It is permissible to take pictures of student activities with the video camera and digital camera mentioned, for the purpose of documenting the activity so that the administrators may study it, so long as these images are not produced in any fixed format such as on paper.
Shaykh Ibn ‘Uthaymeen said:
With regard to pictures made in the modern fashion, they fall into two categories:
The first category is those which have no tangible substance (and can only be seen by running them through a machine), as I was told is the case with pictures on video tapes. There is no ruling at all concerning these, and they do not come under the prohibition at all. Hence the scholars who forbid making pictures with cameras on paper (photographs) permitted this (video pictures), and said that there is nothing wrong with this. Then it was asked, is it permissible to film lectures which are given in the mosques? The (scholarly) view was that it is better not to do that, because it may disturb the worshippers and because they may film things that may not be appropriate, and so on.
The second category is fixed or still pictures on paper (photographs) …
But the matter needs further discussion if one wants to make these kind of permissible pictures. For they are subject to five rulings which depend on the intention. If the intention is something forbidden, then it is haraam. If he intends something waajib (obligatory), then it is waajib. Sometimes pictures may be essential, especially moving pictures. For example, if we see someone in the act of committing a crime against a person’s rights, such as an attempt to kill and so on, and we cannot prove it in any way but by taking pictures, then in this case taking pictures becomes waajib, especially in cases where pictures may decide the case. The means are subject to the rulings on the ends. If we make these pictures in order to prove the identity of a person for fear that someone else may be accused of the crime, this is also acceptable, indeed it is essential.
But if we take these pictures just to enjoy looking at them, this is undoubtedly haraam... And Allaah knows best.” (See Al-Sharh al-Mumti’, 2/197-199)
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) was asked: What is the ruling on videotaping celebrations, conferences and seminars?
He replied: If there is the hope that people may benefit from the videotaping of the party, seminar or Islamic meeting in which there is the call to Allaah, and it is believed that this is most likely to serve a good purpose and that this videotaping will be good and will benefit the people, then there is nothing wrong with that in sha Allaah. End quote from Fataawa Islamiyyah (4/367).
May Allaah help us all to do that which He loves and which pleases Him.
And Allaah knows best.