Actually if your talking about stretching for more flexability it is a bad idea to try and accomplish this during class. It is my understanding that intense 'stretching' for a warmup has more negative effects than positive. That the stretching of muscle, tendon, and sinew has much the same effect as exercizing the muscles for strength that is creating tares and injuries to be rebuilt, however it seems that your tendons and sinew don't have that much tolerance for abuse so trying to stretch for flexability before training will result in an increased chance of injury. Instead a warmup should be just what the name implies, activating the muscles and moving things around a bit just get the blood flowing so to speak. If you want to become more flexible the best time to do this is after risk of injury has past for the day. One experienced martial artist I met said the best stretch training took place before bed and after a warm bath. Whatever you do, do it slowly.
These are, I think, good valid points, and they relate to the idea mentioned previously that for flexibility you should warm the muscles first before asking them to release in a stretch.
I've heard yoga instructors and rolfers (and others) talk about the connective tissue as being like taffy -- if
you go slowly and the tissue is warm, and if
you understand how to use your breathing to release the contraction of the involved muscles, this tissue will stretch over a period of daily training. Just like taffy, though, when cold this tissue tends to be brittle. And like taffy, it only will stretch slowly. Because this tissue has a more limited blood supply, moreover, injuries to it heal more slowly than injuries to muscle tissue.
(If you are interested, a form of Yoga called "Yin yoga" concentrates on very long slow stretches that are never at your "edge" in order to try and access this possibility.)
On a different point, while becoming "flexible" to some extent is useful given how Aikido training asks use our bodies, different people have different set points of flexibility, much the same as with other physiological markers (e.g., strength, power, or endurance).
People who are naturally very flexible don't usually ask about becoming more flexible. Ironically,however, such folks -- not I --have their own set of challenges in yoga about not hyperextending joints under a load.
Where ever one's current set point lies, its critical to respect your body (and it's signals to you) at all times when stretching -- liberate your body, don't conquer it.
In this context, I've come to believe my most useful "flexibility" conditioning is not just about increasing the length of say, my hamstrings (particularly as an isolated muscle structure).
My daily yoga practice has shifted over time to be more centered on structural rehabilitation/integration. For example, in a standing forward bend, I need to give my back body room to stretch by structural alignment and release of other muscles -- this is where the "contradictory force" aspect of yoga is very clear. If the middle of my hamstrings feel tight, as they did this morning, I reach upward towards the ceiling with the back of my pelvis (legs slightly bent) and then alow my breath to guide my legs towards being straight over the course of the stretch. This targets my whole "back body."
When my hamstrings are ready, they let go. (If you're interested, Iyengar yoga stresses careful alignment. It's founder stressed the idea of "non-violence" towards one's self as a tenant of practice.)
This different focus is, from my perspective, like the difference between using weight machines to increase strength of sequentially-targeted muscles through isolation, on the one hand, versus using free weights to increase strength by movements that recruit muscle tissue throughout the body in a (hopefully) coordinated way.
Without suggesting type of training is without value, they lead to a different type of body and a different way of moving.
For me, the isolated flexibility of different muscles is more of a "bell and whistle" that lets me know the basics are in order, not a goal in itself.