This has been a long time coming, but I intend to restart sharing thinking about work I’ve been doing in projects around the world! I am part of a Sheffield Hallam, British Council project for the Indian Institute of Science Education and Research in Pune. The idea is to work with teachers of undergraduate science and maths to develop tasks requiring problem solving skills in settings of genuine benefit. The problem with maths, is that the problems are frequently unrealistic or too simplistic. One of our co-tutors wrote to ask my thoughts on this … Continue reading Research Based Pedagogic Tasks RBPTs
Publishers are feverishly producing complete new sets of text books for English schools using consultants and academics from Shanghai and from Singapore. This comes on the back of a Nuffield Foundation report suggesting that the poor quality of text books is a key issue for schools in England. The overwhelming demand to teach to the test is now accepted, with even Ofsted saying there was; “too much teaching concentrated on the acquisition of disparate skills that enabled pupils to pass tests and examinations but did not equip them for the next stage of education, work and life.” So, in a major crisis of confidence for English maths educators, we look to the successful TIMMS nations. But what are the key elements of the Shanghai Maths ‘Mastery’ and Singapore Maths? Well certainly in Singapore they are keen to assert that this is a reworking of what was best in maths education in the UK from the early days of the ATM with Dienes, Gattegno and Cusienaire. Continue reading WOW Maths: Indian Maths Scheme
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. Continue reading Technology and Maths Exploration
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). Continue reading Talking Maths in the Esoteric Domain: HP Prime Wireless
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. Continue reading Wireless Prime has arrived!
Kender School in Lewisham are the winners of the Mayor’s Fund for London’s Count On Us Challenge.
Very well done to them and very well done to all of the schools who took part. The grand final took place yesterday at City Hall with 13 schools who had won their way through heats and semi finals to compete at solving 24®Game puzzle cards. Each card has four numbers; you can add, subtract, multiply or divide in any combination, but you must use all four numbers to make 24. Continue reading Count On Us Challenge: Congratulations to Kender School!
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 (email@example.com).
Apart from the dodgy hairdos and the rusty cars, 1983 had things going for it!
From September 2014 it will be compulsory for schools to teach financial education. This will be built in to the mathematics and the citizenship curricula. See this article from the Daily Telegraph. Notice the picture of school life that they choose to illustrate the article with. This is how students learn; in rows at individual desks, looking seriously bored! The trouble is that a good proportion of the materials available for ‘financial education’ in schools is perfect for this scenario. Standard worksheet based discussion and practice activities are the norm and work in the same way that makes PSHE such a disappointing subject, taught by non-specialists, with no exam, it is hard to see the purpose when you are in school.
What makes these important things come alive is getting students into the setting. They have to care about the issue in order to engage with the ideas. I have seen fantastic drugs education sessions where former users and dealers have come in and talked to teenagers about their experience and where they are now. It is edgy, but it is real and they certainly listen!
Finance is tricky. Kids in school rarely have any real need to save with interest and if they have a bank account, their main worry is losing their cash. Certainly, they cannot borrow beyond their means or need to budget in a life changing way. Some, certainly, have life experiences that may necessitate any or all of these, but they are a small albeit important minority.
We have been working in financial education for over a decade. As a development of the Number Partners project which I was director of for many years, we designed a series of large format board games designed to set up scenarios in which players have to make important financial decisions: how to invest a small amount of capital, to generate profits to reinvest. Managing money between cash and different bank accounts, to enable purchasing but retaining security. Budgetting for a holiday and managing exchange rates. Making the life transition from school to work, while meeting your life goals.
The power of a board game is that the social setting frames the decision making. You are playing with real people who you have to engage with, framed by the settings of the games. The games were trialled in very ordinary schools, in classrooms with groups of students and have been widely used in different settings since. The effect is impressive. Students talk to each other about their financial decision making, developing strategies to succeed in that setting. Naturally, winning strategies involve good financial decision making.
We set up a web site to showcase the games. So see what you think. All of the games have teacher guides with extra materials and school use ideas. Please get back to us with your questions and thoughts. But, when you plan to deliver financial education this September, get your students into a setting in which they care. Only then will they be able to make decisions in a way that matters to them.
Where we were working in South East London, a number of students would arrive in England for the first time in the middle of secondary school. They would have very little English language and would try to get into local secondary schools. The schools would turn them away because they assumed that these students would end up with poor grades and compromise their exam statistics. So, a unit was set up to support these students make the transition to school. I got together with Gwyn Jones to produce a course designed to teach the mathematics content of GCSE with the minimum of language, but developing the key technical vocabulary of maths and of school while they learnt. The materials were supported by online interactives to see the maths dynamically and practice the ideas in an open format. There was a very low language pre-test, so that the student could show what they already knew, a tracker sheet to choose the maths they now needed to work on, a large collection of activity sheets to develop the maths and a post test with the same language demands of a normal maths test to show the schools how good they were.
In the very first group of students to use the first version of materials there was a student who had just arrived from East Africa. He had been rejected by every school in the borough. He took the pre-test and got 100%. He worked on the advanced materials and did the same on the post test. He took his work as a portfolio back to the schools and immediately found a place. Within 18 months he had an A* in GCSE maths.
We are proud to announce that we have now redesigned and updated this course and made it available to schools. Called Access to Mathematics it comes as one of our course boxes (like our well known gifted and talented courses; Wondermaths and Illuminate). There is a comprehensive teacher guide with notes on running the course. Ten copies of the comprehensive student book (120 pages) and access to the online interactives, test, answers, etc. in the Access to Mathematics web site. Priced at £195 this gives access to mathematics for all of your students for whom English is an Additional Language from those who have just arrived with no English to those who appear to have conversational English, but cannot access or succeed at maths in lessons.
Everything is described diagrammatically, putting the maths into a visual structure. Two colours are used to emphasise the structure and the maths is practised through this structure, gradually peeling it away to leave the formal symbolic maths. The course worked well supervised by non-specialist teachers as it is designed largely for self-teaching. However, with access to a specialist teacher, the materials could be used for a whole range of learners where reading and language demands of any sort are an issue.
Once you have the box, further copies of the students books are available in packs of 10 priced at £45. So, you can use them as a standard class text if you want. The overall content is covers about 90% of a higher level GCSE.
We are very proud of this publication. We have so often seen excellent mathematicians languishing in low achieving sets simply because they are still learning English and find accessing conventional books difficult. Now, they can quietly and quickly show everyone how much they know and can do, while learning the essential school language that they need.
We’ve been very busy at The MathsZone. Feedback from schools suggested they really love our gifted and talented courses Illuminate and Wondermaths, but they already have some of the materials that come with them. So, we’ve done a major re-design. Still the same fantastic courses for your gifted and talented students at key stage 2 (Wondermaths) or key stage 3 (Illuminate), but now in a neat plastic storage box, which will go on your book shelves. Each one has a comprehensive teacher guide detailing the structure and purpose of all of the sessions, with commentary and solutions (where appropriate!). For the students we have organised the materials into a beautiful student workbook. Now your students can keep all of their work in a really attractive book which they keep at the end of the course. Game cards, dice and counters are included for the activities.
There are fewer puzzles directly referenced in the course, so the price is lower, but of course you can buy all of the puzzles separately to extend the activities. Illuminate comes with a CD Rom with all of the course materials and additional materials for projection. Wondermaths has an associated web site with the materials available. When you are ready to run the course for a second time, you can get extra sets of 10 copies of the workbooks. The key objective for the teacher is to get up and running with the minimum of fuss, so you can focus on supporting your students explore their mathematics.
The aim of both course is to give students the opportunity to explore mathematics. Wondermaths has games, to compare strategies, puzzles to develop sustained thinking and investigational maths top explore maths language and move towards explanation and proof. Illuminate aims to develop the ideas of pure mathematics for those who are limited by the algorithmic nature of school exam courses. Students will develop and compare proofs, while exploring the nature of proof itself. Their is a comprehensive section on group theory, fully accessible to ordinary school students. Games strategies are developed and compared and the course ends with a project in fractal geometry. These are really course in the mathematics that mathematicians would recognise.