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The 800-lb gorilla of online math learning. Carnegie Learning's Cognitive Tutor is an adaptive, differentiated learning system in which student understanding is assessed and individually addressed as part of the learning process. It's truly an amazing system, but it's not modular -- in other words, you won't get the best use of it pulling out items for use in your curriculum, because the system's curriculum is intended to be used in full. But it might be worth considering -- results show huge results from this system. See http://www.carnegielearning.com/research/reports/

"Very few people or organizations however constantly discuss and debate "WHY" they do something. It's only by reflecting on the question of "why" that enables us to develop and articulate a meaningful vision for what we should be doing ... and that certainly applies to education." Sam Gliksman, iPads in Education ning

"iEARN empowers teachers and young people to work together online using the Internet and other new communications technologies. Over 2,000,000 students each day are engaged in collaborative project work worldwide."

Thanks for pointing out this one, John! I'd forgotten about it.

"Resources and Annotations from UW-Stout's E-Learning and Online Teaching Graduate Certificate Program. Contributors are mainly from the E-Learning for Educators Course & the E-Learning Practicum Course."

Skip Via explains personal learning networks, or PLNs. Slightly out of date at this point (e.g. Google Wave is gone) but a great explanation of how differentiated learning can happen online.

Tips and tools for educators on how to build a PLN, with lots of examples of great content and resources. 

Information and resources on PLNs for educators.

A passionate and eloquent plea from a university lecturer, attesting to the continued relevance of the lecture as a learning tool. I value her point that a lecture promotes active listening, but I disagree with the notion that a technology that has worked for thousands of years should see continued use simply because it has worked in the past.[1] Given the multitudes of other means of delivery of information today (remember, the lecture was developed when the only other means to spread information was handwriting), the lecture as transmission of information is a tool, not THE tool. She also equates books to lectures, and says that if we abandon one we move toward abandoning the other. A bit of tenuous logic, if you ask me. Still, perhaps worth a read.  [1] See also: http://en.wikipedia.org/wiki/Scriptorium#Trithemius.27_Praise_of_Scribes

"For the inquisitive educator, there are some jewels herein that can lead to stimulating discussions, new resources, and an ongoing supportive network. You just have to know where to look."

Don't know if they're actually "the best," but there are a lot here -- and they cover multiple interests and disciplines.

Free video chat with up to 6 people. Sounds pretty cool.

iPad classroom integrations and information.

A classroom music experience in which 24 kids (many on iPads) and several professional musicians collaborated on a piece of digital music. The piece they created may not shatter any sales records (though it is actually on sale in the iTunes store), but it's certainly not bad for student work. It's unclear how long they worked on this piece, or how many takes were involved, but the resulting music and video are good. And the students are left with a downloadable song that they created. So here are my questions: - are these students learning music? - is their learning transferable to real instruments? - to tweak Sting's words: is technology a legitimate teacher in this case?

An overview of Twitter for professional development as well as some links. "Teachers who are fans say they appreciate the easy-to-use tool as a quick way to network with colleagues. They like being able to ask and answer questions, learn from experts, share resources, and react to events on the fly."

"There is a prevailing conception that students must learn facts and procedural knowledge BEFORE they can then engage in so-called 'higher-order' thinking skills. Educators, parents, policymakers, online commentators, and others point to Bloom's taxonomy (which typically has been portrayed as a pyramid) and say, "See? You have to do this stuff down here before you can do that stuff up top!" But that's not how Bloom and his co-authors categorized the taxonomy..."

"When used effectively, technology plays an important role in enhancing the learning process. Teachers can use digital devices to present supplemental material for lessons or to encourage students to take a more hands-on role in their education. Even with all of the benefits of technology in the classroom, however, educators must use caution to ensure that students are focusing on the lesson and not giving in to distractions. Here are seven ways that teachers can use to help students pay more attention when using technology."

"One of the most common questions we get is, "But where do we find the time to use all this new technology?" To answer that question, we developed this infographic - A Day in the Life of a Connected Educator to show that using social media in your classroom and in your life can be integrated, easy, and fun."

"My 11 year old son just took a course at Stanford. That has a nice ring to it but it is actually meaningless because these days anyone can take a course at Stanford. You don't even have to pay. All you need is access to a computer and a reasonable Internet connection. So what we can say is my 11 year old son just watched a bunch of videos on the Internet. That doesn't make for an interesting post except that this 'bunch of videos' is currently being heralded as the future of higher education." Joshua Gans, Forbes, 5/7/12

Lots of apps and websites to add to your PLN toolbelt.