on university cost of attendance are $10,696". That would appear to mean that $1331 (12027-10696 = 1331) of the distribution was non qualified. A portion of that $1331 is taxable. $237 as the taxable amount sounds reasonable.
Normally the taxable amount is box 2 of the 1099-Q divided by box 1 times the non qualified distribution. Bot in your case (boxes 1 & 2 blank), the calculation is different.
