The most obvious implication of the amount of smartphone ownership will be the assumption of a working knowledge it. With so many people using it, the owners will automatically assume that most people know how to use them. Another major assumption will be that everyone has one. I know on a regular basis now people tell me, "You can do this on your smartphone." That is under the assumption that I have a smartphone. While I do have a phone, it is a very "dumb-phone."
People will want to utilize many of the functions that smartphones have in classrooms, but I doubt that will be allowed. Schools like to keep communication between teacher and students/parents very visible and communication with smartphones will not allow that. I do believe parents will think that the teacher should respond to emails quickly, though. The assumption will be that Jimmy's teacher has a smartphone and will get the email straight to his or her phone.
Technology will definitely be expected to be taught in schools. Maybe not teaching with smartphones, but just technology in general. There will be certain things teachers will be expected to use and teach in the classrooms, just like PowerPoint and other things of that sort were when I was in grade-school. For the students I am sure there will be an even bigger assumption that the children will know the technology.
People assume that me and all the other 20-somethings know technology because we are young and have seen it used growing up. As it was pointed out earlier by Dr. Strange, these children will not know a world before much of this technology. Starting out, Google will most likely be about 10 years older than the children I will be teaching. I know people will assume that they automatically come out of the womb working an iPad.
One idea for learning purposes could be for a science class. Depending on what the kids are learning, it can be assigned for them to go take pictures: examples of flowers/trees, basic groups of animals, clouds, or anything identification. Another idea is to video themselves making a "tutorial." There is the saying "if you can teach it then you know it." This could be for something such as math. Whatever are they are working on (ex:long division) have them make a video explaining the steps and working though it as if they were teaching it. Another video they could make could be one related to a theatre type of lesson. They students could work in groups to make a production and then record it.
The students could also be required to make a portfolio of their work in a subject. It could also be used to simply take pictures on a field trip to aid in a later assignment that could be connected to the pictures taken. If there were a science project the students could do that through technology instead of the stand-up poster boards. Depending on the age, the students could be instructed to write a book and then create or take pictures to illustrate their creation. This could be a great resource for anything that could not be brought into the classroom for children to still get the effect of hands-on.