I am going to answer this from a method approach as opposed to a rationale. I have concluded that any way you can open up a channel for parents to be aware and more involved in their children's learning is effective. In this age of technology, there should be NO reason for lack of parental involvement.
I found an app that allows students and parents to subscribe (receiving extra credit) so I am able to send out mass messages regarding items such as homework reminders and upcoming major assignment / assessment dates. I have been known to send an occasional bonus question via this method. Our student data system allows for parents to connect for the purpose of viewing grades, attendance, and contact teachers via email. Parents are encouraged (students also receive extra credit for this) to join my online management learning system in order to view instructional material and their children's progress. And despite the caution for teachers not to give out their personal mobile phone, I do. And in eleven years, I cannot recall any abuse of my number. Sure, I may have gotten one or two prank or mistaken calls or texts. But, the benefits far outweigh these minor inconveniences. I also ask for my students mobile phone numbers at the beginning of the school year - just in case. They appreciate this when, at the end of a grading period, I contact them in the event they overlooked something resulting in an undesirable grade.
The requirement for teachers to be able to communicate clearly and concisely with both students and parents is no different than the requirement of many professions to be able to communicate effectively. The whole point of teaching is to be able to communicate ideas and concepts to children in a way that they can understand, and to the extent individual students’ parents wish to remain engaged in their children’s education, being able to express concerns in a sympathetic manner is similarly part of the profession of teaching. The larger the class size, obviously, the greater the challenge for the teacher not just in educating students but in responding to parents’ concerns regarding curriculum, one-on-one attention for their children, relationships among students (are friends a negative influence; is there a student who intimidates other students, in other words, a bully; are children with special needs receiving the extra support they need and the law requires, etc.), and other issues that may concern parents.
Parents can be irrational, or possess expectations of the educational process that are difficult if not impossible to fulfill. They can demand special attention for their child which the teacher may not believe is warranted or, conversely, may resent the teacher’s suggestion that the child in question requires special attention. They might have concerns about the children with whom their child is associating, or resent that their child does not have an opportunity to socialize with friends in other classrooms. There is no end to the list of comments/suggestions/complaints that parents have during the course of a school year. And then, of course, there are the parents who are disengaged and display little or no regard for their children’s education, an entirely different and considerably more difficult problem that may require the teacher to communicate with the parents in an effort at getting them interested and engaged.
A teacher who is not a good communicator is not likely a good teacher – or, teaches gym. Effective communications is the key to preventing problems or to resolving them once they emerge. Most teachers are cognizant of that requirement of the job, and perform their extraordinarily important responsibilities well.
Over the past 40 years as teacher and administrator, I've discovered something really important about communicating with parents and students: do it often and don't wait 'til a child has done something bad.
For parents, create a consistent method of sending home information parents can use, not just random articles in a newsletter that they'll trash without reading. If you do that, you'll find that when you just have to send that note about Patty's recent behavior, you'll have a much more attentive and less defensive audience.
Early on, I began by creating little certificates that I sent home with kids for doing something really nice for another child or when their work was particularly good one week. I wrote a little note on the bottom, explaining what the "award" was for. Later, I tried sending home a little "comment sheet" with my students' weekly progress reports which allowed parents to ask questions make comments. I would respond to those comments and send them back to parents ASAP.
Creating email lists by asking willing parents to give me their email addresses took the place of almost all those methods once the entire district was "wired." I could do all of those things via email, and shoot a message to parents quickly. Some parents prefer email to phone calls, actually, because they're not put "on the spot." It gives them time to think and compose a response more carefully.
Most districts now offer Web sites that allow each teacher to have a page where s/he posts messages, homework and "blog" posts for parents. Some allow parents to view grades via a special "code" that will only show them their own children's grades. You can also have your own Wiki page to do similar things on Wikispaces, etc. Some teachers use apps as mentioned in another response to send texts to willing recipients.They're especially good for reminding parents of upcoming field trips or other events that they might otherwise forget.
And there are things like Google MeetUp that allow you to have parent meetings online as well--for free. You could even have homework help sessions after school on certain days for that. MeetUps are good for little workshops that teach parents how to help their kids with a particular project or to keep them up-to-date on things going on in the classroom. You can find sites that will allow you to have "chats" that don't require Web cams, too--Firefox and Chrome have chat apps that can be opened right from the browser. Or you can just have a blog page that allows parents and kids to post questions to you, so that you can answer them when you have time. But you have to monitor blogs and even school sites carefully. It might be a good idea to require all posts to be previewed first!
Similarly, you can have special Twitter, Instagram, Pinterest, Tumblr and Facebook accounts solely for parents and students, too, if you like. Again, they should be monitored and "filtered," but it can be done.
The simplest and most effective way I found to really communicate with students was to have each of them create a little journal that they were given a few minutes to write in at least once a week as "bell work." I responded to their entries and returned them either while they were working that day, or before the end of the week. Students really seemed to enjoy getting a personal, handwritten response from me about something that was going on in class. Some of the entries were heart rending, some heart warming. So that's something worth trying as well.
I hope a few of these methods are useful for you!