under the watchful eye of 在…的监视下；在(某人)的警觉目光下；在某人的密切注视下；在某人的监视下

【例句】
On Saturday afternoons we took a walk in some fields near the school, under the watchful eye of one of our teachers.
到了星期六下午，我们要在一位老师的密切监视下去学校附近的田野里散一圈步。

The children played under the watchful eye of their father.
孩子们在父亲悉心看护下玩耍。