I have toddler twins that are currently in the same class at school. What research has been done so that I can decide whether or not to separate them next year?
This really depends on your twins. There is no generic answer that fits every twin couple. It all depends on the competitiveness of the children. If you see that one is constantly overruled by the other, splitting up might be good. If they really develop well and they like the others company, let it be in one class. We have kept our twins together, but we continue to assess the situation.
Don't separate unless there's a good reason to.
Here's my story, and the reasons behind it:
I spent several years in the same class as my twin, but later (as we moved to a new country) we were put in separate classes. Much later, we were again in the same class.
We were separated because my brother relied too much on me; he didn't make notes on what homework was required, so if I didn't write it down or remember, we were both screwed. By separating us, my brother learned to get by alone, and so it wasn't a problem that we were in the same class again later.
But the separation had social downsides because the two classes were not on speaking terms so we were isolated from each other also during breaks, and having class friends over was always difficult. The teachers knew about this class "war" in advance but didn't think it would matter. It did.
So if there is a good reason to separate, and there are no serious known downsides, then do go ahead. But consider when and how to join them again if other issues arise.
At the same time, make sure they get opportunity to spend enough "twin time" together away from that "split-class" context, like in a sports club or scouts club.
It used to be common for schools to insist twins be separated in school, regardless of the parent's views. Thankfully, this seems to be less common these days. My school district has never pushed to override a parent's preference. After all, they know the kids best, and they have to live with the results. I don't.
That said, I've had twins together, twins with me but different periods, and twins separated to different teams of teachers. I have a set of triplets in the same room this year. My anecdotally supported opinion is that there can be no general advice. Kids are different. Somebody's got to know the kids as individuals and make a decision.