I teach 8th grade computer. Last year while my students were learning about Constitutional Ammendments in Social Studies they were using TT in my class to find stories they believe possibly infringed upon Someone's Constitutional Rights. Mostly these were dress code issues that could be argued limited a person's freedom of speech (expression). they had to type 4 paragraphs, a summary, an argument for, an argument against, and finally their opinion and why.

I'm a 6th grade reading teacher. My kids eagerly jumped into Tween! Here's how I've decided to use it:
- Each week, I will assign a story to read. Students will read the story, comment on it, read someone's response to the story, and comment on that as well.
-Then, students will select a story that they find interesting. They will follow the same format-they comment on it, read someone's response, and comment on the response.
This will be part of their weekly homework assignment. I've been thrilled with my students' responses to the stories on Tween. They think this is a great way to do their homework. Another bonus is that it gets parents involved. I will encourage the parents of my students to read the same stories their children are reading. They can discuss the stories together, which is great for reading comprehension. We'll see how it goes!

Here are some ideas from a Science teacher and a Math teacher:

I was going to use it as a web based homework assignment to post different topics of current events or have the kids post various current events that are related to Biology and other Sciences and they would have to write a critical thinking type of passage that describes the relevance to science and some logical arguments about the topic in general. this way the can get a few things out of this,

1. it teaches them how to research current topics or find details about current topics using creditable sources.

2. it teaches them how to apply what they have learned in class to the real world so they see relevance to them.

3. It teaches them how to make real world decisions based off of what they have learned to make an educated decision or action about real science related events that they will encounter in their everyday lives so that they are well prepared for it when they get out of high school. (Most common example would be family medical relevancies and political topics under discussion for rules, laws, or presidential platforms.)

4. It also teaches them to write and make educated arguments that doesn't consist of texting language and slang conversations.

You can probably dig a few more educational standards or concepts from this. Many colleges and online colleges are starting to go to this type of mandatory out of classroom discussions so it will also help them to prepare for that.

From a Math teacher:

My first thought is to use Tweentribune as a means of providing a few more reasons to read, write, talk and listen. The receptive and expressive communication skills are essential not only to language arts but to all other academic areas including mathematics. The better children can communicate the better learners they become. 
 
As I see it, one of the most important goals of a math teacher is to help students "enjoy" and use math. I want kids to look for "MATH" everywhere. Numbers are everywhere, and were there are numbers, we manipulate them.
 
Math is a gateway subject. Fluency and proficiency with arithmetic, mathematics, and problem solving are necessary for success in life and career. I want my students to look at careers, inventions, technology, games, geography, a trip to the mall, ... with an eye for how numbers and mathematical skills are used. I want them to begin to truly see the relevancy of mathematics for themselves.
 
Given this reasoning, I will use Tweentribune first,as as a small "Extra Credit" opportunity. Students can read an article and, using appropriate writing skills, relate any math connections they make (They may even have to read several to find one they can use, a real bonus the way I see it.).
 
Secondly I will use Tweentribune as a Quarterly Project option where students can use one of the articles to inspire deeper research into how mathematics is used within the context. For example, in the article about the plastic bottle boat (sorry, I can't remember the title), a student might wish to research statistics on recycling, using geometry to navigate at sea,  or charting and measuring storms. The possibilities are only limited by the child's curiosity and imagination. With any luck at all, this will get parents involved too!
 
My final immediate idea is to find articles that relate directly to the content and standards being taught and use them as an anticipatory activity, perhaps bellwork, to spark interest and relevancy and a common experience to promote conversation.
 
I too am interested in hearing what other math teachers are doing.