Tag Archives: Dialogue

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.

The New National Curriulum

Well, mathematical modelling now has a serious place in key stage 4. So, get yourselves ready. Do not look through the document looking for any coherence, though. You won’t find it. This is another pot-pouri. Some very odd things like frequent reference to mechanics as an example of mathematical modeling, even though it is not taught as that at A level. More a collection of known models being applied. The real trick is to get students to develop their own models critically and develop methods for validation. That’s why real engineering projects go through more than one development iteration and A level mechanics problems do not. My Pizza Project article develops the model creating phase here. Also, Venn diagrams are back for probability problems, but set theory is not. Vectors in different format are back, but matrices are not. My favourite is the explicit teaching of Roman numerals (up to 100 in year 4 and then, I kid you not, up to 1000 in year 5).

Mr Gove was on question time yesterday. We cannot learn to be creative until we have a through grounding in the facts and techniques needed, he says. Everyone agrees with this (including our good selves). The trouble is, that no-one questions which facts and techniques and for why. The secretary of state himself quotes long division as an example. But could he tell us which creative mathematics is opened up by being able to do long division. Certainly, at A level we can divide polynomials this way, and for sure, unpicking the process to see how it works, provides deep insights into the power of place value, but, as a technique to be learned, it is just a pandering to an imagined perfect past. The trouble for us, is that everyone … the man from industry, the children’s author and all of the politicians agree with him. I say get kids to memorise Pascal’s/The Chinese triangle and chant their squares, and cubes. That would genuinely help them engage with maths creatively. But 11×12? Why? Is old money making a comeback?

So, there’s a big opportunity. Some interesting if oddly chosen hard maths, that modelling word and even ‘proof’ is in there too. An absence of levels is a major blessing. But, ordinary kids have to be able to do this. Escalante got all of his students to AP calculus with ganas. We must be able to do this too. The stakes have been raised.

BETT 2013: Graphing Calculators

I am booked for a session at the BETT show 2013. So, please come along, say hello and discuss the issues. It’s in the HP stand theatre area at 11:00a.m. on the Saturday, so everyone can be there with no cover needed.

I’ve called it “Dialogic teaching with handheld technology: introducing the HP39gII graphing calculator” to sound flash, but in the end the question must be: ‘How do we get kids talking about their maths?’. Dynamic maths software provides a tool to explore and getting it into the hands of the students lets them talk about it.

I’ve heard that school are getting iPads and Android tablets in class sets. People talk about them as if just having the device will teach students stuff. The question is ‘By what mechanism’. What will produce the change? Clearly you can go to get one person’s didactic explanation of a minute method as per Khan Academy or get free drill and practice in game format like Manga High (or even pay for it with the ubiquitous My Maths). But please teachers, don’t forget that the moment you start to believe this, then you aren’t needed any more! What we need are tools that mediate mathematical exploration. That needs open software that simply gives mathematical responses to mathematical inputs. Look at the current open maths software on iOS or Android and you quickly see how poorly developed they are for educational use. The best software by far is Math Studio (used to be Space Time). This is seriously powerful software (and for an APP prices are now getting a bit more serious at £15), but users will know it is not credible as a school package.

So, how do you get well optimised educational maths software into the hands of students, in an ordinary classroom, with no booking and a very high degree of probability that it will work. Well, you know I’m going to tell you that at present the only solution is graphing calculators. And, heh, as a bonus, they don’t connect to the internet, so no-one will be facebooking when they should be thinking maths (and that’s not a reflection on the activity … adults do this in conference sessions too!), it’s just too strong a temptation.

I’ll make the case in the session by showing off some of my activities, that I hope you will agree, make you think in a qualitatively different way about things like variation and the interrelationships between different presentations of functions.

See you there!

Finding Good Maths Resources

The internet for teachers, blessing or curse? In the past, you would have a set of text books or work cards as your basic resource. The department would have bought a small library of additional books and materials from people like the ATM. If you needed a good idea, you would never have to look beyond the maths office or the maths cupboard (do you still have those?) Every department would have a pile of good physical manipulatives like centicubes and logic blocks, cuisenaire rods and probability kits. A set of large compasses and ruler for board work and a good collection of games and puzzles for activity days. There would be copies of those wonderful books by Brian Bolt (which are still available) for practical problem solving and a set of Points of Departure books for maths investigations. Always excellent, always to hand. Continue reading Finding Good Maths Resources

Cape Town Maths

Two weeks ago, I had a very nice trip down to Cape Town. It is a very beautiful city indeed. However, I did a series of sessions mixing HP Graphing Calculators, GeoGebra and Data Streaming to groups of maths teachers, trainee maths teachers and undergraduate engineering students at the Cape Penninsula Technical University and the University of the Western Cape. South Africa, in the post apartheid era has been trying to bring all of its education systems up to the level of the former elite schools. As you can imagine, this is a tough task, although the government’s commitment is clear having one of the highest proportional spends on education anywhere in the world. The universities I visited are excellent examples of that move to change and I was delighted to work with really enthusiastic students and teachers. Continue reading Cape Town Maths

Brunel AND Nelson in King’s

The ATM/MA london Branch was treated to on of Peter Ransom’s barnstorming performaces last Saturday. A big message that we share with our PGCE students is that teaching is a performance art and ensuring that your lessons have a good dose of theatre will bring students in to your message. Well, Peter brings avery big dose of theatre. Right down to the brilliant stand-up touches … is he really going to drop the cannon ball? Well, yes, naturally. We got through transformational geometry, force functions in suspension bridge chains, cannon ball stacking sequences and the destructive impact of cannon balls by linear and quadratic scaling. So, no messing maths. Please come back soon to see the photos … and come to our next session which will be 10:30 Saturday 24th March (King’s College London, the Franklin Wilkins Building on Stamford Street, SE1, just down from the IMAX cinema), which is the Danny Brown maths Workshops. Read all about it at Danny’s site: www.makemaths.com

Maths Trails

The ATM/MA London branch meeting today was a wander round Parliament Square, up Whitehall and Round Trafalgar Square. Four groups of maths teachers made the trek and were intrigued to see this most famous bit of London in a different light. The trail is one of a number that I prepared during my time working for maths Year 2000 and it’s great to see it used again. To support the session, I set up a new web sight with the great URL of www.mathstrails.org.uk . You’ll find PDF and Word versions of all of my trails plus links and details of a load of other trails and trail related materials. Please visit and most especially, please contribute, you maths trail fans with your own ideas, materials and stories.

In the end, it’s just great to get out and about and look at things in a different way. So, take the opportunity and get your students out too!

Making it ‘Real’

As owners of a games shop we are honour bound to play games at Christmas! No really, we do love them. So, Val, Katie (13) and I played a game of Risk. Now Risk is not so PC overall but, well, when you have made an alliance with the mass armies (in this case of the evil of middle earth) and they have attacked your opponent on your behalf and your turn comes round and you now realise you can renege on your agreement and wipe them out … well that is tough. Emotion, scruples, morality all bound up in tough decision making. Now I think you really (up to a point seriously) do have to debrief after a game like that, but is sure is that you are in the situation making the decisions … a history lesson for sure but not just discussing the issues cold. Continue reading Making it ‘Real’

Why bother with technology in maths classrooms?

Working with a group of aspiring entrants to the teaching profession is always an interesting opportunity. They still have the open mindedness about this noble profession that allows for certainties to be challenged and opportunities explored. The reality is that  dialogic teaching supported  by dynamic technology (meaning both parties: student and teacher, have control over how the narrative plays out) is a very rare event in schools. The mass of technology is either already booked out so kids can be trained to use MS office 2003 or is pre-programmed for zombie teachers to press the next button on their MyMaths lesson. Continue reading Why bother with technology in maths classrooms?