I believe that now, after tPoD, what Cadsuane will teach has become clear. In her conversation with Sorilea, they talk of teaching Rand how to laugh and to cry. All the asha'man are cold to say the least. None of them show much emotion and are they are stoic to the extreme. All in all, they aren't the most likable characters in the book. It seems to me that Rand and the asha'man need to learn how to express emotions and their feelings. If they don't, normal people will fear them and might even turn against Rand. Learning this will not be easy because it will make the asha'man feel pain over what they are doing. Killing will not be as easy as it was. This is why none of them will want to learn, but with this change might come acceptance by the Aes Sedai. Cadsuane, like she promised to Rand, will only do things to help Rand's cause.