Update for HP Prime

Calling all HP Prime owners. Make sure your ROM is up-to-date. The latest update was released early in December. A quick check is to see if you have the full calender function which is new in this release. (Tap in the top write corner to show the setting, then tap on the date. A full calender will come up if you have the new version, if not, go update!). The procedure is unbelievably simple.

You need the connectivity kit installed on a PC and your HP Prime ready to connect with a USB cable. (The connectivity kit software is on the CD or available to download on my web site. Click here). Run the software. It will probably prompt you to update it when launched. Do this and follow the prompts to complete the installation. When complete, launch the software again and plug the calculator in with your USB cable. You will see the your calculator listed. Right click on the name HP Prime and choose update firmware. Follow the prompts. That’s it. Your Prime should be ready. Double check by marveling in the new Calender facility. Check here for a video showing the checks.

The HP community is in full swing now, check out these videos for HP Prime games by the wonderful MicNic Tetris and ’Angry Birds‘ and MasterMind from Tony Galton.

Classroom Maths Dialogue with a Handheld

Now that HP prime is launched and I have a few of them to play with (oh and to run training sessions with …) the implications can be tested of having handheld maths technology that connects easily to the teacher computer in a classroom. Ultimately the connection will be wireless but the dongles will not be available until early next year. So, I bought some 5m micro USB cables and could test it in teaching situations. So far only teacher groups, but I’m getting the hang of it.

Calculators ListThere is free emulator software and the connectivity kit is freely available too. You can try this out yourself by opening a number of instances of the emulator and the connectivity kit on your PC. Just go to http://www.hpgraphingcalc.org/hp-prime-links-and-resources.html for the files. The most impressive thing is how utterly seemless it is. Install the connectivity kit and launch the software. Down the side there are three tabs: ‘Calculators’, ‘Content’ and ‘Class’. Just plug in an HP Prime calculator (or launch an instance of the emulator software and you will see it listed. Here, I’ve plugged in one real machine and am running my emulator. Clicking next to the device brings down a view of all of the content on the machine. Clicking the content tab allows us to author new content and then save it to the machine. You can create tests and polls. (Right click on the thing you want to create and ‘new’ comes up. Click that. When you are done, click the small save icon in the top left of the screen. The dialogues are pretty self-explanatory so I’ll leave you with that. When you are done, go back to the new item you created and right click to ‘send to class’ and it will be on the machine. Imagine being in a classroom in which simply by launching the software and machines being in the room, you can share content with them. No connections no log ins, just get started. But to me it bursts into life when you click the ‘class’ tab. Now you can see the screens of all of the connected machines. (Remember, when wireless is there, connected just means ‘in the same room’.). Class viewThese refresh every couple of seconds (although right click and refresh speeds this up if needs be. Also, right click and ‘project’ creates a resizeable image to show the whole class. So, now I can ask my class to work on a problem and watch what they do. When something interesting happens I can (if I want) bring up that screen to show the whole class. But, there is more, … I can open a messages window. From there I can send a private message to a single machine or a message to the whole class. MessagesThis appears on their screen and they can even respond and we can discuss. Personal in-class responses to individual students work monitoring the outcome of their thinking from the maths appearing on their screen. Now, I always say get students to work one between two, so we’ll have 15 screens up in a full classroom. I tried this with 6 Greenwich PGCE students and it is a bit frantic trying to respond individually. However, really, I should be more teacherly and give the occasional prompt looking our for the ‘Aha’ moments. The possibility to get to the nub of student understanding is tantalising. What do you think? I am dying to get the wireless dongles and try this in a routine classroom with ordinary kids. Then we’ll see what they can do. Exciting times.

What is this maths that we are teaching?

It is with envy that some mathematics educators in England look to our colleagues in the Netherlands where the Freudenthal institute has generated a rich, coherent research debate which has been widely implemented in schools. Realistic Mathematics Education offered the antidote to the formalism of the New Maths based on Hans Freudethal’s view that mathematics was not pre-formed. He said; “… the global structure of mathematics to be taught should be understood: it is not a rigid skeleton, but it rises and perishes with the mathematics that develops in the learning process. Is it not the same with the adult mathematician’s mathematics?” So it is very sad to hear that the Commission for Examinations in the Netherlands is considering banning graphing calculators from public examinations. What is it that a calculator does that could be damaging to mathematics developing in the learning process? A machine can do only what a machine can do. If mathematicians continue to fulfill an important role, then clearly they must be able to things that machines cannot do. In his 2001 novel, Uncle Petros and Goldbach’s Conjecture, Doxiadis’ eponymous mathematician dismisses any process a machine could do as ‘shopping maths’. That of course includes anything a computer algebra system (CAS) could do.

So, learners of Freudenthal’s mathematics should have access to the tools to do the shopping maths, to free up the thinking space to engage with real mathematics; solving problems, generating conjectures, developing proof. These are the art of mathematics, not the mechanical grind. Godfrey Hardy acted as the foil to Ramanujan’s genius, but in the ‘apology’ he makes clear how well he understood that Ramajan’s ability for finding extraordinary new relationships that only he could see, was the real mathematical gift. Getting it into a publishable state was the routine work for afterwards.

The excellent Project Euler takes as it’s premise that mathematicians will have access to a high level programming language (Python, which naturally has a powerful CAS) to engage with problems in number theory. The wonderfully named https://brilliant.org/ designed for potential International Maths Olympiad candidates has a whole section of problem solving requiring programming (and hence CAS) available.

Having a machine capable of high level mathematics available in a public examination in mathematics forces examiners to take a considered view of what the maths is that they are examining. It prevents them from asking students to replicate what machines can do and focuses their thinking on the maths that matters. The maths that Hans Freudenthal was so keen to preserve in the Netherlands, against the onslaught of formalism.

This sad situation was brought to my attention through the English translation of a response by Erik Korthof to an advert for the new HP Prime graphing calculator. He suggests that the absence of graphing calculators in the past allowed the construction of ‘proper exams’. The task of mathematics education should not be to make the lives of examiners easy. Clearly, asking a student to complete a mechanical task that would be simply done by a machine is very simple. To construct a question knowing that the student has access to such a machine is hard. Specifically so, because the question must demand genuine mathematical thinking and that puts great demands on examiners. In the UK, the most progressive mathematics education project (MEI) for A Level students (age 18) have just had their first cohort complete an examination module with a CAS calculator available. The result is thoughtful, highly mathematical questions of exactly the type University maths courses are excited to see. The link will take you to their answer to Erik Korthof’s question: “Is secondary education served with a Computer Algebra System?”. Clearly they answer a resounding yes and MEI are major players in the future of maths education in England.

As I’ve said elsewhere the existence of tools like HP Prime which allow access to powerful mathematical visualization and calculation tools in the classroom liberates students from the mechanical processes that prevent them thinking deeply about the mathematics. Certainly there will be many lessons where the calculators are put firmly away and students will learn and practice these mechanical processes, like drawing graphs and manipulating algebra, not only because they need to see how they work, but also to give them a better feel for the outcomes. Happily teachers are sophisticated enough to manage this. They can also find secure ways to use exam modes to ensure devices adhere to local regulations. Schools are expert in this. These logistical issues should not be used as an excuse for not allowing students the tools that professionals have access to and reducing what is called maths in schools to a collection of mechanical processes. Especially not from the birthplace of RME and the beautiful, powerful view of mathematics presented to the world by Hans Freudenthal.

HP Prime The New Future

HP_prime_front_pictureHP Prime will be launched ready for September and the new school year. Have a look at the teaser YouTube HP released to show you what it looks like. Last week I had one in my hands at a launch workshop in Prague led by GT Springer the lead designer. GT has been central to most of the major innovations in graphing calculator design and he has put all of that experience into a genuinely wonderful new device. Read the interview GT gave to the US tech blog Cemetech. First impressions matter to schools who want to show the smart new kit they are buying and to students who want something really flash in an era where new tech does indeed look good. It is interesting that after a stunned response at the NCTM conference in Colorado there has been a lot of buzz around tech sites like Slashgear and Ubergizmo. Well that’s good, because if the tech savvy think it’s worth talking about then bright young teachers and their equally bright students will take a look.

Being an old fogey myself, all I can say is that it looks very smart indeed,with a brushed aluminium front and a smooth bright screen. The colour is bright and very sharp with extremely clear detail and you just have to keep reminding your self that it is a touch screen and that you can drag and move objects and navigate drop down menus. The touch is smooth and very accurate. Younger folk than me will do this instinctively, I’m sure that they will be wondering how it could be done any other way. It is very well made and feels sleek and smooth all round. It is about 300g which feel sufficiently heavy to be solid but easy to hold and it balances really nicely in tho hands with your thumbs over the Home screen and the CAS button. You really feel you are holding a classy piece of kit. So, part one of the battle is won, savvy young people will want one and schools will be proud to show off that they bought them. So, what does it do?

The biggest headline is: wireless connectivity. Files can be transferred via the connectivity software. However, if you plug a small USB dongle (which you purchase seperately) into the top of the PRIME, it will immediately be recognised on the computer, notably the teacher’s computer in class. Files and settings can then be transferred wirelessly. (Only from PRIME to PC not from PRIME to PRIME). More than that, the PRIME screen can be shown on the teacher’s screen. Then their will be class polling functions allowing the teacher to set a question from her computer and students to offer responses from their PRIMES with the results shown in table and chart form. Just like the polling systems many schools are getting which only do this. That will be just the start of what can be done. The critical point is that this a plug-and-play system. No set up, which is a critical factor for classroom use.

The software itself initially looks like an up-rated version of the HP39gII, which it is, so you will find all of the Apps in the HP39gII working exactly the same. So, anyone who has used a HP39gII will get started immediately. However, there are three new Apps which make a big difference. There is a mathematical spreadsheet, a dynamic geometry system and the advanced grapher. Together these represent a major advance in providing an space to explore mathematical ideas. These tie together with the big pause for breath moment. The CAS button.There is no CAS/non-CAS option. A mathematical machine must speak algebra and this one does. There are two home screens; a CAS screen which deals with exact objects and the traditional home screen which deals with approximate objects. The Apps can use the last object from each of these screens and the choice is always there; CAS screen or Home screen. This recognition of the fundamental pure/applied, exact/approximate distinctions is central to an underlying philosophy which has the potential to transform the way we think about exploring mathematics. For me, this is the thing that will determine future research into maths education technology. The spreadsheet, the dynamic geometry and the advanced grapher can all take CAS and non-CAS statements and allow users to explore the results. Just to get a feeling for what this means, have a look at GT’s handouts from the NCTM conference.

Now the sad thing is that exam boards are scared of CAS and we look forward to a future where CAS systems will transform maths exams by getting beyond procedural questions and towards mathematical problem solving. Well done to MEI for getting an A-level module approved allowing CAS and look to Germany and Australia for examples where CAS is embraced. But in the UK CAS is not allowed. Well, no, CAS is not allowed in public maths exams for which any calculator IS allowed. So, it is quite clear that this machine has a CAS system, so could you use it in an exam? To be sure the answer will be yes, the machine includes a comprehensive exam mode. A menu system allows a vast range of features to be turned on or off, CAS is one of the, but suppose a particular exam disallowed solver apps, they can be turned off too. The system is password protected and the user will simply be greeted with a little round exclamation mark if they try to access or disallowed function or suppressed apps will simply be missing from the menu. For school use, the teachers sets the settings they want e.g. turn off the CAS, creates a password and then beams this setting to all of the connected PRIMES, wirelessly. A series of bright LEDS light up in the same sequence while exam mode is engaged. It is immediately clear to the exam secretary that the machine has only those facilities allowed in exams. In discussion with teachers, it became clear that this feature sets up the possibility to allow younger learners to get started with the machine in a simplified mode and actually presented exciting pedagogic possibilities too.

The exams battle is a big one and many schools still think you cannot use any graphing calculator in a maths exam, so we will need to talk with exam boards and the JCQ to make sure the message is clear enough: you can use this machine in a maths exam and without disabling it as an amazing teaching tool.

I’ve always been a fan of calculators as a learning tool. I’ve said elsewhere that tablets are exciting, but you don’t work and think like that, you need different technological tools for different functions and the resilience of the calculator as a form factor is remarkable  I think for this reason. It’s a highly portable, personal thinking space. I am really excited about PRIME because it has all of the maths you could possibly want with an intuitive touch driven interface, wireless connectivity to support proper classroom dialogue in a package that everyone will want to own.

Please get in touch with me if you see the video and want to be part of early development to get really exciting maths back into our classrooms. I would be delighted to talk to you about the support I can offer.