xiPad + yApps + zAirServer = Engaging Algebra

Algebra gets a ‘bum rap’. Then again, it has a lousy public relations manager. Whoever came up with the whole ‘letters and symbols’ campaign should be sacked. Yes, opening up to Exercise 7D and solving 50 variations of 2x + y = -7 is n0t anyone’s idea of fun. But as I said, Algebra needs a new PR campaign.

DISCLAIMER: I’m just a Primary/Elementary teacher without any official qualifications in High Level Mathematics – No Masters, no Ph.D, just an A+ Average in High School/College Maths and 25+ years teaching kids to enjoy,not stress about, Maths. I may be completely off base with the great mathematical minds out there in what I’m about to describe regarding Algebra but I make no apologies. my students get it this way – including the Year 7-11 students I’ve tutored at home to relieve the confusion caused at their schools. (WARNING: Bear with me, I’ll take a while to get to the point of this post’s title – skip ahead if you want to ignore my Algebra rant!)

Now we have that out of the way, back to my message for today. I have a certain belief about Algebra. I define it as a systematic way of organising, recording and explaining your mathematical thinking using numbers and symbols/letters instead of words and pictures. Where we seem to get lost is that we go straight to the symbol without developing the thinking through the words and pictures/objects. We provide no context or purpose; just a meaningless string of equations with Xs and Ys that need to be solved. I see Algebra as problem solving support, not equation solving.

Last week, I was called in to take a Grade 6 class to release a teacher for planning ( the usual release teachers were unavailable). Maths was on the agenda for the day and I had worked with some of the other Grade 6 students on a similar lesson earlier in the week as a support for some of the high achievers. This time, though, I was on my own and in control so I applied my full tech+Maths kit to the group of students I had for that session.

The lesson/task that preceded this actually had fractions as its focus. One of the teachers had introduced a task involving a a building pattern for shading in grids to make fractions.

The lesson was differentiated to allow for a range of responses. Some needed to build the patterns with counters to discover anything. And then there was “Sheldon” ( not the boy’s real name) whom I walked in on to find him showing his mate the formula for the relationship between square and triangular numbers! When I confronted “Sheldon” to explain his formula and why it worked, he didn’t know how. So began my challenge and the rationale behind the lesson I’m about to recount. In the end, Sheldon actually discovered the key to this lesson I led in the class I took later in the week.

SO…this fraction lesson turned into a pattern and algebra exploration. All the children were able to discover the growing patterns in both number sequences and could describe the change. Square number differences increased by +2, the triangular number differences increased by +1. But that additive thinking was as far as they got. They needed more support to think multiplicatively, to think ‘Algebra’.

Enter (finally we get to the title of this blogpost!) the iPad and AirServer. Yes, I could have done all of this without the technology. I had done so earlier in the week with my small group of advanced students. But the engagement and ease of use was no comparison between the ‘sheets of paper and coloured marker’ group and the iPad and AirServer. If you are unaware of AirServer, I explained its significance in a recent post. Basically it projects multiple iPad screens onto a computer connected to a projector/iWB.

We started with creating the fraction grids using the iPad App Hands On Maths Color  Tiles ( I reviewed this and others in the Hands On Maths collection last year ). Again, we could have hand drawn grids or made them with counters but I had the students more engaged by getting them to make 1 grid each using Color Tiles and getting multiple students to project their grid onto the whiteboard using AirServer. This took 1 minute instead of 10 and allowed us to move straight into discussion with all the visuals needed on the screen – created by students, not me.

We then discussed the three properties visible in these tiles – side length, square size and the shaded (red here) area ( they hadn’t recognised them as triangles yet). I introduced the problem solving strategy of ‘Make a table’ – a strategy that should be embedded in their thinking by now, but it wasn’t. I created the table on my iPad and projected it on the screen. The students then created their own tables, using Numbers, on their iPads and filled in the side lengths, square sizes and shaded areas. Once they had the numbers in tables, they could start looking for relationships in numbers across the properties, rather than just look at the isolated number sequences. It was at this point that some students were able to recgognise that the shaded area numbers increased by adding on the next side length.

From that discovery, some children then saw that by adding the side length e.g. 4 to the square number 16 ( by this time we had recognised these as square numbers, not just square size), 20 the shaded area was half the size – 10. Here we talked about the importance of proving our theory by testing with other numbers. EVERY child in the class then tested this out with the other numbers, using Explain Everything as a whiteboard to quickly write out equations and project them on the screen to show their proof. Again, this could have been done on paper but by spotlighting everyone through the AirServer iPad mirroring it engaged those children who more often than not pretend to do the work and then let the teacher pleasers to put their hands up and call out the answers. This process really had everyone involved at all times. Some of the less than stellar mathematicians were excited about this discovery. But we were not finished.

I wanted them to see what type of numbers they were creating with the shaded areas – most still didn’t realise. This time I went back to old school methods -

counters. AirServer and my iPad still played a role. I asked the group to use the counters to create the sequence of numbers in the shaded area column in rows. As they began, some weren’t sure what to do. Instead of telling them what to do, I used my iPad’s camera to spotlight pairs who were building triangles onto the screen, thus giving support to others who needed a hint. Every group then wanted their triangles on the screen as well! This idea of spotlighting using iPad and AirServer can work in many ways to maintain engagement – kids like to be on show and recognised .

Once this was done, the students realised they were creating square and triangular numbers and that there was a relationship between them. Children started to recall the rule we had discovered – square the side plus the side then half it gave us the triangular number. But I posed one final challenge – why does this work and how can we show it with our tiles to explain the relationship? Back to Color Tiles we went. We recreated our two coloured square tile pattern. Then we added an extra column/side length. Bingo! The students recognised that this created two equal halfs, a red and yellow half- two triangular numbers!

4×4 Square with extra column of 4 results in two equal shaded areas- triangular numbers!

The final step in the process now was to put all of these theories into one explanation and come up with a formula – finally Algebra was coming into play. The important thing here is that they were thinking algebraically all along – I just didn’t tell them because Algebra is such a dirty word. Now they were quite excited that they were doing algebra.

I asked them to take screenshots of the tiles and the table and import them into Explain Everything. Then we looked at the table again. I explained that the only difference between what we had been doing and algebra was that we needed to replace our words and ideas with letters and symbols. What was the starting point? The side lengths. What will we call them – we decided on s ( could have been x,y, l etc). What is the square number? s x s or s^2. What did we do next? +s. Finally we halved the total ÷2 . With all these symbolic represenations students were able to create a formula for finding a triangular number: (s^2 +s)/2

Now thinking they were expert mathematicians, the students were able to record their understandings in Explain Everything AND find any square and triangular number without creating a long sequence. And they got it because we started with the thinking and investigating, not the formula that “Sheldon’ told us about. By the way, he worked this out independently and actually helped out my thinking with the idea of adding the extra side to the square grid – that’s the first time I had visualised the two triangular halves. This shows that our high achieving students can support the learning in the class – they just need a biy of guidance in their thinking, He was happy with knowing the formula. Now he UNDERSTANDS the formula and why it works. His discovery helped the less able students to also understand the thinking behind it all. And the iPad, the apps  and AirServer kept them engaged long enough to get there.

Oh, one more thing. I mentioned earlier context and purpose. I put this whole task in the context of a tile designing company. I talked about how the construction of Federation Square ( a modern structure in the City of Melbourne laden with geometric designs ) was not a random design. It was very mathematical. I put to them the scenario of customers wanting a design like the one we investigated created at a size of their own choosing. As employees of the company, we needed a method for quickly calculating how many of each tile we would need – the formula we discovered would get the job done.

Algebra need not be hard. It’s just logical thinking written down in an organised, symbolic way. Taking students through the right process can demystify it all. And it doesn’t hurt to use a bit of tech like my good friends the iPad and AirServer to help them along the way.

AirServer – 30 Apple TVs for the price of One (and instant sharing and engagement in the Classroom)

This is not a Plug. I actually happily used AirServer’s competitor, Reflector, before I discovered AirServer, and it has some features AirServer lacks ( namely the ability to record the iPad screen in action on your computer). I also am a happy owner of an AppleTV at home.

What is your tech of choice for getting groups of children interacting with technology? Interactive Whiteboards? I was a big fan early on. I used to prepare my whole day on my computer at home with all my lessons set up on the software available and come to school all ready to go, After a while I saw a teacher ( or an individual student – maybe two) standing in front of an expensive whizzbang electronic version of a blackboard, doing the same chalk and talk method we’d been doing for decades. A lot of money invested, not sure if it was value for money. What about Apple TV? Much cheaper than iWBs, able to mirror iPads on screen, pass the iPad around to engage children in the learning, but still only one at a time. You still need a screen, TV or iWB, and it’s still a fair investment at $99-$129 ( depending on country) per Apple TV.

Last year, I discovered a better AND cheaper alternative. First it was Reflector, then AirServer. Both were originally Mac OS X only apps, then limited PC versions without audio, but now regardless of operating system you get the full feature set. So what is AirServer? ( I often assume everyone in Tech and using iPads has heard of everything I use but I always discover it’s not the case.)

AirServer is basically a MAC/PC app that turns your computer into a mirroring device for iPads, iPhones and iPods ( depending on the version you have) as well as Mac Laptops running Mountain Lion . Your entire iDevice screen appears on the computer screen and whatever you do on the iPad et al, is seen AND heard on the computer screen. Connected to a iWB, data projector (and speakers) or LCD TV, an AirServer enabled computer becomes an Apple TV. The creators were, and probably still are, more interested in marketing it as a way for iPads to replace Wii/Xbox/Playstations as a game console on a big screen, but I see it as a far greater tool for education, IF you are serious about iPad implementation at your school.

 Compared to Apple TV, or a iWB with software included,AirServer + iPad has several advantages.

First the price. Check the screenshot above. $3.99 per computer! For that price, we are virtually fitting out our whole school with Apple TV functionality for the price of one Apple TV.

Portability and ease of connectivity. Last year, when we first started using iPads in the classrooms, if we wanted to show what was on the screen, we had to attach an iPad VGA connector to the VGA cable and remain tethered to the iWB. With AirServer, you just swipe up ( or double click Home Button)swipe across on the iPad App switcher bar at the bottom, hit the AirPlay Button and the iPad is on the screen. You can even do it from another room.

Multi-view. This is the ‘game changer’ ( ugh! I swore I’d never use that cliched buzzword but…). The biggest difference between Apple TV (0nly one screen at a time) and AirServer is the fact that you can mirror multiple iDevice screens on the computer/iWB/TV screen at the same time. Instead of waiting for control of the whiteboard pen, students and teachers can just project their iPad screen straight onto the larger screen. No longer do we have to wait for the teacher of student to finish writing on the board and then getting out of the way so we can actually see it. The work that is done on the iPad screen can be instantly shared without wasting time reproducing it on the iWB. Time saved, time used more productively. This has so many possibilities in the classroom.

  • A Maths classroom where multiple strategies created by the students are shared simultaneously and discussed.
  • A Literacy classroom where students can share their notes, collaboratively write paragraphs, edit shared texts and compare choices, or share drafts for others to read to feedback on, with the writer making real time changes as the feedback comes.
  • Multiple videos showing different views of the same event or object.
  • A music classroom using Garageband with children combining different instruments at the same time to create a digital orchestra,combine parts of the same song for harmonies or multitrack experimentation or simply share their individual creations wirelessly.
  • A Science classroom where different observations, diagrams, videos of experiments are shared and compared.
  • A video and text can be played simultaneously to compare and contrast how a particular part of the story is portrayed in different media.
  • Ideas can be shared concurrently instead of waiting for turns, allowing students and teachers to focus on a specific point of their choice rather than waiting for turns.
  • Collaborative teams presenting the work without having to spend time cobbling all their individual efforts together into a single PowerPoint/Prezi etc. Each student can just mirror their iPad on the screen at the same time and control a video, audio clip, slideshow, comic strip, ebook, themselves.

Multiple iOS devices on the one screen

I could list many more possible uses but I’ll let you brainstorm for yourself. Feel free to share here. Remember, all the screens are fully operational at the same time. That includes App switching, multiple audio,video and game playback at the same time, file editing, and with very little lag time ( depending on your wi-fi quality, of course.) I have mirrored seven iPad screens on the iWB at the same time but there comes a time when they get too small to view. Of course, you can select a single screen to enlarge to full screen, while the others remain connected in the background, waiting their turn to take centre stage. (UPDATE:apologies for being slightly misleading here: while this is certainly a very useful feature on Mac computers, this enlarging function doesn’t seem to be available on PCs. Hopefully, this will be added in a Future update. I spend most of my time on Macs with AirServer and I will update if other features aren’t available on PCs at our schools. Sorry for the misinformation. Should have checked)
It’s easy to set up, a couple of swipes and clicks to activate and cheap compared to the alternatives. Reflector, which I discovered before AirServer has similar functionality plus the ability to record what is mirrored. The big difference, and its not a plug but reality, is the price difference.Individually, there is little difference but when it comes to bulk purchasing, $3.99 per computer versus $55 for 5 computer licences made AirServer my only choice in the end. Both are great, though, and have the potential ( I hate using that word but….) to make a big difference to educational technology and education in general if done properly.

Download AirServer and give it a go. You can download a 7 day trial for free to see if it works in your school environment before you spend the money.

And again, please add your suggestions to my list of uses by posting a comment.

Essential Paid iPad Apps for Schools

I’m not a big fan of Top 10 lists but after a year of experimenting with apps on iPads at school, it’s getting to that time when decisions need to be made on what apps we will invest heavily when the App Purchasing Program comes into full effect in Australia, hopefully soon( Yes, rightly or wrongly, I have been running multiple copies of apps from one account for testing purposes, waiting for Apple to release its Purchasing Program so we can be 100% legit. If they had it in place from the start, I would have done it from the start.) So I’m starting to put together a list of what I think are the essential apps that are worth spending the money on for bulk purchasing.

In making my choices, I’m considering multi-purpose apps that can be used across all curriculum areas, apps that take advantage of the multimedia strengths and apps that can help us use technology in new and innovative ways that can change the way we teach, not just do it the same way with a different tech toy. Some apps are needed to handle the shortfalls of the iOS in a shared network setting and others are chosen because they can make the iPad interact with other tech in the school.

I understand that for some schools the cost for a large number of apps for a 1:1 iPad setup may become prohibitive but in our setting of sharing small numbers of sets, the price is controllable. I’m also from an era where we spent (and still do ) $1000s on Microsoft Office licenses that restricted us to using 3 programs with creativity limitations or $1000s on licenses to use a couple of CD-ROMS that quickly became obsolete. For far less and with free upgrades, we can buy a wide array of apps that offer great creativity options for different learning styles. So here are my essential paid apps, in no particular order. Feel free to agree or disagree. (Prices are in Australian $, similar but sometimes slightly  more expensive than US prices, despite our dollar being higher!?!) Get an app like AppShopper to keep track of sales – I actually bought a lot of these apps at discounted prices. Also, even though I haven’t had access to it yet, my understanding is that The Apple App Purchasing Program discounts prices when apps are bought in bulk.(These prices are current as of August 22nd, 2012. Prices do change.)

FileBrowser ($5.49)- effective access of school network for transferring files through open in… command, transfer of picture/video saved to photo library, views a large range of files. Here is a post I did earlier on this app, including video instructions. It’s the best solution I’ve found for working with our school’s network and is an effective way to get a lot of work created on our shared iPads onto individual student’s folders. It means we can delete work on iPads when they are completed, freeing up space for others to use.

iCab Mobile ($1.99) – full featured web browsing with great downloading capabilities( especially video) and sharing functionality . Great for capturing clips of the internet that could then be imported into iMovie to make documentaries. The collaborative research possibilities are endless with the range of sharing options. I wrote about this app in this post on Safari alternatives.

Notability ($0.99) – Low cost word processing (if you don’t want to spend money on more expensive word processing apps more compatible with Word) with sufficient formatting and image importing and labeling. Its main function is as a  full featured note taking app with-

  • in app web browsing and web clipping ( great way to collect websites and quickly access them
  • note synced audio that links audio to specific notes automatically – great for reviewing presentation notes
  •  simple drawing capabilities including graph paper backgrounds for creating hand drawn graphs and charts
  • efficient filing system for sorting and organizing notes including search. In a 1:1 iPad environment, this can enable Notability to replace multiple exercise books, with each subject having its own category for all related notes.
  • Good file transferring setup with automatic syncing to Dropbox and other options.
  • Can save as native Notability file to open on another iPad or as PDF or RTF ( which can then be edited in Word if necessary. )

GoodReader ($5.49) – my favourite PDF annotation app because of its extensive file system and sharing options. Can link to all major cloudservers, mail systems, WebDAV, etc. for sharing files with other students or staff. Save a truckload of paper by avoiding handing our photocopies ( that then get lost or damaged ). Set up folders in your favourite file servers that students and teachers can download PDF versions of anything you want them to read and work with. You can create Folders for arranging and storing files. A great range of annotation tools for taking notes on PDFs, including highlighting, multiple shapes, text annotation, underlining and arrows/pointers.

Explain Everything ($2.99)
This screencasting app is one of my favourite apps for use at school. There are free alternatives but they are linked to online accounts or lack saving options or advanced features. If you can afford this app over ShowMe or Educreations, get it.

  • Useful across all curriculum areas
  • Alternative to PowerPoint for Slideshow making (instead of buying an extra app like Keynote)
  • Great way for creating tutorial videos for flipping classroom
  • Can be used to record student work in any subject, including audio recording of the student’s thinking and explanation accompanying all of their drawing, writing, working out, notes
  • Can save as videos to photo library which is not an option in some of the free screencasting apps

SonicPics($2.99) – A really simple to use app for any age group ( Grade 1s have used it at our school ), SonicPics is a great way to collect photos together into one file and add commentary. Because of the portability and multimedia capabilities of the iPad, you can take it on excursions with junior grades, snap some photos and record the students’ comments right on the spot. Of course, you could come back and do the recordings in class. The fact that all you have to do is import photos and swipe from one to the next while the audio recording is operating makes this a breeze to operate. Great for language experience, oral language practice, recording ideas for writing, reflecting on and reviewing Maths experiences,working with children with special needs who may not be able to write but can talk about the pictures in front of them. a simple, must have app for me.

Strip Designer ($2.99) – I believe in the power of comics as a communication tool. This comic creation app is easy to use and offers a great range of creative options to allow children to plan, tell and retell stories, record reflections and brainstorms, organise explanations and procedures across curriculum areas, make posters… the list can go on. I love the Comic Life app too, especially the Mac version, and in some ways it looks more polished, but Strip Designer is cheaper and has more options. Features include:

  • basic drawing tools to create your own artwork for your comic
  • lots of photo editing and filter options to alter the imported photos
  • Multiple page creation to make a full scale comic book using a large range of comic panel templates
  • Text editing ( reshaping, resizing, colour)  to make graphic Titles
  • Highly editable speech bubbles and text boxes for recording ideas or narrations
  • “Stickers”  add graphics that enhance the comic’s story telling capabilities
  • Exporting options include iCloud, Dropbox, email, Facebook, Flickr, PDF export, emailing or export to iTunes Strip Designer file to edit on another iPad and save to Photo Library as image ( one page at a time)

iMovie ($5.49) – it’s not in the same league as its Mac Desktop companion but coupled with the built in camera and audio capabilities its a great, quick way to put together an edited video with basic titles, sound effects, back ground music and transitions. It’s easy to use once you work out its idiosyncracies ( it has a good help section that explains each function in detail). In a 90 minute class today with Grade 5 students, all students were able to record, edit and publish videos in one session with a five minute overview of features at the start. The students were absolutely absorbed in the process ( the grade tends to be a noisy bunch in general). Students from Grade 2-6 at our school have created iMovies this year with iPads in Maths, Religion, Inquiry, PE and Literacy. Multimodal texts are an important part of learning today and being able to create them, not just view them is essential. iMovie on iPad makes it easy for young students. I’ve just started investigating Avid Studio on iPad – it has a lot more features which I will probably find more useful, and older students might as well – but for simplicity and expediency, I think iMovie is worth the cash.

Creative Book Builder ($4.49) and Book Creator for iPad($5.49) – I put these two apps together as they both create ebooks – Creative Book Builder has more features and a workflow more suited for older students ( late elementary/primary or middle school); Book Creator can be used even by Kinder/Prep students. I think both (or either) of these apps are essential in today’s classroom where we are trying to make writing more authentic by providing an audience to our students. Students at my school from grade 1-6 have already published ebooks across a range of curriculum areas and seen their publsihed books being read by other students in other grades on the iPads. It’s a great incentive to the writers to see other people read their books. We can even email the books to parents to read on their iDevices at home. Both apps allow text, photos and video to be included in the books. Creative Book Builder lets you include weblinks, glossaries, tables of contents, charts and tables in your books. This allows students ( and teachers) to create complex non fiction texts.

Numbers ($10.49) – Apple’s iWork apps are all useful but a little costly buying all three. Notability can do a good enough job as a word processor, Explain Everything can be a Keynote substitute. Numbers, though, as a spreadsheet app is necessary. It’s not a perfect spreadsheet app and is no Excel in terms of overall features but then I’m talking about students not office workers or adult professionals. Spreadsheets are underused in Maths classrooms often because Excel is full of functions that make it too complicated. I love Numbers’ simplicity. I’ve been using it a lot with my extension Maths group recently to support problem solving and modelling using graphs. They have been absolutely engaged in using the app and love how they can easily make several separate charts for related tasks on the same page. The touch screen workflow seems to come easily to them as was dragging graphs and spreadsheets around the iPad screen. Having easy access to an app that can quickly create data and graphs for analysing in all curriculum areas is a big advantage. Critics of Numbers have to stop evaluating it at an adult level when talking about its use in education. I think its a winner, especially in Primary and Middle School grade levels.

Wolfram Alpha ($1.99-drop in price recently from $4.49) – A powerful app for searching for information. Click here for more info about this app – it has too many features to explain. For Maths, though, I find it indispensable.

Garageband ($5.49)- As a Music teacher among other things, I love this app. But it can be used for so much more. Students have used it to create Radio programs, mixing different recordings of news, interviews, competitions, talkback, music ( created in Garageband or imported in). The drag and drop UI of Garageband makes this process so easy. Other students have used it to record songs they have written as creative responses across subjects, adding voice and music. Other uses have been Readers’ Theatre recordings and recording children read for assessment and feedback purposes. And yes, I have also had students create their own multi instrument musical masterpieces in music workshops. For  creative purposes, Garageband is a must have.

SplashTop (Currently $7.49 but was $0.99 last month – keep an eye out for price drops because it regularly changes) - A great app for wirelessly accessing and controlling a computer from your iPad. Great for moving around the room and letting  students control what’s on the interactive whiteboard your computer is connected to. Needs the free Splashtop Streamer installed on computer

Reflection/AirServer - Not  iPad apps but an app to install on your whiteboard-connected computer. This is a much cheaper option that Apple TV. It allows you to project any iPad screen in the classroom onto the whiteboard. Students in my grade have loved showing their work on their iPads with a simple swipe and click on the Airplay button. More info on their websites. ( click on the links at the start of this  paragraph.)

These are my must haves. I love Art Rage ($2.99) for realistic artwork and Snapseed ($5.49 now but I got it for free – watch for sales) for easy photo editing if you want other creative options. I’m sure different teachers have different favourites and I’d love to hear about other essentials from readers. Technology is not cheap but sometimes if you want the best, you have to pay for it. ( Total cost of listed apps at current prices $64 – with an eye on sales you can get much cheaper). I wouldn’t go into an iPad classroom without these.

COMING UP – Essential Free Apps.