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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."

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

"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."

"One of my favorite parts of being a part of Maker Faire is sharing all our amazing Makers with teachers who come from all around the Bay Area-really from all over the world!-and then hearing from the teachers why this is such a special part of their year. We're delighted to welcome teachers to the event, whether they are coming with a whole classroom to our special open hours during the new Friday@MakerFaire, riding in style to Maker Faire on one of the buses generously sponsored by Google, or just attending on their own on Friday, Saturday, and/or Sunday. (Click on the flyer at right to print a poster to get your school to come Friday 1-5pm. Parent-organized groups of 10 or more coming after school are very welcome too!)"

"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."

"A whole year and a half ago, I wrote up a five part blog series about how I got to use a set of 20 iPads for two weeks. It was a phenomenal two weeks. "

"The Finns are pretty bemused by Americans' preoccupation with whether to put iPads in every classroom. If a tablet would enhance learning, great. If it wouldn't, skip it. Move on. The whole thing is a little tilting-at-windmills, anyway. That was the gist of the conversation one recent morning at the Finnish Embassy in Washington, D.C., where diplomats and experts gathered to celebrate the country's education accomplishments as Finland turns 100. And Americans could stand to take notes. (Yes, from Finland-again.) Coding and programming are now part of the curriculum in the Scandinavian country, and they're subjects kids tackle from a young age. But unlike in some parts of the United States where learning to code is an isolated skill, Finnish children are taught to think of coding and programming more as tools to be explored and utilized across multiple subjects."

"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."

"When you can get students talking and teaching each other, adding movement or gestures into the process, the students learn and retain more. Whether you call this process "Brain-Based Learning" or "Whole-Brain Learning," the concept is the same. The goal of brain-based learning is to "engage your learners and do it with strategies that are based on real science" (Jensen). Their learning increases because they are engaging more parts of their brain during the teaching process."

"In some ways you can think of Ooomf as a kind of "Pinterest for apps." Users can build catalog of apps that follow a particular theme, and share catalogs with other users. Founder Mikael Cho says if you "identify as a creative, or a traveling nomad, or a hustling innovator, and we have different apps in each category, but the entire idea is to be a part of the whole life cycle of an app, from idea to creation.""

"YouTube is definitely one of the video repositories we teachers and educators use to look for educational video resources to share with our students. But what if the video you find is 30 minutes long and the segment that you want to share from this video is only two minutes long.Would you share the whole video then forward play it to the part you want or is there another simpler way to do it?"

"Feedback is an inevitable part of teaching. Naturally, you're in a position where you're giving a whole lot of feedback, but you're likely on the receiving end of feedback as well. We've all been on the receiving end of feedback in various aspects of our lives, and I'm sure we've all experienced some feedback that was less than desirable - for a variety of reasons. Even if the feedback itself is inherently negative, the delivery and process of the feedback doesn't have to be. The handy infographic below (from ASCD) offers 7 important things to remember about feedback. These are important items to remember both when you're giving and getting feedback. Keep reading to learn more."

"At my district, the MSD of Wayne Township in Indianapolis, we have found that changing the way we think about teacher training not only benefits staff developers and administrators, but schools, the district as a whole, teachers, and ultimately students. A critical part of our revitalized PD plan has been the use of professional learning communities (PLCs), which are essentially groups of educators that work collaboratively and share ideas, often in an online format."

"According to a study conducted in the chemistry department of the Catholic University done by Diane M. Bunce, Elizabeth A. Flens, and Kelly Y. Neiles in Washington D.C., it was found that while the original belief of the 10-15 minute attention span may be true, it was not the whole truth. Here is the rest of the story. It is true that the first lapse of attention (or first break in attention) occurred at approximately the 10-18 minute mark, but after this initial break, the later attention lapses occurred more and more frequently. By the end of class, attention breaks were cycling every 3-4 minutes. In other words, in the last parts of class, students are only paying attention for 3-4 minutes at a time! So what does this mean for you? This means that introducing different elements into the routine may benefit both you and your students by helping them pay more attention so that you can be a more effective teacher. This is where the pomodoro method comes in."

"What is needed to start a Makerspace in a classroom or school? Passion - You need to have passion and a belief in the educational value of maker-style projects. Space - This can be a whole room or only part of a room. Supplies - Start small with simple craft materials. Often sending a message out to colleagues and the community asking for donations of materials works well. Storage - Create a place to store materials when they are not in use and student projects as they are being worked on."

"In today's world, many parents (myself included) are sending kids to after school classes, summer camps, … in the hope that kids will learn something that are missing from school. But one thing we forget while sending kids to these extra curriculum activities is there are a lot we can do right at home. Today we put together these cool STEM (science, technology, engineer, math) activities for kids that you can do in your kitchen. Kitchen science activities have always been our favorite. Now we start expand from Science to STEM. We try to pick the ideas that only use materials you already have or can be easily get from a grocery store nearby, and activities that can be done safely at home, so the whole family can explore and have fun together, no matter the age of kids. It is more important for kids to have the interest to learn than to have the knowledge itself, and the more the learning being an integral part of life, the more they will be interested in learning. And of course, they would love to do activities with their parents. So here we go"

"I will be sharing about our Pinball Machine Mayhem that is happening in our Technology and Innovation class. We started with a brainstorming session on the process this week. We began with the Project Idea phase: This is where we explained that they would be making pinball machines. How they made them or what they used is completely up to them during this process. Next we moved into the Prototype Design students during this phase was given a blank piece of paper about the size of the actual pinball machines that they will make. The goal here was for them to start to apply the different pieces of their pinball machines to this document. What was incredible about this whole process was before we released the students to go work we asked them what subjects do they think will be covered throughout this process. Right away hands went up and students started sharing. Math - Area, Perimeter, Height, Length, Pythagorean Theorem to find the slope of their machine. ELA - Research, Creating a story for their pinball machine Social Studies - History of the pinball machine, Research on different pinball machines Science - Volume, Friction, Gravity, Art - Theme of their board, Creative look of their pinball machine. Tech Ed - Lights, sensors, buzzers Makerspace - Students talked about using little bits, robotic kits, makey makey board, along with legos and Knex's"