OK, so I'm still thinking about Math Anxiety and how to prevent or overcome it. One way to prevent anxiety in math is to make sure that our students have a solid grasp of our numerical system. Our number system is based on tens (and so is our measurement system!), so it stands to reason that our youngest students must have a strong understanding of what ten is, and how using tens can help us with computations and estimating. Therefore, working with ten frames is EXTREMELY important for our Kindergarten and Gr. 1-2 students. How much is ten, and how can we partition ten? What numbers go together to make ten? Knowing these facts fluently will lead to ease with mental computations, namely the "Making Ten" strategy of addition and subtraction. But let's not just do drill and kill. There are so many fun ways to learn and practice our 10 facts. Using ten frame manipulatives is imperative, and a topic that I've written about before (click here). I've also written about some of my favourite math apps (click here), but today's post will deal with iPad apps that strengthen students' grasp of making and partitioning 10. The first app (shown above and at left) is called Make Ten+ and is available free from the iTunes store. It's actually lots of fun. Students must click a number at the bottom that goes with the top number to make 10. The game is similar to Tetris in that if the numbers in a whole row are not clicked after a certain time, they rise and you must clear them before they hit the top. Lots of fun, especially for Gr. 1-2 students. The next app is extremely popular with all of the students with whom I've share it. Subitize Tree has several options, but the ten frame option is my favourite for K-Gr. 2 students. The sensei asks players to quickly subitize (say how many without counting) the number of objects shown when the doors on the tree open. If students correctly identify the number, they get a point. Four points sets free an animal that is held captive in the tree. The game gets tense, but not anxiety-type tense! It's available for $0.99. Friends of Ten has six different games that can be played, and all of them involve ten frames. Students can count how many, fill in ten frames, make friendly numbers, and add and subtract. It would be a great math centre! $0.99. The next app I'd like to tell you about is called What's Hiding and is shown above left. Students are shown a ten frame with counters on it. They must identify how many there are by counting as they touch the counters, reinforcing the matching concept that is so important for Kindergarten students. Then the ten frame is covered up and some counters are removed. Students must say how many are left, which we can use to teach the Making Ten strategy, and also the Think Addition for Subtraction strategy! These strategies are so important for Gr. 1-2 students! What's Hiding costs $0.99.
The last app is called Franklin's Friends of Ten. I'm not sure what Benjamin Franklin has to do with Making Ten, but his image is kind of cute! :) This free app involves students identifying the matching number to make 10. When the correct number is provided, fireworks go off. This is a new app for me, and I haven't tried it with any students yet, so let me know if you've used it with your kiddos. Feedback would be appreciated!
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Math Anxiety was a topic at the NCTM Conference in New Orleans that I was so lucky to have attended this month. One of the sessions (of the 750 that I could choose from!!) was called "Convert Math Anxiety into Math Achievement," and was presented by Carol McGehe, a math content specialist. She presented some truths and myths regarding math anxiety. The Truths:
The Myths:
I see educators differentiating their instruction so well in subjects such as ELA, Social Studies, Science and more, and yet, many teachers continue to teach in exactly the same way that they were taught themselves. One lesson to the whole class, followed by a worksheet or exercise from the textbook, and when all your work and corrections are complete, then you go to the math centre. The math centre is where technology is often used as a reward. We absolutely have to learn to differentiate our instruction in math class! Technology should play a huge role in making math more relevant and creative, and not just as a reward when all the work is done. We have to stop creating anxiety by using timed drills and competition between students. We have to show our students that math can be interesting, relevant and even beautiful (look at music, art and nature that uses mathematics!). We have to stop using math as a punishment (stay in at recess and do this math worksheet as your negative consequence). We have to show our students the reasons behind the procedures rather than relying on memorization. We have to teach our students strategies for learning facts, and we have to continue to encourage our students to know the facts with automaticity - something many parents and media think we are not doing. We have to encourage discourse in our classrooms, beginning in Kindergarten. We have to be upbeat and positive about math in body language as well as words. And we need to dispel the notion that math is hard, boring and irrelevant to our world. My next few blog posts will focus on ways to accomplish just that. Tellagami is a free app for both IOS and Android devices. With Tellagami, the user creates an avatar and records a message, called a gami, which can then be sent or shared in a variety of ways. Click on the gami to the left to see an example. Here's how to make a gami. When you first open the app, you are asked to create your avatar. There are just enough choices to personalize the avatar, and you could choose to make your avatar look like like yourself, or another character. Each tine you cick on head choices, the head gets larger, resembling a bobblehead, so that's really fun! You can also choose the main emotion your avatar is feeling. Your next choice is the background. There are lots of choices in the free app, with even more backgrounds available as in-app purchases of $1.99 each. You could also import an image you have saved in your camera roll or open the camera app to take a picture. Another option is "doodle," where you can draw on top of the image you have selected. One of my favourite backgrounds to add is an image that I have created from another app. The example at the top of this page includes a word cloud I made using the app Word Collage. I've also used Pic Collage to make a pretty cool background. Any time you use more than one app during creation, that's called "appsmashing!" Now you're ready to record your message. You can choose to record your actual voice, but be careful if you are adding your students' voices, as the gamis are stored online, so you need parent permission to display student work, including recognizable features, online. The messages are only 30 seconds long, which I feel is a limitation of the app, but it does force your students to get to the main idea quickly. Instead of recording voice, you also have the option of typing your message (limited to 440 characters). When you choose this option, you can also choose the type of voice used by the gami. Kids (and adults) will have some fun with this, and is a great option if you can put your students' work online, but parents don't want their child's voice online. If you click the image to the left, you can hear the gami from the message I typed above. For this gami, I used the Doodle Buddy app to draw a picture, saved it to my camera roll and then imported it for the background. When you are finished making your gami you have several options for sharing, including adding it to a blog, wiki or website, emailing it, or uploading directly to Twitter or Facebook. Here are some ideas for using Tellagami in the classroom:
This is a very user friendly app and would make a great addition to any workstation where students are asked to work either collaboratively or independently. If you have any other ideas for using Tellagami, please add a comment below. I'm always on the lookout for new ideas! What are word clouds, you ask? Well, the image above is an example. Basically, a word cloud is a visual representation of text. They are lots of fun to create, and I have collected a list of ways they may be used in the classroom:
So how does one make a word cloud? I'm glad you asked. I'll start with a couple of websites. Wordle This is the first word cloud website I heard of, and I've used it many, many times. It's very dependable, and easy to use.
Tagxedo Tagxedo.com is a website i've only just recently come across. It's so fun! With this website you can make your word clouds into shapes. There are a variety of shapes to choose from, and you can even upload a photo of your own into the site to make one-of-a-kind word clouds. Tagxedo uses the words over and over again, unlike Wordle, and there are many more options to choose from. When your word cloud is finished, you can save as a jpg to your computer, and even order merchandise with the image. Very cool! To get started with Tagxedo, click "create," then "load." Then enter your text, or copy and paste. Click submit when you are finished (you can edit later if you want to). Again, I think the other tabs are self-explanatory. If you want to add your own shape, click the arrow beside "shape," and click "add image." Be sure that your photo has lots of contrast, or it won't look good. There are some great IOS apps out there that do the same thing on your iPad. Word Collage is an app that works much the same as Wordle ($.99 on the app store). WordFoto ($1.99) is similar to Tagxedo in that you upload the picture and the app fills the photo with the words you input. Path On ($1.99) is not really a word cloud. I'm including it because you input a photo and then draw a line where you want the text. Next you input the text and the words follow the line. It's pretty cool too! See the example below of my lazy cat Sammi. So that's it. That's all I have to say about Word Clouds. Try them in your classroom. Your students will love them! Partial Products is a nice little method for multiplying large numbers. I recommend showing students how to do this method of multiplying before introducing them to the traditional algorithm - the way I learned to do it in school, which was the only method we were ever taught. To multiply 2-digit numbers, have kids begin by splitting up the numbers into expanded notation - hundreds, tens and ones. For example, to do 38 x 7, think of 38 as 30 and 8. Now multiply those numbers by 7. So, 30 x 7 = 210 and 8 x 7 = 56. 210 + 56 = 266, therefore 38 x 7 = 266. The picture above shows this thinking symbolically. Use this method for larger numbers as well. 38 x 45 is 30 x 40, 30 x 5, 40 x 8 and 5 x 8. The picture at the left explains this thinking a bit more clearly. Once you have all the multiplication finished, just add the products together to get the final product of 38 x 45. To those of us who are used to multiplying with regrouping (carrying the tens, hundreds, etc) this sounds complicated, but kids will get the partial products method way faster than the traditional method. Once they understand how to multiply larger numbers, then definitely introduce the shortcut, which is the traditional algorithm, but don't introduce it too soon! If kids learn to do the steps of the traditional method before they understand why those steps work, we are setting them up for a lifetime of math phobia. Check out my YouTube video below for a full explanation of this method, as well as the Partial Quotients method of dividing large numbers, which I explain below. OK, now let's use this method of partial "answers" and apply it to division as an alternative to long division, which is a much hated concept across middle years students (at least, I hated it!). To begin the Partial Quotients method of division, I like to start with a quick list of multiplication facts, which will lessen the mental load I'm carrying while I do the division. So if I'm dividing by 3, I make a list of the 3x facts that can help me - specifically, 3x1, 3x2, 3x5 and 3x10. The example in the picture above shows the facts of 42 that I can draw on to solve 687÷42. Next I think about how many groups of 42 I can take from 687. I use the facts I recorded to check. I see that I can take 10 groups away, so I record that, and take the 10 groups away. Now I still have 267, so I can take 5 groups of 42 away from that, which is 210. I still have 57, so I take one more group of 42 away and I have 15 left over. That means I have taken away 16 groups of 42 and there is a remainder of 15. Therefor, 687÷42=16 r15. Easy peasy. As I mentioned with the multiplication strategy above, introduce this method before you show students the traditional method of "long division." If you introduce the standard algorithm too early, there is the danger of kids learning the "dance steps" without understanding the concept. This is setting them up for failure down the road. I encourage you to watch the video, as the method is easier to understand when you see it in action. Good luck! |
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Lori EmilsonTravelling Curriculum Support Teacher Archives
April 2017
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