To be an effective adult in the workplace, you need to communicate your ideas in a clear and concise manner. To collaborate on group presentations in college, you need to share your ideas and listen to the ideas of others. How do we develop these skills? It all starts in elementary and middle school. 

Collaboration no longer happens solely within the four walls of a classroom. Students connect online with both their classmates and with peers around the world. Here are some tools that facilitate social learning: 

  • Skype: All you need is a webcam to chat with people down the block or on the other side of the world. 

  • ePals: Digital pen pals! Find a classroom or project to connect with. 

  • Edublogs: Create a classroom blog where you can communicate with your students or where students can upload their own posts. 

  • Wikispaces: Create a classroom workspace where students can communicate and work on writing projects. Teachers can assign students into teams and manage the completion of their projects. 

  • Open Study: Just what it sounds like! Students can meet other students, study together, and get live help. 

  • Edmodo: A place for students and teachers to collaborate. Teachers can continue classroom discussions online, give polls to check for student understanding, and award badges to individual students based on performance or behavior.

This marks the end of our technology in the classroom blog series! I hope you've discovered a new resource or two that you're excited to implement this coming year. There's an overwhelming amount of digital tools available and it can be tricky when you want to implement them all at once! The key is to start small- choose just one website or app that will seamlessly integrate into your current teaching style. When you're comfortable with that tool, choose one more. Before you know it, you'll have a tech savvy classroom!

You've finished a unit and it's time for students to demonstrate their understanding with a project or presentation. There was a time when book reports and poster board presentations would suffice. That time has passed. Now there are a myriad of options for creating presentations online, from slideshows to animated comic strips with voiceovers. Not only are these types of projects far more dynamic and fun than a book report, but they help kids practice skills they will need in college and beyond; skills that include navigating various programs and designing multi-layered presentations. 

Here are some tools you can use in the classroom to create and publish kids' projects:

  • Creaza: An app that allows you to create digital stories through cartoons, movies, slide shows, and radio talks.  

  • Wordle: Create a "word cloud" that emphasizes important parts of a text, newly learned vocabulary, themes of a unit, and more. Each Wordle can stand alone or be incorporated into a larger project. 

  • Popplet: Visually capture, sort, and connect ideas. The end result is a visual "semantic map" that represents what the student learned throughout the unit of study. 

  • VoiceThread: Adds audio to a presentation. Seamlessly integrates with various programs, such as Blackboard, Sakai, Angel, Canvas, Desire2Learn, BrainHoney, and Moodle.  

  • KerPoof: Create an interactive story with dinosaurs. In addition to stories, kids can make pictures, movies, cards, and drawings. 

These are just a few of the many tools available to create visual, well-developed presentations that demonstrate what students learned throughout the unit. What are some sites or apps you use? 
We've been discussing the use of technology in the classroom. Last week we took a look at some tools that teachers can use to plan and create visually appealing lessons. Over the next few posts, we'll change gears and look at tools for students to use. These range from online games and activities to ways that students can create projects and presentations. 

  • Funbrain: There are so many different categories and types of games on Funbrain, you'll use them across many content areas. They also have games that complement popular kids books, such as Diary of a Wimpy Kid and Camp Confidential. 

  • MangaHigh: Play math games with characters that look like they stepped out of a Manga. You can play a free version of each game. 

  • Carrot Sticks: More math games! These are geared towards kids in grades 1 - 5

  • Diigo: This isn't a game site, but a way to make reading into a fun activity and learning experience. Back before apps were cool, I had my students jot notes on post-its as they read. Now they can create digital post-its with Diigo! Way cooler. Highlight, create notes, jot post-its and more to help kids generate ideas and record information as they read. 

  • Socrative: A smart student response system that engages kids through a series of educational exercises and games which can be accessed on both computers and tablet devices.

There are countless websites and apps with games and activities for students. These are just a small sampling. Feel free to post some of your favorite in the comments! 
I'll spend the next few days looking at useful sites and apps for teachers to use in the classroom. Technology has become a crucial tool in education that can not only save time but enhance a student's learning experience. Using technology, kids interact with the world and organize information they learn in new ways. As teachers, we can expand both how we teach and the content we teach. 

We'll start by looking at tools to help you brainstorm ideas for lesson plans and visually create them. While today's tools are most useful for a teacher to use, in the next few days we'll discuss different sites and apps specifically created for kids' use. 

Lesson Planning Tools

  • Planboard: You can search through posted lesson plans, collaborate with teachers across the world, plan out your lessons and units, and ensure that your lessons are aligned with Common Core Standards. 

  • Mastery Connect: Track student's mastery of standards, share resources such as assessments with an online community of teachers, and access tools that make grading easier. 

  • Youtube EDU: Find educational videos to supplement your lessons. The content ranges from young elementary appropriate to college-level. Also useful for finding supplemental videos: Ted-Ed.

  • Google in Education: Connect with other teachers and share lesson plans, resources, assessment tools, etc. Get organized with Google Docs, Groups, and Calendar. There are also plenty of education apps along with tons of other resources- you can spend a whole day just on this site alone. 

  • Quizlet: Need to assess students' mastery of the content after a lesson? Create your own quiz or browse through pre-made quizzes. 

Lesson Presentation Tools (ever miss when you had to copy pages and pages of notes from the blackboard? No? Neither do we. There are so many better ways to present content these days, from Smartboard presentations to interactive slideshows)

  • Prezi: Create presentations and share them with others. Get inspired by viewing tons of uploaded presentations. 

  • Slideshare: Upload materials you create, such as videos and presentations, and share them with your students or fellow teachers. View presentations others have posted. 

  • TimeToast: Add a timeline into your lesson with this easy-to-use timeline builder. 

  • Glogster: Mash up photos, videos, and music to create a cohesive presentation. You can add effects and animation to make your lesson unique.   

  • Jing: Take a screenshot or record your mouse movements on the computer to create narrated tutorials. 

Are there any lesson planning and presentation tools you love to use? Share them in the comments!

The Story of How Coursera Changed the Life of a 17 Year Old with Autism

This is a story that warmed my heart and made me recommit to never underestimating the mind of another. Coursera offers massive open online courses (MOOCs) to people all around the world, free of charge. They partner with universities such as Duke, Stanford and UPenn to present courses in various disciplines, from engineering to graphic design. I've taken a few courses with Coursera and I've been impressed by the depth and breath of information each professor has offered. I've been impressed by how many people enroll in MOOCs- 140,000 students registered for this course alone! But now I'm also amazed at how Coursera became a platform that allowed an autistic boy to show that he, too, can hold his own n

Find out how Coursera changed the life of this 17 year old boy with autism. When you're done reading, I'm sure you'll agree that it's not impossible to educate all of our children, regardless of their disability. 

Google Earth: Connecting to the World

I like to teach my students how to use Google Earth early on in the school year. Once they get over the fun of looking up their homes and their friends' homes, I use it in a multitude of ways: comparing different landforms, distinguishing between the different oceans and which land masses they border, naming the attributes of urban vs. rural environments, etc. If Google Earth existed back when I was in school, I would have been much more interested in the geography lessons instead of being lost in my daydreams. There was something about one-dimensional maps that didn't excite me, but the visual and three-dimensional aspects of Google Earth keep me (and my students!) engaged for hours. 

I thought I came up with pretty cool lessons using Google Earth until I came across this site. Here you can learn how to lay pictures over the ground, use placemarks, and understand how network links function. They include tons of exciting lesson plans. Bring your students on an adventure through different time zones around the world with, "Exploring Time Zones, A Travel Experience." You can tour Russia, Spain, or learn about endangered species around the world, all from your classroom. 

ePals: Connecting to other classroom

Remember back when you had a pen-pal in school? You'd write a letter, wait a month or two, then get a letter in return. Connecting to other kids around the country or world has become much easier and faster since then. With ePals you can find a classroom in over 200 countries. Teachers and parents list projects, such as, "Class in Virginia, USA Seeks Intercambio Cultural with Spanish Speakers." Each project is accompanied by activities and lesson plans. What an awesome way to make your classroom part of a larger global community!
A week into teaching fractions and your students are dividing M&Ms evenly into 4 piles and cutting pies into 3, 4, even 6 equal parts. You think they’re ready to move on so you start teaching equivalent fractions or adding fractions or comparing fractions...Only to be met with blank stares. So it’s back to basics. Here are some strategies for teaching fractions that worked in my classroom:
1. Start with what kids already know: sharing fairly. 
    Students come to school with a sense of “fairness.” Build 
    on their informal understanding with sharing exercises: if 
    you have 12 jelly beans, how do you divide them equally 
    among 2 people? How about 3 people? Now 4? When 
    students can divide discrete objects, present them with 
    whole objects, such as apples or oranges: How would you 
    divide this orange so that you and your friend get the 
    same amount? Don’t introduce the language of fractions 
    (one-half, thirds, quarters) or begin labeling the fractions until students demonstrate that they can correctly divide objects. If you don't have fraction manipulatives in your classroom, try Donna Young's printable paper manipulatives.  Students can explore fractions (and other math topics) virtually using this fun tool from McGraw Hill.  

2. Use the sharing examples above to introduce comparing and ordering fractions. As the 
    number of people sharing something increases, the amount they each receive 
    decreases. Would you rather share the jelly beans with three people (receiving 1/3) or 
    five people (receiving 1/5)? 1/3 of the jelly beans is greater than 1/5. When comparing 
    and ordering fractions, I also present my students with a chart, similar to this one, that 
    helps students easily visualize how fractions are related to one another and identify 
    equivalent fractions.
3. Connect fractions to students’ everyday lives. For 
  • How much time is left until lunch? 1/4 of an hour.
  • Have students take a survey of the class: How many people like chocolate ice- cream?  1/3 of the class.
  • How much glue is left in the bottle? About 5/8. 
  • Would you rather strike out 2 out of 5 times or 3 out of 4 times? 2/5 is less than 3/4. 
    See how many representations of fractions students can come up with. Check out this 
    lesson plan on explaining how fractions are used in everyday life.  

Using Cuisinaire rods as fraction manipulatives
4. Make fractions visual by using physical 
    manipulatives. One study demonstrated 
    that students average test scores were 
    higher when fraction concepts were 
    presented using physical manipulatives 
    instead of drawings of fractions. 
    Manipulatives include fraction sticks, 
    Cuisinaire rods, and folded strips of paper. 
    A fun alternative to the usual classroom 
    fraction manipulatives: Play-doh!  When students are able to demonstrate their understanding of fractions using physical manipulatives, you can present concepts using virtual manipulatives. One of my favorite resources is the National Library of Virtual Manipulatives (scroll down for the “fraction” resources). Students can also create fraction models and convert them into decimals and percents with Illuminations. 

5. Use an “anchor” in all of your fraction lessons. For example, keep an image of a 
     fractions labeled on a number line posted throughout your lessons. This reminds 
     students that the numerator and denominator aren’t separate whole numbers but that 
     the fraction as a whole is a rational number. If your lesson involves examples where 
     students are creating fractions out of apples, keep an image or actual apple visible: this 
     helps students understand that each piece of apple is part of the whole apple. 
6. I can’t stress the use of NUMBER LINES 
    enough. The core of so many problems 
    with fractions stem from a lack of 
    understanding this simple fact: fractions 
    are rational numbers that lie between 0 
    and 1 on the number line (excluding 
    improper fractions). Demonstrate how 
    to plot fractions on a number line. 
    Create giant number lines on the floor 
    and have students tape fractions on the 
    number line. Teach comparing and 
    ordering fractions using a number line. 
    Use virtual number lines.  

7. Does this sound familiar: “The num..ater.. of the fraction 1/3 is 3.” Even after my tenth 
    lesson on fractions, even after my students could demonstrate how to add fractions 
   with unlike denominators, they just couldn’t remember the difference between the 
   numerator and denominator or correctly pronounce the terms. This is where you step 
   in.  On each lesson or worksheet, have
   prominently displayed. Color code them. Use the terms constantly in your fraction 
   lessons along with the definitions (“The numerator, top number, of the fraction…”) and 
   have students use them when explaining how they solved a problem. Keep the words 
   displayed until every student can use them correctly. 
Fractions are important. If we can help our students build a better foundation with fractions today, they will be better equipped to calculate ratios, proportions, probability and rates tomorrow. What are some resources or techniques you’ve used to help your kids understand fractions?

Fractions were one of the trickiest topics for my students to learn. Prior to fractions, numbers made sense: they were whole, they increased in value as they got bigger, and they usually became larger when multiplied and smaller when divided.

With fractions, numbers were suddenly stacked on top of one another!  Confusing words like “simplify” and “common factor” had to be memorized!  When the numbers grew larger (1/4, 1/5, 1/6) their value decreased!  In fact, they weren’t even called “numbers” anymore, but “numerators” and “denominators!”

It’s no wonder that fractions left my students scratching their heads.

But fractions aren’t only difficult for students with learning disabilities. On the NAEP (National Assessment of Educational Progress), half of all 8th graders couldn’t correctly order 3 fractions from least to greatest. So why are fractions so tricky for our students? Here are some common mistakes my students have made and why they made them:

Students view the numerator and denominator as separate whole numbers instead of a single amount. They know that 7 is larger than 4, so naturally 2/7 must be larger than 2/4.    

Students treat the numerator and denominator as whole numbers. Here they apply the properties of whole numbers to fractions: just as you would add 3+1=4 and 4+4=8, students apply their knowledge of addition to each separate part of the fraction. 

Students struggle with multiplying and dividing fractions because the operations don’t result in the answer they expect. With whole numbers, students learned that division results in smaller numbers, and multiplication results in larger numbers.

However, the opposite is typically true for fractions. Division yields a larger quotient while multiplication yields a smaller product.

While students are often taught the procedural steps for multiplying and dividing fractions, they do so without understanding the underlying concept, leading to confusion in the later grades.    

Students may have difficulty simplifying fractions because of a shaky understanding of division. 

Students often order fractions incorrectly and cannot place them on a number line. They cannot easily count fractions the way they count whole numbers (1,2,3,4…). Instead, there are infinite number of fractions between each fraction-- a fact that even college students have difficulty grasping. 

Students overgeneralize rules for computing fractions. Once they learn that to keep the denominator the same when adding and subtracting fractions, they do the same when multiplying and dividing fractions. 

Now that we know common mistakes students make with fractions and the underlying misunderstandings, what can we do about it? Our next blog post will explore simple instructional techniques teachers and parents can use to build their kids’ confidence with fractions. 

When introducing a new math concept, begin by anchoring students' understanding in a concrete representation before progressing to a semi-concrete and then abstract representation of the concept. 

                                                concrete ---> semi-concrete --> abstract

For example, let's say you're teaching multiplication for the first time. Instead of beginning by showing students the times tables, you'll want to develop their understanding that multiplication is repeated addition. Start in the concrete stage:
Have students manipulate counters, buttons or other objects, creating an array. An array is simply an arrangement of objects into rows and columns. This array has 3 columns and 3 rows, illustrating the multiplication fact 3 x 3. Students can count the total number of counters to reach the answer "9."
When students fully understand how to create arrays out of counters, move to the semi-concrete stage:
In this stage, students are moving away from using concrete objects they can manipulate, such as counters. Instead, they represent these objects on paper by drawing the array using circles, tally marks, stars, etc. Here you can begin introducing more mathematical language ("We are multiplying three times three...") and show how the array is represented by the equation 3 x 3 = 9. 
Finally, after students demonstrate mastery drawing arrays, they're ready for the abstract stage:
When your students can draw arrays to show their understanding of multiplication, it's time to take away that support. In the abstract stage, students are dealing solely with numbers. Numbers are abstract because they're merely squiggly lines that don't mean anything until they're attached to an amount. It's in this stage that students begin to memorize their times tables and record 3 x 3 as an equation ("3 x 3 = 9) without the use of counters or other manipulatives. 
The amount of time it takes your student or child to progress from one stage to the next varies. Some kid will take a few days, some may need a few weeks. The key is to give students the time to internalize the concept at each stage before moving into the next. 

              To summarize the progression when introducing a new math concept:
CONCRETE: using physical objects students can manipulate
SEMI-CONCRETE: making a drawing or other visual representation of the manipulatives without physically holding them
ABSTRACT: using solely numbers without the use of manipulatives or drawings to solve the problem

Consider how you might use this progression when teaching subtraction, adding fractions with like denominators, or comparing decimals to the tenths. How have you progressed from the concrete to the semi-concrete and then abstract with your own students?
I'm thrilled to be writing our very first blog post- welcome! We opened the doors to Luminous Learning nearly four weeks ago, after months of planning and researching and creating materials. With each passing day, we become more excited about the positive impact we can make in students' lives. I want to pass on some of that excitement to you by telling you a bit about why Luminous Learning exists and how you'll find our blog useful. 

I worked with a teacher whose students would go to the corner deli during their lunch period. Midway through the school year, the teacher noticed that his students returned with suspiciously little change for the snacks they purchased. Accompanying his students to the deli, the teacher watched as his students went up to the cashier to pay for their snacks. One by one, the students received the wrong amount of change. 

The students were affected by a myriad of learning disabilities-- ADHD, dyslexia, speech and language impairments, dyscalculia-- that hindered their mathematical reasoning skills and their ability to perform basic math calculations.  Rather than struggling to decide how much change they should receive, the students trusted the cashier to hand back the correct amount. The cashier took advantage of this; five dollar bills became one dollar bills, coins disappeared. Fortunately, the teacher was able to intervene and prevent his students from getting shortchanged. 

This is a common problem for students with learning disabilities but there won't always be a teacher or parent present to protect their students. We're here to help make sure your students don't end up in a similar situation.  

Luminous Learning allows students to practice the math skills necessary to become confident math learners.  Our worksheets are specially crafted with visuals and clear examples that support students' understanding of math concepts. Together, we can help your students and children navigate math in the real world on their own. 

We're creating our blog to be a resource for teachers and parents of students with learning disabilities. We'll be summarizing the latest education news and highlighting the best instructional practices in teaching math, especially to struggling math learners. We want to give you practical tips and strategies that you can begin to implement in your classrooms or with your children today. 

We hope you're as excited as we are to help your students and children become more confident mathematicians. Check back with us regularly to learn math strategies and tips! And please always feel free to leave comments about your own experiences in education.