Thorny Issue…
There is no “Catholic” position on this question so I will offer a merely personal perspective.
Let me begin by stating my support of teaching the Ten Commandments in any legitimate forum where they can be well-received. These commandments contain basic precepts that should be apparent to reasonable people of good will and have similarities with other ancient codes. As such, they are foundational to western society.
However, we live in a culture that values free will more than good will. The Ten Commandments will inevitably be seen as an expression of Judeo-Christian faith. Should they be posted in public schools, then groups harmful to the common good could and would request the posting of their teachings as well. I believe the end result of such an action would be a detriment to the formation of our youth. Therefore, I would urge caution in displaying the Ten Commandments in public schools.