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"It's no secret that fractions are a very difficult concept for students to understand. But why is that? Fractions are an extremely abstract concept, and without adequate concrete and representational experiences, students do not develop mental images of what the abstract symbols mean.   In Texas, students begin formal fraction instruction in 2nd grade under our newly adopted TEKS, but the symbolic notation for fractions (1/4, 2/3, etc.) is not taught until 3rd grade. The 2nd grade standards include: partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole Let's take a closer look at each."

"Whole Child Learning is a thing; Whole Teaching should be a thing too, no? Here at TeachThought, Jackie Gerstein's usergeneratededucation is at the top of our reading list, in large part for her thinking about the human side of formal education. Much of our content-that is, the content here at TeachThought, and that on her site-overlaps because of our shared perspective on teaching and learning: self-directed learning, the role of play in learning, the idea of citizenship, student-centered learning (and student-centered teaching), and more."

Teresa Penedo posted this item in the #change11 Facebook group. The one-hour video tells us "most of what we think we know about technology in general is false." According to Andrew Feenberg, "Our error stems from the everyday conception of things as separate from each other and from us. In reality they belong to an interconnected network the nodes of which cannot exist independently qua technologies." This leads to ten 'paradoxes of technology': "1. The paradox of the parts and the whole: The apparent origin of complex wholes lies in their parts but in reality the parts find their origin in the whole to which they belong. 2. The paradox of the obvious: What is most obvious is most hidden. 3. The paradox of the origin: behind everything rational there lies a forgotten history. 4. The paradox of the frame: Efficiency does not explain success, success explains efficiency. 5. The paradox of action: In acting we become the object of action. 6. The paradox of the means: The means are the end. 7. The paradox of complexity: Simplification complicates. 8. The paradox of value and fact: Values are the facts of the future. 9. The democratic paradox: The public is constituted by the technologies that bind it together but in turn it transforms the technologies that constitute it. 10. The paradox of conquest: The victor belongs to the spoils." from Stephen Downes OL Daily

How do we motivate students to embrace challenge? How do we encourage students to rise to challenges of their own? What is the connection between a meaningful, challenging curriculum and lasting achievement? ASCD's newest e-book, Challenging the Whole Child: Reflections on Best Practices in Learning, Teaching, and Leadership, addresses many of these questions and is available for download free of charge starting today and running through August 16, 2009.

"Each morning as we start our day together, I draw attention to things that my students may have missed or mentions from our Twitter feed. This short time together each morning discussing our Twitter feed has resulted in rich discussions that prompt thinking, cause us to wonder and lead us to seek out further information. There are many opportunities during the school day to incorporate the use of twitter. A good place to start is to read the tweets from the other classes you follow, ask questions or provide comments as a whole class. The following examples will give you some ideas on how to involve Twitter in literacy, math and science. All of the Twitter activities explained can be done as a whole group, small group or by individual students. "

"Everybody is talking about 21st Century skills and preparing students for a whole different world. The truth is that our students have become digital and there are a whole lot of educators around the world who are still "analog". That is why I would like to share my work with my two secondary school groups with as many teachers as possible. Internet and Technology in the Classroom have made a huge change in my daily teaching experience."

"It really all started with the 20+ iPads we loan out to educators. Those suckers are constantly in demand and constantly in need of charging. They're each firmly encased in Fintie Kiddie cases, which, laugh all you want, those things can stop a bullet. And they stand up. And they recline, have carrying handles and come in neon colors, perfect for locating 20+ loaned out units during the chaos of an event, but that's a whole other blog post. Anyway, we've been loaning these iPads out in tote bags, and just tossing the chargers in higgledy-piggledy. Mainly because if you have done any shopping around for charging carts you likely have needed to be resuscitated at least twice when looking at the prices. The cheapest we could find that works with our beloved Fintie cases started at $399.00, and there was no guarantee everything would fit. We've borrowed another department's iPad charging tray a couple times, but a) it cost them closer to $1,000.00, b) weighed close to 25 lbs and c) had no wheels, thus entailing that their tech guy** lug it four blocks each way. The thing about the Fintie cases is that part of their magic durability is that they surround the iPad in thick molded foam rubber - perfect for tossing in bags and bike panniers (guilty!) but problematic for trying to buy a pre-made charging cart, as the slots in those are generally cut for slimmer, uncased iPads. Plus can we get back to the whole cost thing? Are school districts really running around with so much cash? I know I'm not. And thus, with no more rambling, I present: How to Build Your Own iPad Charging Cart Out of Office Supplies"

"Hexagonal thinking is a rich new way to inspire discussion. Now, if you're like me, high school geometry was about as appealing as high school cafeteria beef stroganoff, and you're not too sure about this whole math-English crossover thing. Don't give up! Hexagonal thinking is a really unique way to get kids thinking about connections they might never otherwise make. When you give kids a series of ideas on hexagons, and ask them to connect the cards into a web with clear reasons for each connection, you get them thinking critically, debating, giving evidence, and basically, lighting up a whole bunch of parts of their brains. Each card could connect to six others, or just to one or two. Every person in every group will have a different concept of how things could connect. There will be no right answer."

The Whole Earth Catalog was groundbreaking, enlightening, and spawned a group of later publications.

"10 Ways Technology Supports 21st Century Learners in Being Self-Directed"

"Yes, the Flipped Classroom (Video lessons watched before class time) is a fashionable topic but whilst there's still chalk-and-talk together with standardised testing I feel I must continue to push it. And no, it's not just chalk-and-talk in disguise. It creates a whole new learning environment for the student."

"I've been spending a lot of time in iBooks recently, and have showed teachers a whole slew of features that are new, or not as well known, in Apple's default e-reader. So, without further ado, here are a few of my favorites."

"Want to make like Elton John and Billy Joel, dueling across from each other on two pianos, playing the hits from both of your huge ouvre of pop tunes? Well, except for the whole you're-not-either-one-of-those-guys part, you can play two piano-like keyboards across from another friend on your iPad, with new free app, Duette."

"Google is a whole lot more than searching and gmail. It has a detailed list of resources perfect for any teacher, student, or administrator looking to enhance their education experience. From grants to videos to lesson plan search, there's a lot to see here. This course will cover how to find all the nooks and crannies of information on Google In Education. Take This Course Students "

"Now that we have ushered in 2013, we are at a point where we should look back on the applications that have been gracing the home-screens of many iOS users over the past year. 2012 as a whole was a year of social media advances: developers everywhere found amazing ways to improve and extend the way that we are using social networking websites, and moreover, users who were fed up with social networking being seen as useless have been finding educational ways of making use of social networking and iOS applications in general. Let's take a look at applications old and new that have made their mark over the past year."

"To some people, Finland isn't a whole lot more than a chilly, northern country boasting a population of around 5 million people. Whether you've been to Finland or not, you probably haven't had the chance to take an up-close and personal look at one of Finland's greatest accomplishments to date - its high-achieving education system. Students in Finland have, over the past several years, risen to the top of the academic food-chain, and they've become some of the top scholarly performers in the world. Compared to many other developed nations, including the US and Canada, Finland's high school graduation rates have continued to grow steadily and impressively. Furthermore, a huge percentage of students continue on to earn college degrees, and students at all levels perform exceedingly well on standardized tests."

"I love learning new things and SnapGuide is a fantastic free app that you must explore! Pinterest is a great place for gathering new ideas, and SnapGuide takes this concept to a whole new level. SnapGuide is full of how-to guides that show step-by-step instructions on how to complete a variety of tasks. You and your students can even create your own how-to guides using this free service!"