Almost all the children were chattering and it seemed a poor learning environment. I didn't say anything to the teacher because I didn't want to put my foot in it. But I do want to raise the matter. Could you advise me how best to do it?
Answer: I am glad you didn't say anything at the time. It might have got you off on the wrong foot with a teacher who had made you welcome. I cannot say often enough that going into school as an individual you are there to learn, not judge. You will gradually build up your knowledge, which will help you come to sensible decisions as a member of the governing body on a wide range of policy matters which are the governors' concern.
But any comments on the way classrooms are organised or the way teachers manage lessons are for the governing body acting together. Even then it is not the governors' role to comment on the way classrooms are organised or the way teachers manage lessons - unless there is evidence of a real problem, such as a school which the governors agree has gone to extremes of informality and where this view is reinforced by bad results.
There has been some movement of opinion back to whole-class teaching and more formal organisation. Nevertheless, most primary schools still have a classroom style which seems free and easy to older outsiders. It can achieve excellent results.
The class you describe would have contained children of varying abilities.Some of the pupils were advanced enough to do calculations in the abstract and on their own. At the opposite extreme, others would find it hard to concentrate without help, but the learning process is the same. The children in between were, it seems, exploring concepts of length and capacity.
It sounds as if the ability range was fairly typical and the classroom well organised. As for noise, we oldies like peace to concentrate, but teenagers often do their homework in the most unpeaceful atmosphere they can devise. Wait a while, and carry on visiting. If as a group you feel the school goes too far in any direction and are worried by its results, you must discuss that with head and staff. Meanwhile, ask teachers to talk to the governors fairly often, simply for information, about how they organise their teaching and the outcomes. It is good for them to justify whatever styles they favour. You will also notice that different teachers achieve the same results in different ways.
In the end all are probably most successful with the methods they believe in and are skilled with. A school does not necessarily need total uniformity.