Hands On Maths with the iPad

Earlier in the year, I wrote a couple of posts on the iPad and Maths Apps. I questioned whether there were apps out there that went beyond number facts drills and calculation games. One of my readers of those posts, Melissa,  let me know about a group of apps called Hands on Maths. This set of apps provide a range of digital versions of hands on manipulative tools that are needed to develop important Mathematics concepts and skills. I am in no way suggesting that they replace the physical tools entirely but they do provide always available, easy to manipulate tools that are linked to independent investigations generated by the app itself.

These apps include digital versions of geoboards, counting charts, Base 10 blocks, attribute blocks, fraction strips, grids, coloured tiles, abacuses and other maniuatives that support the development of basic number and spatial concepts.They would be particularly useful in supporting individual and small group learning plans for students who need visual aids and teacher aide intervention. Each app is customisable and allows for different skill levels and different types of tasks within the same app through a simple user interface. The settings are changed through the “cog” icon, the activities are accessed via the arrow icon and there is a home button to return to the beginning. There is also a tutorial included to explain the use of each app.

What follows is a brief overview of some of the Hands On MAths apps available on the iPad used on how I have used them. For a more expensive look at the apps before purchasing them ( each app is $1.99 AU or the equivalent in your country) the company Ventura Educational Systems has an excellent website providing detailed information about all their apps, including downloadable PDF instruction guides. I wish other app creators would provide this much information about their apps so that you could make informed decisions about purchasing.

BASE 10 BLOCKS

 Hands On Maths:Base 10 Blocks is a virtual mamipuative app that allows you to explore both whole number and decimal place value using the familiar base ten blocks, known in some countries as MAB. It also allows for addition and subtraction of numbers with and without regrouping. It is limited to 3 digit numbers from 100s through to hundredths. It works through simple dragging and dropping of block into a work space and the values are automatically generated as you build the numbers. A useful feature is built in that allows for groups of smaller values to automatically transfer into the higher value accompanied by an arrow that shows where the values transfer to. ( e.g when you make 12 tens in the tens place, it will change 10 tens into a hundred and leave the remaining 2 tens intact). this works in the decimal format as well. As I said in the introduction, I’m not suggesting we do away with the physical block usage as many younger mathematicians in training need to manipulate physical models. Where digital virtual manipulative excel is in instant feedback, quick turnaround of use, instant access and reuse and unlimited resources ( we often run short of blocks in whole class settings). Together with discussion with a teacher on a one to one or small group basis while manipulating the virtual blocks, I see this as a good tool for working with at risk students. I like that the app allows for the use of decimal place value as well, even though here is a school of thought that we should use different models for decimal place value. Me personally, I like to maintain the link between the base 10 system across whole and decimal numbers to show the consistent relationship.

INTERACTIVE HUNDREDS  CHART

The Hands On Maths Interactive Hundreds Chart is a counting board which you can set up starting from 0 or 1 and use to investigate, explore and discover number patterns and sequences. Users can mark out multiple counting sequences using different tools including crosses, ticks, circles and squares( transparent, opaque and solid) of different colours. Using these tools, students can discover patterns, common factors and multiples, predict the next few numbers in the sequence by studying the pattern show so far. They can create their own or follow sequences given by the teacher or other students. Used effectively, much discussion can be generated about number sequences as a precursor  to Algebraic patterns through visual representation. Again the advantage of the digital tool is the quick turnaround in exploring patterns and the instant reuse of the board.

INTERACTIVE COLOUR TILES

Hands On Maths Color Tiles has a huge range of options for developing important Mathematical concepts. The tiles can be used to create arrays for exploring multiplication and division. Addition and subtraction can be explored by adding or subtracting tiles by dragging on or off the workspace. These operations mentioned are supported by a built in pad that supports the calculations being done with the tiles. This pad can be customised to show fractional. decimal and percentage proportions of tiles on the workspace as well. There are also built in grids that can be used to support calculations or be used as graphs or co-ordinates. Symmetry can also be explored through symmetrical grids that create duplicate reflections vertically, horizontally or both as you place tiles on the grid. By exploring this app you will find more and more applications for the range of tools it provides. Read the PDF guide that is available on the website listed above. It gives further ideas. The moe I explore it the better opinion I form on this app. Check it out.

OTHER NUMBER BASED APPS AVAILABLE IN THE RANGE

There are a number of other apps in the Hands On Maths Range that address number concepts. I’ll provide the links here and direct you again to the company’s website so you can check out for yourself what these apps offer.

Number Sense provides ways for exploring whole numbers, fractions and decimals

Number Balance can support the introduction and development of equality, equations and algebraic thinking by providing a balance tool that enables you to crate equations that equal different value combinations on either side.

Tangle Tables and Multiplication Toolkit both give many opportunities to explore basic multiplication concepts in a hands on, concrete way.

Hands On Maths also has a number of apps that support the teaching of geometry and other spatial concepts. I’ll discuss them in a later post.

When I first discovered these apps, I thought they were nice little activities for the juniors to explore. As I explore them deeper, though I can see their applications in higher grades as well, used creatively and in context. In tutoring middle/high school children on the side, I get frustrated by the lack of hands on explorations of concepts by teachers in these schools. I can see a place for some of these apps in the right  context.  I recommend that certainly elementary/primary school teachers give these apps a go. Even if you don’t buy them, check out the company’s website ( I have absolutely no affiliation with them – I just discovered the site today file researching for this post). You might find some great applications for using the real versions of these virtual manipulatives that you can use to improve your maths teaching.

 

The iPad and Maths – Are we there yet? Pt 2 (non Math apps do the job?)

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Can ubergeeks like me find Mathematical applications in the non Maths apps on the iPad? Skitch app and Leaning Tower of Pisa meets angle measuring

My last post focused on the state of apps related to Numeracy education and concluded that the iPad has a fair way to go in how it is being utilized to develop number skills through the current crop of Maths applications. On the whole, there are too many apps focused on rote learning and simple number facts and equations. Having said that, I actually believe the iPad has much to offer teachers and students in Mathematics. However, don’t go looking for the apps in the Education section of the App Store.

I’ve always been a big proponent of making Maths real in the classroom. Yes, every teacher out there wants to make Maths interesting and relevant for their students but sometimes this just comes in the form of “Real life Maths” textbook problems. The danger of Apple’s foray into textbooks on iPads is that we will continue to get the traditional textbook experience with the bells and whistles of interactivity and ‘magic tablet dust.’ The good news from my perspective is that the iPad already is ready to replace textbooks and make Maths an engaging real world experience. What it takes of course, as I have been pushing in this blog since its inception, is quality teaching practice coupled with great, easily accessible technology. And it comes not from Maths apps but the already available, successful apps across all walks of life in the App Store.

Screencasting/Whiteboard apps
Whether you choose Explain Everything, ShowMe, Educreations or ScreenChomp (depending on price, features or usability), using these apps to record children’s learning is a killer feature of the iPad for me. Yes, we can sit them in front of Khan Academy or YouTube and get them to watch someone else teach them how to do Maths but any good educator knows that students learn more by participating in the teaching and learning process rather than being passive receptors of information. With these apps, children can record visually and with audio the strategies they use to solve equations, real problems, geometric tasks, statistics, virtually any Maths task and share with others in the classroom.

If you are lucky enough to have access to an AppleTV and a full set of iPads, the whole class can switch from one student’s iPad screen to another to participate in an engaging real time discussion without waiting for their turn on the interactive whiteboard. Their recordings can be saved and posted to blogs or other online options to share with outside audiences, with possibilities of feedback or collaboration.

This kind of use of the iPad would do far more for developing deep understanding and granting access to authentic assessment than any textbook. It would also encourage the less confident students to share their knowledge without getting up in front of the class. You could just watch their recordings and comment later.

Drawing Apps
Doodle Buddy is a popular app already being used by many students for a variety of reasons. It has many possibilities in the Maths Classroom. Younger students can create pictographs by using the stamp tools to record their survey results. It can then be used to develop more “mathematical” visual representations by drawing around those pictures to make column graphs. The app comes with special backgrounds, one of which is a dot grid. Students could use this to draw paths following directions, create shapes and angles and use it to create line graphs as well.

A more complex drawing app is iDraw. This application can be used for shape exploration using its tools to create transformations through rotations, reflections and resizing. Scale concepts can be introduced and area and perimeter explored through drawing plans of houses, gardens, playgrounds and the like.

iDraw

Further engagement could take place through a specific house design app called Home Design HD, which not only gives you a wide range of tools for precision drawing and measuring of house plans but also converts the plans into 3D models.

With the Skitch app, students can import pictures then use annotation tools to divide them into grids to make arrays, plot a path on a map screenshot, annotate graphs, draw angles on an image then measure with a real protractor. They can use this for real trigonometry problems instead of detached examples from textbooks.

Video Apps
Children can become engaged in sharing their Maths understanding by making learning videos with iMovie, recording entire lessons with concrete materials as support for presenting what they have learnt.

iMotion HD is a time lapse/stop motion animation app that could be used to record shape transformations made with real materials then played back and slowed down to discuss the transformations as they happen. Time lapse photography with this app could be used to record experiments related to measurement and time relationships then played back at different speeds to explore how long it took for ice to melt, for food to cook or a snail to travel over a certain distance. Possibilities are endless for authentic learning here.

Navigation Apps
Imagine exploring average speeds by looking over the results of a car trip, run or walk recorded with an app like MotionX GPS. The app can present its findings in graphs showing distances, elevations, speeds and maps (with wifi). By looking at the break up of the distances travelled and the time taken, engaging authentic discussions can take place about what caused the fluctuations in times taken to travel certain distances, differences in elevations and how that affected the journey, all real life applications of Maths. At a simpler level pedometer apps can be used just to track distances and times on shorter walks around the school to support earlier estimations of distances/lengths

Other Measuring Apps
The Theodolite app mimics the function of a real theodolite and can be used for real angle readings to determine the height or distance away from an object. Just like my earlier Skitch example, this could be use for practical applications for geometry and trigonometry that written problems in a textbook can’t compete with.

Clinometer, Gigantic Compass, Multi Protractor and the Best Ruler are tools that can replace traditional tools for measuring angles, directions and lengths while also providing quick reference to real numbers that can be used for relevant equations. Clock Pro HD provides a range of time recording tools that can be used for many tasks in a creative Maths environment. There are a range of conversion apps that can be used to support work in measurement tasks.

Wolfram Alpha is a workhorse app (Google on steroids)  that can do just about everything in Mathematics information that will support  all areas of Maths. Just read the description on the store to find out more. Here’s a detailed review from YouTube

Cat Physics

Games
Use physics based games like Angry Birds (does anyone need a link for this!?!), Cat Physics, PocketTanks and Super Stickman Golf to explore the use of angles then apply them to the creation of real life models. YouTube already has examples of Angry Birds Physics lessons here. The beauty of Cat Physics is that it shows the path after completing each level so you can actually measure the angle you used and then try out the real model you build. Pocket Tanks actually gives you the angle you are using. Playing these games can inspire students to test out other real applications for angles like golf club design, ramps, pinball machines, mini golf courses and so on.

Yahtzee, Monopoly and Solitaire games all have great possibilities for developing number concepts. There are also dedicated dice and decision making apps like DiceBag, Wheel of Chance and Undecided that can be used to enhanced Probability lessons.

Maths is all pervasive in our lives. So are iOS devices, be they iPods, iPhones or iPads. All it takes for the iPad to become an essential tool in the Maths Curriculum is creativity in finding Maths in our daily lives and using the related apps available. So while I bemoaned the lack of creativity in Numeracy related apps in my last post, I finish this entry confident and excited about how the iPad can make Mathematics an exciting experience for students across all grade levels. A lot of what I have mentioned here may not be staring at you in the face when you look at your country’s Curriculum standards or national standardised tests. But I don’t mind that. Get kids doing real maths, make the links to what the Education Departments want and it will all take care of itself. Be brave, but above all, be creative and real.

This is by no means an exhaustive list of apps or ideas. I would like to hear from others how they have used apps in Maths lessons. I haven’t mentioned spreadsheet/graph making apps like Numbers or Office like apps because we’ve been using them for years. I’m looking for something new.

Can you share iPads – the case for Yes.

PART TWO – the case FOR Sharing
In my last post, I sort of positioned myself in the “iPads can’t be shared” camp. When the boss first asked me about the possibility of getting iPads into our school, one of my first concerns was ‘ for sharing or individual use’. As teachers trialled them last year, they passed them among some eager students and came to the belief it was fine to share them with children who wanted to use them. Everyone has different opinions on the matter. Depends on how much you believe the kids could or should use the iPad. Reality in our situation though is that we are not going 1:1 so sharing is the only option. That being the case, we have to find solutions to the problems I discussed in the previous post.

Dropbox
This is the most obvious and best solution. For those who don’t know, Dropbox is a cloud based network with dedicated mobile and desktop apps that make saving files as simple as saving to a standard file folder. If you want more info, look it up.
With the Dropbox app installed on an iPad, children and teachers are able to save their work from many ( but far from all ) apps and if there is a compatible app on a computer, open it up there as well. Dropbox integration is available in most publishing apps (Pages, Numbers and Keynote being big exceptions) and a lot of other content creation and file sharing/reading apps. You can save attachments from your mail, the internet and other apps as well.

In some apps, like Notability, my favourite note taking app, even have automatic syncing to Dropbox. In my personal use, Dropbox has been a great way of accessing saved files. It is definitely a way of saving and opening files outside of the iPad file system.

However, there still are issues using Dropbox to support shared iPads. The hassle of having to login and log out of the Dropbox app every time a different user wants to access files could make it difficult for easy use. Some students and teachers may forget to do this and save their work in someone else’s folder. The fact that not all apps have Dropbox integration results in inconsistent access. The biggest problem at our school is that Dropbox doesn’t fully function over a proxy server setup that most schools in my system use. You can download your files but you can’t save to Dropbox. I’ve heard some schools have found workarounds to this but we haven’t solved it yet.

So is Dropbox a solution to sharing apps? Sort of – yes.

Googledocs.
Another possibility for sharing is Googledocs. Many publishing apps have Googledocs integration so files can be accessed and saved in the same way as I described in the Dropbox explanation. Same problems arise as well. So again, Googledocs is a “sort of – yes” solution.

Network accessing apps
There are a number of apps that allow you to access the file structures of our computers or network servers. my favorite app, and the one I use successfully is called FileBrowser. It allows me to login to the school network and my computers at home and access any files that the iPad can open. With compatible apps, you can also copy files back into the file system. When it’s possible, it’s a good solution. However, like all of these options, not every app allows you to use Filebrowser to save back, although you can pretty much always open files already in FileBrowser in any app ( except Apple’s own apps like Pages.)

iCloud
No. Least useful option. Good for syncing between personal iOS devices but that’s it. Apple has to do better here. At least integrate Dropbox with your apps. Feel free to disagree.

Email
20120123-195115.jpgMost fiddly but most reliable sharing option. Every content creation app has an email option. As long as your school allows children to email, this will work. It’s just a lot of steps to get access to a file. Having said that, five years ago, it’s what we all did.

Printing
Not quite sharing but obviously a way to hand completed work to someone so you don’t have to keep the file on the iPad. Printing difficulty is another of the criticisms of the iPad which I’m not going to argue about now. It can be done. While there are ridiculously few AirPrint compatible printers currently in schools, my advice is get one Mac on the network ( if you’re getting iPads I strongly advise having a Mac a your syncing computer; Windows and iTunes have a testy relationship at best) and spend $20 bucks on installing Printopia ( click for info). I’ve used it at our school without any problems.

My final solution – don’t care.
Seriously, if you just want to share the iPads and not worry about who’s accessing what, then there is no problem to begin with. If you decide that the iPad will  not be the main content creation device at your school and will be used for specific purposes it best suits, then it’s not an issue. At our school, where the 5/6 students have access to about 100 laptops and desktop computers, the iPads can exist happily as a specific use device.

However, if you are seriously considering iPads as replacements for shared computers and not value added devices, you will need to consider the issues I have raised. Can you share iPads? Sort of. It’s not my ideal setup but it’s something I’m going to have to come to terms with in my current situation (and get that Dropbox issue resolved!).

Again, I would like to hear from others who have successfully shared iPads in their school environment or others who have solved their sharing problems with solutions I have mentioned or ones I haven’t.

 

Web 2.0 = iPad fail?

One of the biggest moves we made in the 5/6 level last year was the integration of “Web 2.0” tools into our teaching and learning practices. Many of the tools entered the classroom psyche through tech savvy students bringing in presentations made at home that wowed adult and child alike. Other tools were introduced by teachers after discovering them on the Net themselves or through my recommendations on our Edmodo page.

Once the students were introduced to them, the ‘digital natives’ took them on board and before we had a chance to ‘check the site policies’, we had projects presented through Glogster, Xtranormal, Prezi, YouTube as well as iMovies from the “Mac Kids”. And the quality and depth of their work was outstanding and engaging! So the last thing we want to do is take these tools away ( although once the dust settled and I had the chance to check the site policies, some of these tools were supposed to be out of bounds for our “Under 13s”. This is something we will have to deal with this year with some deft policy/user agreement and parent permission note writing!)

Which once again brings us to Part 2 of “Do we NEED iPads?” titled “Web 2.0=iPad Fail?”.

Probably the single biggest criticism of the iPad since its birth has been its inability to work with Adobe’s Flash technology. So many interactive websites use it for their animation, video and content creation tools. While a new standard known as HTML5 is slowly being embraced on many major sites like YouTube and many big news websites so iOS users don’t miss out, in the Education Website world which we live in, Flash dominates. Javascript is also an issue.

The problem is that so many sites that the children started using last year for their projects and presentations DON’T work on the iPad. Glogster? Useless. Prezi? No go ( the iPad has a Prezi viewer app but students need to create them first ). Xtranormal? Nope. On top of that, popular sites like NLMV for Math Manipulatives and Jenny Eather’s Maths Dictionary for Kids are also non-functional on an iPad because of Flash and Javascript incompatibilities. Lots of sites the students find with Google for research or online Maths and Literacy games end up having a ton of Flash based animations that bring up blank pages and expressions when visited on iOS devices.Even sites that just offer file uploading options don’t work with the iOS file system.  It might be OK for Steve Jobs RIP and my fellow Apple disciples  to tell us “Flash Sucks” and they hardly notice it missing in their world but in the educational world, it is quite pervasive.

That being the case then, is the iPad too crippled a device to invest in when so much of what is on the WWW for education is out of reach? Short answer – No. Long Answer – No with a bit of Yes and Maybe thrown in the mix.

What the iPad lacks in Web 2.0 access it easily makes up in alternatives through its Apps. To begin with, some Web 2.0 tools have now released their on iPad apps so that they can be used anyway. VoiceThread is a good example of this; Popplet and Coveritlive are others. Any unqualified to speak, anti-iPad blogger who is still pushing the “iPad is for media consumption, not creation” line is completely unaware of the huge array of apps that children can use for content creation. Apple’s own iWork apps ( Pages, Numbers, Keynote) as well as iMovie and Garageband are great, easy to use tools that produce fantastic results for students. There are now ebook creating apps like Book Creator, Demi Books Composer,and Creative Book Builder and other creative options like StoryPatch that make great books for others to explore. Creative visual story/animation/comic apps abound that give children great scope in presenting their learning. Try out some of the following:

ToonTastic  SockPuppets  iStopMotion ( yes its on the iPad)  iMotion HD  Animation Desk
PhotoPuppets  Comic Life  Strip Designer  ScrapPad

Then there are the photo editing apps like Snapseed, Iris and Pixlromatic that are so easy to use and produce great results and Screencasting apps like ShowMe and Explain Everything that can be use to demonstrate their learning in so many ways. Not to mention all the Maths and Literacy apps that easily match the stuff on the Flash Web.
Don’t get me wrong. I love the Web apps like Glogster, Prezi and Xtranormal. So do the students. I want them to use them. Eventually, many of them will convert from Flash to HTML5. Rumour has it that Glogster is close to doing so. Others will follow. We hope.
From what I hear from others on PLNs I’m part of, a lot of these sites are blocked by a lot of schools anyway. That’s a shame but helps my argument. At our school, iPads or not, they still can still use the web tools with the access to laptops and desktops they have anyway. So we can have the best of both worlds. My point is though that the iPad can offer plenty without the Flash dependent world of Online Ed sites. My argument in my last post was that the iPad had to be a different experience to warrant the cost anyway.With the app model instead of Web 2.0, they are.  So does No Web 2.0 = iPad fail? I don’t think so. But what do you think? Is no Flash a no iPad for you?
Next up: my biggest challenge. Can we share iPads?

iThinkthere4iPad

DISCLAIMER: I am a self proclaimed Apple disciple. I just completed the full set over Christmas and my household is now the happy owner of 1 iMac, 2 MacBook Pros, 2 iPads, 2 iPhones, 2 iPod Touches, 2 iPod Nanos, a iPod Classic and now an Apple TV, all linked by a network controlled by an Apple Airport Extreme. The point: I was always going to be asked  to do this!

In mid 2011, my wife’s boss invited us over to dinner to get me to set up his new iPad. At the time, I didn’t have one but as a long time iPhone user, I was up to the task. The following week, after having a good play that night and getting used to it, we got ourselves a brand new iPad too. It was meant to be a shared experience for the family…but it quickly became an extension of my body at school and the good wife had to wait for after dinner to get her fix of Flight Control HD!

At around the same time, the iPad entered the scene in our local school area and the principal was quick to seek them out, having seen me use it constantly at school. Being a rational thinker, I asked her to explain her rationale for wanting to purchase the iPad. Being unsure, I suggested that I would put together a proposal to present to the Leadership team, outline the pros and cons of the wonder tablet ( Apple disciple or not, I’m careful not to pretend there are not issues!)iPad-proposal

After the presentation, which was much appreciated by all, I was asked what to do next. I proposed a small purchase of 8 test iPads to put in the hands of willing testers. The next day I was handed 18OK, so I had 18 iPads to set up and distribute but who for? We decided to get them in the hands of the teachers first but set up a user policy and testing program that was open to anyone prepared to follow my rules.ipad-agreement They were allowed to hand them over to the children to test as well.

At least one teacher from each level took on the task of testing the iPads out, as well as members of Leadership and the PE teacher. On different levels and for different reasons, the initial reaction was very positive and many uses were quickly discovered. They quickly became note taking tools for assessment, task organisers/calendars, book readers, video cameras, story creators, and as I started adding educational games to the iPads, many games were tested out for their usefulness. Enthusiastic teachers attended Techie brekkies to learn how to use them and ask questions. It was all going well…until endofyearitis set in! It was then I realised it was time to get the iPads in the hands of the children – it was their turn to show us what tech can really do. The challenge for 2012 is how to get the children involved.