Meetings should be run in a professional manner. I've written quite a bit about how to make meetings more effective and purposeful, but mainly from the perspective of the whole team. There are, however, more personal reasons to make meetings more formalised.

Meeting like this is not recommended!What is a formalised meeting?

A formalised meeting has these characteristics:

It is a formal occasion. That is, it is not the same as a quick get-together in the staffroom over a cup of tea. It's arranged in advance (apart from emergency meetings, of course), follows a predictable pattern, and lasts a predictable length of time. Certain standards of behaviour are expected, such as 100% attendance, and being there on time.
It generates paperwork (or virtual paperwork). That is, it is supported by proper documentation, which is not usually the case with an informal meeting.

Reasons for making meetings formalised

Expectations? Paperwork? That doesn't sound like much fun. Nevertheless, there are good reasons to make departmental meetings more formalised:

It sets the tone for both staff and students. A professionally-run meeting looks professional, and makes its participants look professional.
It shows respect for the people who have to attend. Having been obliged to go to more than my fair share of meetings that have started 20 minutes late, with no indication of what the meeting is about, and people chipping in throughout on a seemingly ad hoc basis, I think respecting people's time is paramount. So is respecting their professional expertise by giving them proper opportunities to contribute, as opposed to having to effectively barge their way into the conversation.
It enables you to keep a record of what was discussed in each meeting. This is very important for the following reasons:

* It enables you to know who has been to which meeting: if you know that Mrs Jones was out of school when you discussed homework marking, then you can ask her for a quick 5 minute meeting just to make sure she understands the minutes of the meeting about that issue.

* It enables you to refer to specific meetings when discussing issues with the Principal. It is much more effective to say "When we discussed the school Learning Platform in our meeting on 4th March, we agreed that ..." than "Well, we discussed Learning Platforms some time ago, I think; yes, I'm sure we did...."

* By the same token, it enables you to demonstrate to school inspectors and other visitors that you have formally discussed particular issues.

* It enables you see very quickly which issues have not been discussed, and which therefore ought to be addressed in a forthcoming meeting.
Another reason to formalise meetings is that it creates an audit trail, in effect: you know what was discussed, when, by whom, and which actions were assigned to which team member, and when they were to be completed by.

Ways to formalise meetings

Formalising meetings is not difficult. This is what you must do:

Establish a calendar of meetings. This will probably be done for you, in the sense that you will be told that departmental staff meetings take place after school every Thursday. Even if you are given the authority to do so, it is not good practice to turn this into an extra free period in effect. Perhaps you may want to do that occasionally, but not as standard.

You may argue that there is no point in having meetings for the sake of having meetings, and you would be right. However, there are always issues to discuss on a formal basis, even if there are only two of you and you see each other all the time. In that sort of circumstance, perhaps the formal part of the meeting need last only 15 minutes, say.
Use formal meeting documentation, ie an agenda, followed by minutes.
Use formal meeting procedures, ie apologies for absence, approval of minutes and any other business. This sounds like overkill, but it does not have to be.. For example, "approval of minutes" should not take long, assuming the minute-taking was good (see below) and the meeting lasted only an hour.
Minutes should be useful. The purpose of the minutes is to ensure that there is a record of what was discussed and decided in a meeting. Being realistic, you are highly unlikely to have secretarial support, and you really don't want the minute-taker to be concentrating on that activity to the detriment of his or her participation in the meeting.

Therefore, what the minutes should consist of is a list of bullet points with names and dates attached, like this:

1. Fred apologised for absence as he is on a field trip.

2. Minutes from last meeting were approved.

3. Joan to look into latest Becta report about Web 2.0, and give us a summary in our meeting of October 10th.

4. David reported that the new after-school computer club was becoming very popular.

...

8. Any other business: Debbie asked if staff could be reminded to switch the printers off at the end of lessons.

9. Next meeting: September 13th, 4pm, Room 2.

So where does the "personal reasons" come in?

Part of leading a successful area of the school is to do with personal benefits. The sort of personal benefits that can come from formalising meetings are as follows:

Less worry when it comes to requests for information.
Your department will run more smoothly.
Your reputation as a serious professional who knows what they're doing is almost certain to be enhanced.