Here are a couple of strategies I have used with challenging classes in the past. Honestly the Whole Brain Teaching sounds a little "out there" but it really does work. The strategies are active and the sometimes noisy. You have to be ready to move and be on your shoes. Kids that are talkative and active are able to channel all of that energy in a positive direction and they can't help but have fun. It is hard to ignore having fun. Active engagement definitely improves.
Here is a link to their website. They have a lot of strategies.
whole brain teaching dot com (with no www in front and no spaces)This one does not come up as a link for some reason.
The other strategy that is a bit calmer for teachers, is the clip chart. The difference between this chart and the one above is that it has more steps in the positive direction than the negative. It helps me to focus on students who are modeling positive behaviors. There are consequences for students not ready to learn but not near as strict as the ones listed above. This one is on the New Management website. Will include a link to the ebook about the clip chart, but again there are a lot of free tips on their main website.
Christine Bainbridge does an outstanding job of explaining how the clipchart system works in a second grade classroom on her blog with links to her website.
I hope these resources help! You already have one third of the year completed. These classes do move on, and luckily so do unsupportive administrators.