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"'ve been reading a powerful new resource titled Beyond Pizzas & Pies, by Julie McNamara and Meghan M. Shaughnessy.  They describe fraction sense this way: Fraction sense implies a deep and flexible understanding of fractions that is not dependent on any one context or type of problem.  Fraction sense is tied to common sense: Students with fraction sense can reason about fractions and don't apply rules and procedures blindly; nor do they give nonsensical answers to problems involving fractions."

"It's one thing for celebrity hijinks or cute animal stories to take off on social media. That happens all the time. It's not too often a math problem goes viral, especially when it doesn't involve a complaint about Common Core. Over the weekend, Singapore TV personality Kenneth Kong posted a logic problem on his Facebook page that was given to high school kids competing in a math olympiad."

"Jean Piaget once said that "play is the answer to how anything new comes about." As educators in the digital age, it is important that we embrace the power of play in our classrooms. One of the ways that we can redefine our practice is by using game education in our schools. Game education is a powerful way to engage 21st century learners in a variety of cognitively complex tasks that lead to deeper levels of understanding. Educational games help students to learn about certain subjects, expand their thinking on specific concepts, and reinforce skill development while they play while increasing engagement, empathy and excellence in the classroom."

"Google Forms allows you to create pages so that all of the questions are not all on one screen. In some circumstances the questions do not apply for every student. If students answer no they are not participating in a sport the section of questions about which sports the student participates in can be skipped. If you are using a Google Form as a formative assessment quiz you can direct students to a page with instruction on the topic if they get the question wrong or go to the next question if they get the question correct."

"Have you ever considered letting your students listen to hardcore punk while they take their mid-term exam? Decided to do away with Power Point presentations during your lectures? Urged your students to memorize more in order to remember more? If the answer is no, you may want to rethink your notions of psychology and its place in the learning environment."

"I do not use a lot of worksheets in my math program.  So much so, that last week, I gave a worksheet during math to my grade 2 students to do and one of my students cheered.  CHEERED! For a worksheet!  I asked the child in my class why she cheered.  I figured that she would have responded with, "I like worksheets."  If she had answered that way, I would have been fine with that. I believe that we all have our own learning preferences and some children enjoy doing worksheets.  However I would never have anticipated what she said to me.  She responded with, "I like doing worksheets better than using the iPads because I don't have to think as much."  "

""One thing we can bet on is that 'making' engages kids," Dale Dougherty, Maker Media founder told Engadget. Anyone that's ever been to a Maker Faire knows that's a solid wager. Children routinely crowd around booths and attractions at the event peppering proprietors with questions about how their devices work. They drag their parents to the marketplace to buy Arduinos, soldering guns, and DIY kits. Getting littles ones excited about science and crafts is easy when it's right in their faces, but then what? That was the question on Dougherty's mind, "what happens on the Monday following a Faire?" The initial answer to keeping kids interested in STEM (Science, Technology, Engineering and Math education) topics was an online summer camp. A virtual meeting place for kids looking to expand their DIY skills and connect with other like-minded makers. Of course, once summer is over, those same kids are left in the lurch. Some schools have implemented a by-the-book rote memorization curriculum with very little hands-on opportunities. So now Maker Camp is leaving its summer roots and going year round with weekly projects."

"We all have them, some good and some bad. We pick them up from friends, family, and even strangers. But we may not recall who we picked them up from or when they began. Because we've practiced them over and over, these seemingly thoughtless repeated habits or behaviors, the pathways in our brain have become so broad, fast, and efficient in carrying them out that we do them automatically without even thinking. Yet these unconscious habits and behaviors add structure and order to our lives and help us to make sense of the world we live in. Our classrooms are full of them. We teachers are pros when it comes to employing and modeling good habits and routines that enable us to manage and carry out the many tasks and demands of teaching. And when it comes to teaching mathematics, we model and teach our students how to carry out procedures and algorithms flawlessly. But why is it that these same students often struggle when confronted with a problem to which the immediate answer is unknown?"

"We understand the worries and headaches that often go along with trying to design and create a makerspace. Just knowing where to begin can be overwhelming. In fact, we hear enough concern over how to create a makerspace that we host an entire workshop on the subject. So, what's the secret to a "correct" makerspace? (I'll answer that below), and how do you get started? Here's how our students did it."

"For too many students, doing mathematics means just plugging numbers into a memorized formula to get an answer. And because they don't understand the formulas they're using, they often fail to use the right one. Take a look at Isaac's work below, for example. He is a fifth grade student who tried to find the surface area of a rectangular prism by incorrectly adapting a previously memorized formula for calculating perimeter. He calculated two times the length plus two times the width (2L + 2W) and tried to account for the height by multiplying it by 4, then adding it to the previous sum. Unfortunately, Isaac is not alone in this type of approach. Students who use formulas by rote may never come to see mathematics as sense-making and may never understand the formulas they use. And there are so many formulas to memorize! Teachers who prematurely introduce students to formulas risk denying them opportunities to develop the necessary conceptual foundations for mathematical understanding."

"What strategy can double student learning gains? According to 250 empirical studies, the answer is formative assessment, defined by Bill Younglove as "the frequent, interactive checking of student progress and understanding in order to identify learning needs and adjust teaching appropriately." Unlike summative assessment, which evaluates student learning according to a benchmark, formative assessment monitors student understanding so that kids are always aware of their academic strengths and learning gaps. Meanwhile, teachers can improve the effectiveness of their instruction, re-teaching if necessary. "When the cook tastes the soup," writes Robert E. Stake, "that's formative; when the guests taste the soup, that's summative." Formative assessment can be administered as an exam. But if the assessment is not a traditional quiz, it falls within the category of alternative assessment. Alternative formative assessment (AFA) strategies can be as simple (and important) as checking the oil in your car -- hence the name "dipsticks." They're especially effective when students are given tactical feedback, immediately followed by time to practice the skill. My favorite techniques are those with simple directions, like The 60 Second Paper, which asks students to describe the most important thing they learned and identify any areas of confusion in under a minute. You can find another 53 ways to check for understanding toward the end of this post, also available as a downloadable document."

"As many of you are aware, I am a big advocate for integrating coding into classrooms of any age. Coding makes students think critically, look beyond the surface, solve problems, debug, collaborate and share. Coding is like solving a giant puzzle, where some answers are more efficient than others, but every kid gets an opportunity to create a solution. It's a student-centred environment which provides immediate feedback and let's kids take risks without fear or judgement."

"I get questions ALL the time from our dear PLN & blog readers! Mostly through Twitter and sometime through email. Let's answer this one I got this morning about my recent coloring & makerspace blog posts!"

"In 2014, The Joan Ganz Cooney Center, a research lab focusing on children, digital media, and education published Family Time with Apps: A Guide to Using Apps with Your Kids. (free on iBooks). A Spanish-language edition of the guide, Apps en familia, became available last fall as an iBook and downloadable PDF. The 20-page booklet addresses the educational value of digital media and offers best practice suggestions. Research-based findings on using apps and recommendations on some of the family activities available through them-from creating photo albums to bird watching-are also included. A separate section answers parents' questions and provides resources for locating quality products. Share the guide and some of our Spanish-language and bi-lingual app recommendations for children with the adults who use your library, and if you don't have any Spanish-language apps on your library devices, it's time to begin a collection. The annotations below excerpted from the School Library Journal reviews when available; title links will bring you to the full review, price links to iTunes, Google Play, or Nook downloads. All of the apps listed are available in the United States. Feel free to add the titles of some of your favorites."

"Are you thinking about buying a 3D printer for your school or classroom?  Before you buy something that could turn into a very expensive paperweight, I recommend you consider these factors. How is a 3D printer going to enhance your curriculum?  Are you going to buy it first and explore the possibilities, or do you already have ideas for utilizing it with students to benefit their learning?  If you would give the second answer, keep reading.  If it's the first, you need to do more research.  If the sole purpose of the printer will be to perform as a 21st century copy machine operated only by the teacher, then you will be doing your students an injustice, as the cost would definitely outweigh the benefits.  The only reason to buy a 3d printer for your classroom is so that students can learn and create. Once you decide that this printer will benefit student learning and you have concrete ideas for curriculum integration, then you need to think about some down-to-earth questions like these"

"The new year is in full swing. Teachers across the world are back to work, sharing thoughts, ideas and resources...ready for what 2016 may bring. With this in mind, we thought when better than to share 16 ways to use the Thinking Kit. Using the Thinking Kit Creator (currently free), educational activities can be created on any browser. The user saves the activity, gets a code, then uses that code in the Thinking Kit App (free) to download the activity onto iPads (or get students to). This teams two really strong themes together - learning using iPads AND digital content creation, whether by teachers or the learners themselves. Activities involve one main goal/objective/question and snippets of information or images to help learners complete/answer it. The Thinking Kit App can be used individually, but works brilliantly as a group activity too. It seamlessly allows for multi-touch and engages learners in face to face collaboration as they learn. There is a dedicated Reflection Stage and lots of tools to help them become better problem solvers, critical thinkers and team players. So, without further ado, let's get started…"

"The Maker Movement has proved itself to be a valuable component of STEM (science, technology, engineering, and math) education ecosystem. The underlying philosophy of this movement involves open-ended creativity, development of critical thinking and intellectual flexibility, as well as instill confidence and a sense of accomplishment. The blueprints for building a makerspace are fairly straightforward, and usually incorporates a few key items like 3D printers, sewing machines, power tools, soldering gear, and maybe a laser cutter. But is it as simple as "build it and they will come?" To help answer the question of "So you have a makerspace, now what?" Jaymes Dec, middle school technology teacher and founder of NYC Makery, served up some valuable advice at our recent SOWING Circle Meetup (SOWING stands for Science Outreach Working to Inspire the Next Generation, and is a gathering for anyone who works as a STEM educator to share resources and brainstorm ideas). In his talk, Jaymes outlined a series of questions to help educators maximize the impact of making in STEM."

"Do you know the differences between JPEGs, GIFs, PNGs, and other image filetypes? Do you know when you should use one instead of the other? Or which is best for storing your photos? How about the difference between lossy and lossless compression? If the answer to any of these is "no," you might be using the wrong image filetype! Here are the basics you need to know. (If you don't want to know the specifics, and just want to know which filetype you should use, skip to Which Image Filetype Should You Use? at the bottom.)"

"I led a training last week on blended learning and asked teachers to brainstorm the biggest challenges they face in the classroom. One answer resonated with me. "Learned helplessness." On my drive home, I kept mentally returning to this phrase. Then in my own classroom last week, my students were beginning a research project that would culminate in student presentations. We've done this type of task before, yet I was bombarded with questions: "Tucker, what should we title this?" "Tucker, how big should the font be?" "Tucker, how do we add an image to the background of our slide?" I have a stock response I use in this situation, "Figure it out." That may strike some teacher as harsh, but I disagree. Our students are conditioned from a young age to ask a teacher for help the minute something doesn't go right or the moment they have a question. Where is the curiosity? Why don't they want to figure it out themselves?"

"Kathy Perez has decades of experience as a classroom educator, with training in special education and teaching English language learners. She also has a dynamic style. Sitting through her workshop presentation with like being a student in her classroom. She presents on how to make the classroom engaging and motivating to all students, even the most reluctant learners, while modeling for her audience exactly how she would do it. The experience is a bit jarring because it's so different from the lectures that dominate big education conferences, but it's also refreshing and way more fun. Perez says when students are engaged, predicting answers, talking with one another and sharing with the class in ways that follow safe routines and practices, they not only achieve more but they also act out less. And everyone, including the teacher, has more fun. "If we don't have their attention, what's the point?" Perez asked an audience at a Learning and the Brain conference on mindsets. She's a big proponent of brain breaks and getting kids moving around frequently during the day. She reminded educators that most kids' attention spans are about as long in minutes as their age. So a third-grader can concentrate for about eight minutes before losing interest. It's a teacher's job to make sure there are lots of quick, effective brain breaks built into the lesson to give children a moment to recalibrate. Perez says teachers must be prepared for a diverse cross section of learners with a large toolkit of strategies for teaching in multiple modalities, with many entry points to participation and content."