There are a total of 52 + 38 = <<52+38=90>>90 parking spaces in the school.
Since half of the spaces are filled then, 38 x 1/2 = <<38*1/2=19>>19 cars have parked at the back.
So, a total of 39 + 19 = <<39+19=58>>58 cars have parked in the school.
Therefore, 90 - 58 = <<90-58=32>>32 parking spaces are still available.
#### 32