Technology and Maths Exploration

20151008_110555 - Copy (450x800)It is always good to get the chance to actually teach real kids in a real school. I have always said that if you are going to teach students about linear functions, it would be a crime to do it without any technology. So, up comes the topic and in I go with the technology. We have organised a class set of HP Prime handhelds for the school and my job was to get students started using them, so they would be sufficiently familiar at the start of the linear functions topic.

My argument is that if we have a device that speaks mathematics, then we can ask open mathematical questions and then students can explore. So we started with the obvious ‘tell me some interesting calculations that make …’ (e.g. 27 or 3115 or 5.2). Clearly the purpose is to get used to the calculator but when students are allowed to use any function, they really start exploring.

Next, to find the correct app and enter functions, I simply told them the format (something x plus or minus something) to enter in the symb screen on the function app, then asked them to create pairs of functions that matched some pictures I gave them (different slopes, parallel or not).

The exciting thing is to note how quickly students feel comfortable with the technology. The teacher is nervous and not keen to become familiar on their own, but kids feel no fear. The trick for the teacher is managing the classroom in this setting. Make sure the students write down in their note books the outcomes they find (otherwise they will be lost when they need to feedback and so we can see that they are progressing). They are fun to touch, so whenever we had some spoken feedback time it was essential that all students placed the HP Prime face down on the table. Changing mode from paired investigation to class plenary needs some clear management.

It was clear that the students liked the machines and that is nice, but mostly they felt comfortable to explore and try stuff out without fear of being ‘wrong’. The next lesson(s) got students to explore the details of relationship between the functions and their graphs and emphasised the technical mathematical vocabulary used to describe them. I’ll tell you more about this soon.

HP Prime Instant Set Up and Update

I had the opportunity to visit the very beautiful Swiss city of Zurich last week to run a session for Swiss senior high school maths teachers. It is always very interesting to see the differences in the way that mathematics teaching and indeed schools are in different countries. Firstly, the school is for ages 16-19 and has roughly 3000 students in a city centre environment. Striking interior architecture, excellent catering facilities, a range of fascinating teaching spaces and a very well equipped presentation room were all very impressive (and that’s not to mention the three floors of underground heated car parking!)

In Switzerland, they make things. Engineering is highly valued and of extremely high quality. So, a relatively small proportion of these students will go to University and a relatively large proportion into apprenticeships. So, they are interested to see technology that enhances students’ ability to engage with the subject. The discussion was a comparison between HP Prime and TI-nspire. This is a good thing. No-one needs convincing that graphing technology is useful. People are not saying “I’ve just bought some iPads, what can I do with them”.

So, where does HP Prime win? Well, firstly the free teacher emulator and connectivity software kit makes the overall purchase price of Prime rather lower. Secondly the data streaming kit was seen to be very impressive. Instant collection of data, followed by analysis. No set up, just plug in the sensor, press start and watch. I did the experiment where you attach an accelerometer to the end of a steel rule, hold the other end on the desk and ‘ping’ the end with the sensor. It produces a beautiful exponential with trig function, where you zoom in and see the sin curves perfectly smooth. You can easily measure the wavelength to compare with other ruler types and model the decay rate with a two click export to a stats app. However, the biggest win is the simplicity of the wireless system. We were in a very long room indeed and all of the devices connected and stayed connected throughout the session. The total procedure was to plug the USB aerial into my laptop. Plug a dongle into each handheld. Launch the connectivity software and click the monitor button. Select the network on each handheld with three taps of the screen. That is enough to see what everyone is doing, find something interesting, expand that student (teacher/delegate)’s work and ask them to explain to the class. We collected data to compare height and shoe size and almost immediately were having a discussion about about the strength of the correlation (they said low) and it’s measure r=0.91 (which didn’t sound too low!)

The two issues we need to work on are to be sure the software will run on Macs and this should be soon now. Secondly, students develop their work as a project report. So, how can they integrate their algebra and graphs into a text report with commentary? On a desktop, running the emulator together with a word processor will work well enough. However, using the handheld or even working on a tablet, the integration may not be so smooth. I will have a think about these issues and post soon.

The final issue that is really working well is exam mode. With the wireless connectivity this is very impressive. On Prime the exam mode is so highly configurable that exam boards in many countries are now convinced that it is indeed suitable for use in public exams. But the set up takes seconds. The Swiss teachers seemed genuinely impressed by the control this gave the teacher even in a classroom setting. In France, the requirement is that the calculator has it’s memory wiped, which is sad if you have personalised it. But the backup mode is now so simple there is no issue. In the connectivity kit you right click on the calculator name. Choose backup. This creates a zip file of everything on your machine which you can suitably name and stores it in a specially created backups folder. Wipe the machine for exam use and then afterwards, plug it in again and right click again. Choose restore and it will find your backup files, choose yours, click OK. That’s it.

In a school setting with busy teachers, things just have to work. It was good to be in a teaching environment and that is exactly what happened. HP Prime vs. TI-nspire? Well they are different, despite having overall similar functionality, but it seems that Prime does genuinely have that plug and play simplicity that school use demands.

Talking Maths in the Esoteric Domain: HP Prime Wireless

At the ATM London Branch conference on Saturday, Kate Gladstone-Smith from Langdon Park School in East London, presented her research into the nature of communication she had observed in maths classrooms and how this differed according to the set, the students were in. (Anyone not from the UK will need to know that in English schools teachers decide in advance how well students will do with a subject and place them in ‘top’ and ‘bottom’ sets (i.e. class/teacher groups) accordingly).

Kate used a sociological analysis known as Social Activity Method (SAM) devised by Paul Dowling of the Institute of Education, London. He suggests that a practice (in this case mathematics education) has discourse in one of four domains of action. If the content (e.g. solving an equation, constructing a proof) would be recognised as mathematical and the symbols and technical vocabulary recognised as mathematical (e.g. evaluate 3x+1=10), then this is ‘esoteric domain’ discourse. This is contrasted with ‘public domain’ discourse where the content and the symbols/vocabulary would not be recognised as mathematical (but nonetheless a discourse in maths education). Importantly, the task of the mathematics educator is to induct learners into the esoteric domain of mathematics.

Kate found that students only rarely maintain any discourse in the esoteric domain. The teacher would mostly restrict their discourse to metaphor (in solving an equation: “get rid of the x’s”) or make appeals to common sense knowledge (“What is a square? It’s like one of those ceiling tiles”). Perhaps unsurprisingly, lower achieving students had very little discourse in the esoteric domain, while higher achieving students had at least some. However, this was in response to the restricted discourse of their teachers, not necessarily to what they could achieve.

So, I billed this blog as being about HP Prime Wireless. Well, later in the day, I had my first opportunity to use the system in a classroom setting. The class was a group of teachers and maths educators and I gave them an activity to explore conics starting with the form x^2 + y^2 = 9 in the advanced graphing App. I could observe the class’s conics by monitoring their screens in the Connectivity Kit monitor. When I saw an interesting example (a larger circle) I would double click on the screen and show it to the class. I asked; “How did you make the circle bigger”, to which their were two response to the two times this happened; “I changed the constant” and “I zoomed out”. This immediately sets up a rich discussion about the relationship between graph and function and the scaling of the graph. I then said; “Has anyone found a non-closed curve?”, which led to a new burst of activity. When I saw one I could ask; “How did you do that?”. Here, the teacher discourse is generally just teacherly prompting. However, the student discourse is predominantly in the esoteric domain of mathematics. The HP Prime only gives access to esoteric domain mathematics (the graphs and functions in symbolic form) positioning students to make esoteric domain responses.

The second activity was a new way of doing a classic. I sent out a poll asking for shoe size and handspan data. My class entered the data on their handhelds and pressed send. Within seconds a whole class worth of data was available for analysis. In the poll results screen in the connectivity kit the points are plotted and a line drawn, showing an overview of a possible relationship. However, selecting the HP Prime emulator and sending the data to it, generates a new APP on the emulator with full two variable statistics facilities. So, we can see a relationship. We can see the correlation coefficient to see it is a  weak relationship. Then we validate the relationship by seeing if my hands and feet fitted the model. I was a poor fit, so we could discuss why my hands/feet relationship was different from the group (they were all women, which suggested a new hypothesis to test). Issues of experimental design were discussed. Within a few minutes of setting up an experiment we were having a well framed and well informed discussion, entirely within the esoteric domain of statistics.

This was unexpected. Kate’s research suggests it is very difficult for teachers to sustain discourse in the esoteric domain they aim to induct their students into. Harder still for students to work in that domain. Yet by putting students into a setting where they work with technology that only communicates in this domain and by keeping the discourse framed by the technology based activity, the vast majority of discourse is generated in the esoteric domain. See my previous post for a description of the software and how to set up the polls and the monitor. Suffice it to say it is not difficult to set up. Inevitably there are a few teething troubles (notably my 13″ LapTop screen is just not big enough to see the screen of enough connected Primes). Also, it is amusing to see how classroom management techniques are still needed. Calling the class to order and announcing the arrival of a message with instructions is still necessary (even with teachers!). But, teachers using a HP Prime wireless kit could use it in almost any lesson, so they will quickly become fluent in the changed classroom environment.

Please get in contact to share your thoughts or if you would like to see the system in operation. ( Click here to link to the HP Prime pages at to see pricing etc.

Wireless Prime has arrived!

I took delivery of a box of new Primes with the wireless kit last week. This is really exciting. From a pedagogic point of view, it seems to me that the big move is to generate genuine classroom dialogue, supported by serious technology. The Prime solution gives you enough machines for a class, in a box you can easily hold in one hand. You give them out to your students. They turn them on. You launch the connectivity software on your PC and that’s it. Everyone is connected.

The auto-update feature on the software is a joy. The emulator and the connectivity kit both prompt you on launch to update. It is two confirmation clicks and the software is updated. In both cases these are important updates, so you must say ‘yes’! If you plug in (via USB) a calculator while the connectivity kit is running, then that will check to update the firmware. Again if you have any which are not brand new, say yes. It takes about 30 seconds. The wireless kit and the calculators both come with a CD which gives direct access to the software if you haven’t installed it before. There is a small aerial stand which is a USB connection to your PC. This is installed without anything else being needed. The wi-fi dongle is very small and neat and fits under the slide cover. Once this is installed and the software is running, the calculators are listed and their screen visible in the connectivity software on the teacher PC and hence projected for the whole class..

When the dongle is first fitted to the calculator, it is necessary to find the network. This simply involves touching the info panel in the top right hand corner of the Prime screen and touching the network icon that is there.This directs you to a screen with a drop down list which shows that a network is available (HP_Classroom_Network).

On launch the connectivity kit will not show the screen monitors. So, just click the buttons in the top right hand corner to show the monitor and the messages. CC_Monitoring

Here you can see screen shots from 10 Primes plus the emulator. The messages pane is open above.


Although it is very tempting to maximise the screen area for the monitors, You should avoid this, so there is space in the middle to set up an instant poll. (The grey area; if you cover this all up then you will not be able to see the poll window).


When we see a student has done something interesting, we can just double click their screen and a freely resizable window opens, to show to the class and get them to explain.

Click the add (+) button and add a poll. This can have many questions and a multitude of pre-set formats. This is a range of variations on; choosing from list, one or two number input or free text. You can set up a whole class quiz, but better to gather data as you go. For example do the classic hands and feet survey. set up a poll asking for a ‘point’ i.e. two variable data. You click on ‘add’ choose ‘poll’, type a name for the poll and then the poll interface comes up.


Go to the entry for your poll in the content list on the right hand side, right click and choose send. (Before you do this, make sure that none of the screens in the monitor have been clicked as this selects specific machines to send the poll too. you should see a button in the messages pane saying Send to Class (All) and then you know they will all get it!)Capture_5

Now, every machine has the instructions and can go on to enter the data. (Clicking send when they are done).

Now double click on the results entry that will have been created automatically in the content list. Capture_6It defaults to a suitable view according to the type of data making the speed and ease is very impressive.

With emulator running you can choose to send the data either to all of the students or just to the teacher emulator, for further analysis. (Click the machines’ screens you want it sent to). Capture_7



When you do this, a new App of a suitable type (1 or 2 variables stats) will be created with the name of your poll. Capture_8




So, now we can find the regression line and model the relationship and get the summary stats.

This opens up a whole world of dialogic classroom opportunity. Classics like the class survey become incredibly easy to get the data and get ready for analysis and comparison. However, we can now ask all students to use the function app to enter an equation parallel to y=x. We generate 30 responses immediately. Pick out different examples. Ask students what is the same and what is different. We can poll students to choose a whole number between 0 and 10. Look at the distribution of their responses in a box and whisker plot. What do we think of as ‘between’? Now we get deeper conversation, with everyone involved, with software that allows thoughtful mathematical responses.

This cannot be done with iPads or Android tablets. Even if it could, the software is still not a patch on what Prime can do mathematically. For the maths (and science and computing) teacher this remains the way to go. Please get in touch if you would like me to show you the kit in operation or try it out with your students.




Pinch to Zoom on the HP Prime!

If you have an HP Prime (if you haven’t then naturally, you must get one!), plug it into your computer via USB, launch the connectivity kit and prepare to be amazed by the smoothest upgrade you’ve ever seen! On launching, the connectivity kit asks if you want to upgrade the kit and the calculator. You certainly want to do both. When the connectivity kit is finished, launch it again and turn the calculator on. You will be promPted to continue, but aside from that it will get on AND update the calculator’s firmware. Total about 3 minutes, with the the calculator part taking a minute or so.

This sort of thing really matters in schools where their arrival of an update is greeted with utter dismay in the maths department, who look down at their box of graphing calculators and decide if they are going to lose them for a couple of months to the IT technician (err sorry IT techs … many of whom will do it the same day, but well, maybe just sometimes there is a delay … !) or spend an evening doing it themselves and it never works properly. So, seeing this work so smoothly and so easily is a major thing. You can get on with your marking with a pile of Primes beside you and just plug the next one in every minute or so and hit return and that’s it. All in your control and all done.

This time it is a big deal. Your students will no doubt have tried pinching the screen on a graph to zoom in and out. Well you could swish, but you couldn’t pinch. Now you can. The final piece in the graphing puzzle is there. This will make it perfectly natural to all of your students and make exploring graphs seamless. There are also some additional statistical functions (chi-squared and regression) and the dynamic geometry has been substantially uprated, but that will need another post.

The other bit of major news is that the HP Prime wireless system has been announced and is available for order. See the specification sheet. But mostly look at the connectivity kit after the upgrade and imagine what you could do if every students’ machines were connected the same as your current USB connection, but simply, wirelessly, because they were in the room. Double click on the screen shot to project it. Send messages to yourself. Set up an instant poll and analyse you response! Start planning for the first time you can get true dialogue with your students while they have dynamic software in their hands. This is a whole new world and it looks seriously exciting.

IT supporting kids learning in maths: what is the problem?

I completed my PGCE in 1983 (oh my!) and went to work in a comprehensive school in Corby new town in the East Midlands. (Then it was the largest town in England without a railway station, somewhat depressed by the closure of the largest steelworks in Europe). The walls of my classroom had a large bench running all the way round. On this bench were set out about 8 RM 480Z work stations. For anyone who doesn’t remember, these were competitors to the BBC Micro. When I taught transformational geometry, I could pause in the lesson and get my students to gather round the computers and engage with an activity I set up for them where they would create a shape and transform it using LOGO. They would make hypotheses and test them, seeing the result immediately, visually, dynamically.

I have recently observed a number of lessons on transformational geometry in London comprehensives. Despite every classroom being fully equipped with a networked computer and an interactive whiteboard and in every case, the teacher having been trained within the last year on using GeoGebra to teach transformational geometry, not one single diagram moved at all in any of the lessons. Students were shown object and image and asked what transformation connected them. An agreement was reached (often with much disagreement and uncertainty) and that would be that. There was no way that anyone could validate the agreement or see the transformation enacted. This is the traditional teaching method of ‘proof by teacher says’ or its slightly more inclusive counterpart ‘proof by agreement’. Now, just in case anyone who was there in the room with me can recognise themselves, I should share that everything else about all of those lessons was really good, sometimes quite outstanding. It is simply that giving kids experience of the mathematics, rather than showing them how it works, seems to be such a long way from conventional school practice, that even with everything else in place, teachers find it hard to achieve. Yet in 1983, it was just what you did and we had reliable technological tools ready in the classroom to support it.

I have had lengthy discussions about technology in the classroom with colleagues in teacher education and most recently I have heard about the various classroom manager systems that are being developed by the hardware companies and the IWB people. The essential premise is that you connect to handheld devices that the students have. The screens of their devices are available in thumbnail format on the teacher machine and hence the classroom screen (and able to be enlarged to show the whole class the work of an individual). The software has polling and analysis, so questions and messages can be sent and answers received and engaged with. With this level of technology available, it will again be possible to do what I was happily doing in 1983, interrupting an ordinary lesson in an ordinary classroom to engage with an idea dynamically using technology and seeing what the students are doing (I wandered round and looked at the screens and if I saw something interesting, I got the others to come over and see). At the moment, teachers feel they have to book the computer room to achieve this effect and we all know how unlikely/impossible that is.

But it is a compelling thought. Now, the teacher can manage the dialogue, setting a task, students can engage with the software and discuss the issues. When ideas emerge these can be shared with the whole class. A real dialogic engagement. So, what’s stopping us? Wheel the trolley of laptops in and they will connect seemlessly to the network with no fuss and then it’s OK? Of, course it doesn’t/won’t. Not least because controlling dynamic software from a track pad is a nightmare, but have you ever made a half class set of Laptops connect to a network? So, bring in the set of iPads the school just massively invested in. Agh. No manager software and as yet only a very cut down version of GeoGebra.

The Holy Grail is that everyone turns their smart phones on and launches the iOS or Android app they need, and we get some generic tablets for those that don’t have smart phones and these all connect. Even then we would need better software (unless you invest £30 a head for TI-nspire on iOS which is really good). I hope to get delivery of a trial set of HP Prime wireless graphing calculators very soon. Naturally, they do everything that that I have said. The massive difference is that they have an auto detecting dongle (the same as the ones that make wireless keyboards work). No installation, no logging in, if the device is in the room, the screen appears on the teacher machine. People say: ‘what’s the point of graphing calculators these days?’ I say: it is a piece of bespoke hardware with an optimised interface for the range of maths functions you need, with really well developed and well thought out maths software. Moreover, compared to iPads they are really cheap. They are small, easy to carry and importantly easy to charge. You just have to be able to grab the box on your way into lesson and hand them out the same as you would hand out rulers and compasses and they just work when you turn them on. Only then can we get back to 1983 and have technology seemlessly integrated into ordinary lessons in ordinary classrooms. Only now we’ve got rather classier software to play with.

I would like to work with anyone who is using any comparable kit that can achieve the same effect. I would be delighted to set up a research project where we can examine the actual classroom use of these technologies. I would be keen to hear from schools who think that this sort of kit will solve the problem of static teaching and would think they could use such technology all the time (not just special occasions). I would happily support such work with loan equipment and support materials. Contact me (

Apart from the dodgy hairdos and the rusty cars, 1983 had things going for it!

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 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 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.