Mathematics for Smart Dummies

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At this particular moment, with the general election just moments away, All Change Please! feels it would be inappropriate to indulge in Partly Political Posts because of the influence it might have on the millions of followers it doesn’t have. On the one hand, almost anything would be better for education than another term of the hopelessly unqualified Messers Mickey Gove and Nicky Morgove teaching the class, but on the other one has to wonder just how much better informed the other parties are.

Take this recent article that reports that Labour’s plans for all students to continue to take maths until the age of 18 are the “best protection against unemployment”. And apparently “Our future success as a nation depends on all young people taking maths to 18”, not to mention that “It is essential that everyone is mathematically literate in this scientific age”  – as a number of leading and in no way biased mathematicians predictably proclaimed with 110% certainty and no margin for error to an infinite number of decimal places.

Now this is fair enough if a student is going on into a technical or scientific area but the vast majority won’t be. When was the last time you factorised a quadratic equation involving a surd, constructed a perpendicular bisector and solved a linear inequality?

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“All I wanted to know is how much it would be for a cup of coffee…”

The problem is that the sort of Maths taught for GCSE, and presumably beyond, is not particularly interesting, exciting or relevant to the everyday maths skills that are actually needed in the typical workplace. And anyway, even then it seems to have completely escaped everyone’s notice that Siri (the vocal iPhone assistant) is more than capable of solving maths problems for you, and showing you how it worked it out. And, even better, there’s also Photomath, a free App that enables you to take a photo of an equation, and it will calculate it for you.

Now of course you can’t take a Smart Phone into a formal examination – but All Change Please! wonders if anyone has yet thought about the future need to also ban iWatches, which once they incorporate a camera, could unobtrusively run the Photomath app as you seemingly check to see how much time you’ve got left?

To be fair, Marcus du Sautoy’s remark above has, surprise surprise, been taken somewhat out of context. In this article he suggests a second maths GCSE course might:

 “…expose students to the big ideas of maths: concepts of infinity, the maths of symmetry, the challenge of prime numbers. It is finding out what maths is really about that might change the national mindset…”

“What will be important is making sure that the maths we expose students to is both relevant to their future and the future of our country.”

Although All Change Please! would like to suggest that the logic and rationality in the world he seeks needs tempering with a good dose of creativity and imagination as well. But what is quite clear is that the teaching – and examining – of maths needs a major 21st century overhaul.

Meanwhile the key maths skills that politicians probably need right now is the ability to furiously calculate the complex permutations of coalition party members they will need to work with in order to form the next government.

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6th May Update…

Would you believe it – someone just has:

Students ticked off by ban on watches in exams

Photo credits: Flickr / Mulan / Sean MacEntee / Mulan

Alas! Schools and Journos: Have you ever Bean Green?


Mel Smith, as the man who thinks he knows everything, and Griff Rhys Jones, as the man who knows he knows nothing, return to catch up on what’s been happening in education, ill-informed as always by the Great British Press.

Smith: Haven’t seen you around for a while then?

Jones: No, not much has been happening recently has it, especially now that Gove chappie has been permanently excluded from schools?

Well, my friend, just wait until you see this in the papers – apparently last summer not nearly as many children managed to pass their GCSEs

Oh, so weren’t they very bright then?

No, no, no, it wasn’t that at all.

All their teachers went on strike then?

No, no. Listen, what happened was that the Tories made the exams they sat much harder to pass. They thought that would make all the kids cleverer.

Oh. That wasn’t a very clever idea then, was it?


And it’s a bit unfair on a whole generation of teenagers who now won’t have as good qualifications as their elders? And I expect all the schools requiring improvement will be given those special tape measures now?

What? Anyway I’ll tell you something else. You won’t believe this. Listen, it says in the paper that apparently a lot of your posh public schools have gone right off the boil and are now at the bottom of all the league tables.

What you mean they are in the Vauxhall league?

Yes, sort of, except it’s now called the Vanarama League.

Vananarama? Is that a new girl-power band or something then?

No, apparently it’s a van leasing company, but that’s not got anything to do with what I’m telling you.

So Eton and Harrow have gone into the van-hire business now then?

No, no, no. Do try and pay attention. It seems their students were all taking the wrong sort of exams that didn’t count in the league tables anymore.

Why were they doing that then?

Because the public schools say the exams their students did were harder than the GCSEs, but the DfE says their new exams are now the most difficult.

Ah, they’re both playing hard to get then?

Yes, I suppose you could say that.  Well it just goes to show you only get what you Gove, don’t you? Anyway, what’s more Camoron wants all schools to be above average in Maths. That’s going to be a bit of a challenge. And then there’s this Little Missy Morgan who’s all in a spin and is going to sack headteachers if they don’t improve their children’s literacy.

Well, it’s important kids learn to throw their litter away in a bin isn’t it?

Exactly. And then there’s their numeracy.

What’s that then?

You know – learning their tables.

Oh, you mean like the difference between a dining table and a bedside table? Why’s that important then?

Well I suppose if you went to IKEA, you’d want to be sure you were buying the right sort of table wouldn’t you?

Yes, and they could use those special tape measures to make sure they were getting the right size.

Anyway after the election in May everything will be different when the Greens get in.

Who are these Greens then? Are they from Mars?

No, don’t be daft. Well I don’t think they are anyway – though looking at some of their policies…

You mean our politicians will all be like green vegetables – sort of limp and tasteless and foul-smelling?

Yes, I expect so.

Oh.  No change there then?

Anyway, I suppose at least they will have a lot of posh vans and drivers to move them around in.

PISA Takeaways

P1050498-1Does Pisa lean too far to the left or right?

Well, the question of whether the leaning tower of Pisa leans more to the left or right very much depends, of course, on which side of it you are standing. At the same time, if you happen yourself to be leaning either left or right, then it appears to be perfectly upright and proper.

What’s that you say? Oh. Not that sort of Pisa?

(At this point All Change Please! does a quick double-take in the hope that no-one will notice its mistake and think it as stupid as a child from, say, Peru – the country that came at the bottom of the table and was consequently relegated from existence – a position that doubtless England will occupy in three years time after the 2016 PISA World Cup?)

Ah, you mean the PISA that’s been widely reported in the media over the past week in which the right-leaning Gove blamed the left-leaning Labour for the poor results and they then both blamed schools, teachers and pupils in such a way that it didn’t really make a jot of difference to anybody, anywhere?  Yes, well, All Change Please! was just coming to that sort of PISA.

The question about these PISA tests that no-one seems to be bothering to ask, let alone answer, is what exactly is it about them that English children find so difficult? Looking at these examples of test questions:

they actually appear to be quite easy-PISA? And while All Change Please! doesn’t know the answer to the problem of why England does so badly, it just might have a theory…

Which is that at secondary level, a teacher is usually appointed to a school because of their subject expertise and academic ability (acquired at University), and they are then labelled, for example, as a History Teacher. They will be largely judged on the success of their pupils obtaining History GCSE and A level results and the number who then go on to University to study History or a related subject. So they then stand in front of their Year 7 (and upwards) class and think that, as the chances are that one or two of their future high-flyers might be sitting in front of them, they had better start preparing them now, just in case. And as a result they approach their lessons through the delivery of a deep, conceptual academic / theoretical understanding as if all the pupils were going to end up become life-long historians. And it’s the same for English and Maths. Instead of concentrating on reinforcing basic literacy and numeracy first, children are being prepared to be (failed) creative writers, literary critics and mathematical geniuses.

So perhaps the problem is that the PISA questions all come with a friendly photo and are placed in a recognisable everyday practical problem-solving context, something our children are ill-prepared for. But ask them instead to:

‘…generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes; use these to calculate theoretical probabilities; and know that the probabilities of an exhaustive set of mutually exclusive outcomes sum to one.’  (New National Curriculum KS3)

and presumably they’d be well away?

Of course there are other theories too, such as the fact that our exam-fixated students doubtless ask if the PISA test will count towards their GCSE grade, and on learning that it won’t, then treat it with the utter contempt such a waste of their time deserves. Or perhaps they have read PISA-topping Singapore’s Minister of Education, Heng Swee Keat, recent speech in which he sets out the need for a new push towards ‘a more multi-dimensional education that goes beyond academics.’ before going on to say:

‘…time spent doing more drill-and-test means less time for play and rest, for exploring new ideas, for developing social skills. A balance is necessary, but there is no magic formula as to what the right balance is because every child is different.’

and then announcing that he is looking for ways to transform learning so that students are independent thinkers and resourceful learners with a can-do attitude, and ‘to make learning a more joyful journey‘!

Which all sounds exactly like the sort of namby-pamby nonsense the UK Government and the media will do its best to undermine in order to ensure that the exclusive all-inclusive English education system will continue to support the natural right of the social elite to dominate the higher levels of educational attainment.

And then there is of course another point of view entirely:

Which at least manages to see the situation from an alternative perspective, as opposed to the unquestioned assumption that improving our performance in PISA tests is the best way forward for our education system: OECD education report: UK needs new ‘gold standard’ to compete with world’s best

And with that in mind, it remains to be seen whether in three years time Gove will come to be acclaimed as the rightful PISA delivery man…

With thanks to Rob B.

The forgotten majority


“Eng-ger-land! Eng-ger-land! Eng-ger-land!”

For somewhere around 20% of the population of under 12 year-olds – the 20% that are potentially academically able and motivated – the news that GCSEs (England) are to become a great deal more demanding is good news. But for the remaining 80% it’s decidedly bad news. The prospect of perhaps achieving a 1 or a 2, or even perhaps a 0 (to replace a U?) is unlikely to encourage them to even bother turning up on the day of the exam. Unless of course they are crafty enough to realise that they could then claim on their CVs that they have ten 0 levels?

“In maths and science, questions and content will be more demanding, so that state school students can compete with their contemporaries in Singapore and Shanghai, acquiring the skills that the rich pay handsomely to pass on to their children and that are the guarantee of future opportunity,” Gove wrote.

“Exams will test higher-level skills, such as more essay writing, problem solving and mathematical modelling, that universities and businesses desperately need.’ DfE

The whole misguided premise seems to be that simply by asking more demanding questions, academic standards in state schools will rise and children from poor backgrounds will all go to Oxbridge. And All Change Please! still remains to be convinced that businesses need higher-order skills in essay-writing and advanced ‘there’s just one-correct-answer’ problem-solving.

Meanwhile for the long tail of the forgotten 80% we can perhaps expect to see a substantial growth in non-academic subjects that do continue to include coursework, such as art & design, design & technology, engineering, drama, P.E., etc. What’s really needed now is a means of more formal recognition of success in these so-called ‘soft’ skills – surely what most employers are actually looking for these days, alongside some sort of certification that identifies an ability to read and write, do basic maths, follow instructions and be able to deal with the public – as opposed to being able to write essays about a Shakespeare play or solve quadratic equations? Someone is going to have to pick up the pieces – maybe there is some hope for a Better Future here?

But perhaps the best news of all is that ‘iGoves’ will go down in history as one of the shortest living ideas in education. And instead, in an attempt to revive our world rankings back to their heady 1966 levels and to differentiate them from the easy-peasy, lemon-squeezy, my mum did my coursework for me in her lunch break Welsh GCSEs and Scotland  where of course they sensibly don’t actually have GCSEs, the new GCSEs will actually be known as GCSE (Eng-ger-land! Eng-ger-land! Eng-ger-land!*). Perhaps the intention is that the prospect of achieving better results than their Welsh and Scottish counterparts will drive our children upwards to even higher academic achievements?

Or perhaps there will be an outcry when it is realised that in order to mark that many essays they will have to be out-sourced to places like India and China in addition to Australia, as is already the case? Or that perhaps the number of marks needed to get a 5 (the so-called pass-mark) will be mysteriously adjusted so that an acceptable percentage of children appear to pass?

Perhaps, perhaps, perhaps…

*Eng-ger-land is apparently what the English sometimes chant at football matches because it’s easier to say (it just rolls off the tongue).

Image credit: Flickr: crabchick

Some things just don’t add up

Being a blog, sadly All Change Please! does not qualify for any sort of pension, even though it feels it is trying to provide some sort of public service. As a result, it’s hard at work today as usual.

In fact All Change Please! had quite a surprise yesterday when, just for a fleeting moment, it realised that it actually agreed with something that nice Mr Gove was saying  at his speech at the Royal Society, and that it would be a good idea for there to be a ‘much greater focus on fundamental number concepts, fractions and the building blocks of algebra in primary school‘, and that GCSE maths should include more on statistics. Of course, then he had to go and spoil it all by suggesting that the vast majority of students should continue to study maths to the age of 18, just in case they suddenly all decided they wanted to study physics or engineering at university. And then he cleverly compounded his lack of awareness of education by adding:

Itunes now gives everybody with an internet connection access to the world’s best educational content. Innovations such as the Khan Academy are putting high quality lessons on the web. Extremely cheap digital cameras and the prevalence of the internet allow teachers to share best practice and learn from errors.

Beyond the fact that the Khan Academy certainly are not putting high quality lessons on the web, he might have been a bit more convincing if he (or whoever wrote his speech for him) had written iTunes instead of Itunes.

But perhaps what makes Mr Gove most concerned that school-children improve their Maths skills is in fact the findings of a recent report by the Sutton Trust charity, which reveals that only one third of pupils correctly understand how the new tuition fees system works? After all, it’s essential for them to be able to work out exactly how much debt they will be in at the end of their studies.

Oh, and if you haven’t read this yet, you should!

Educashun still isn’t working

I was recently clearing out some old papers from the loft when I came across a newspaper cutting from the early 1980s. Entitled ‘What employers want’ it was a report of speech given by the director of the Manpower Services Commission at an NUT conference. It included a list of what employees wanted from school leavers:

  • the ability to read, write and do arithmetic
  • some understanding of the need to produce and sell goods at prices people could afford
  • an appreciation of the need to work consistently, quickly and accurately, and to be punctual
  • an understanding of the different types of jobs and industries
  • the ability to communicate, to join in group discussions, and to use a phone
  • the ability to produce practical solutions to everyday problems
  • the capacity to learn from experience
  • the ability to get on with a range of people, and to recognise the need to share knowledge and skills with them

The speaker also called for a new look at the the effect of university entry qualifications on decisions about which courses of study to follow in school ‘that go far beyond traditional academic disciplines‘. He called for subjects to be grouped with clear academic and vocational aims, and that ‘a new approach is required‘ to improve young people’s knowledge of the world of work than is covered in the traditional curricula.

Now, there’s more to education than simply preparing people for the world of work of course, but nonetheless, some thirty years later, we are still pursuing a university-led system in which vocationally-related areas of study are seen to be soft options. And the basic needs of employers are still under-valued in terms of formal assessment, particularly when one now adds in such things as team-work and flexibility. At the same time thousands of school leavers with sound academic A level qualifications are now having to look for employment instead of gaining a place at a university.

But I guess there is one thing that has improved since the early 1980s – now at least, most young people seem to know how to use a phone…

Just In Case

In my Polyunsaturated facts post I mentioned the concept of Just In Time learning, in which one only learns what one needs when it is specifically needed. Since then I came across this item in which the author interestingly discusses what he calls Just In Case education, referring to the approach in our schools of filling children up with knowledge ‘just in case’ they need it in later life.

Indeed ‘Just In Case’ is a way of life we are used to: “Eat up you lunch just in case you don’t manage to get any supper tonight”; “Buy some extra tins of soup just in case you can’t get to the shops again, or they run out”, etc.

While ‘Just In Case’ is indeed quite a good description of the rationale behind a lot of education provision, the more interesting question is how does the current model need to change to accommodate the world of information snacking?

For starters, we need a ‘must eat to survive’ course which provides everyone with the absolute essentials for life – how to read, write and do basic maths along with some basic communication and creative problem solving skills.

Then on to the main course – a ‘choose what you want and eat as much as you like’ tasty smorgasbord of interesting and unusual wider contextual knowledge and understanding of the way the world works – a general sense of language, geography, history, the science of the universe, logic and creativity, analysis and evaluation, the physical and psychological needs of ourselves and others, attitudes and values, order and chaos, risk and change, learning how to learn, etc. These are not so much pre-cooked stodgy school dinners, but more like delicious, tasty take-aways, individually chosen according to one’s tastes and dietary requirements and the needs of the local community.

And finally for dessert, the icing on the cake – a more in-depth study of a narrow range of ‘subjects’ that reveal the need for detail, accuracy and quality in life and the world of work.

Although this alternative curriculum is described here as a three course meal, there’s no need to consume them in that order or manner. Indeed there are many who suggest that six smaller meals a day is better than three large ones.

So there is no longer any ‘Just In Case’ learning here, but the foundation of a sensible diet that puts information snacking into context, and provides everyone with enough starting questions and potential sources of information to explore when the time comes.

Training Tomorrow’s Teachers Today

A recent comment on another post has raised important issues about the current provision for initial teacher training. If nothing else, we are certainly going to need a highly capable, committed and motivated workforce to deliver the appropriate and effective educational experiences that we need to start to provide in the 21st century. Which is why it was worrying to read the account of an ITT lecturer’s experiences of preparing tomorrow’s teachers today. Are five A*-C GCSEs and three C grade GCEs enough to qualify someone to train to be a competent teacher?

Here’s what ‘Roberta’ wrote:

“After 35 years in education (secondary and higher), not including my own, I think that perhaps we do need to take a pragmatic stance on primary and secondary education. Perhaps it is for the production of employable people who will be able to take on the roles required by their employers, people who are punctual, civil, creative, responsible, curious, eager to learn new skills and information, who are literate and numerate. I am not talking about ‘factory fodder’ here, but young people who will join the professions.

Universities are now experiencing ‘bad behaviour’ amongst a large proportion of first year undergraduates, these include Primary Teacher trainees, whose antics are those that one might expect from Year 10 and 11 pupils. This inappropriate behaviour is manifesting itself in the lecture room, a situation which has never occurred before this year, with the open use of mobile phones and MP3 players, laughing and talking over the lecturer’s voice and during session tasks, absenteeism, eating and drinking (including alcohol) and complaints when asked to make contributions to teaching sessions.

Admonition is greeted with complaints that lecturers are being patronising and since the students are paying fees, they are able to do as they please.The idea that they may be disrupting the learning of others does not occur to them. Their refusal to carry out tasks, unless they contribute to formal assessment and final degree classifications, is bewildering for those of us who see learning as a continuum. The idea of engaging with learning because that is why they are attending university seems to be beyond their comprehension. This is from people with a minimum of three C grades at A level.

For the most part, these are young people who have chosen this career path, not ‘ended up’ teaching through Clearing, due to unexpectedly poor A Level grades. They are recruited to Initial Teacher Education early in the academic year before they finish secondary school and references and good predicted grades are being given by their schools. What is happening? If this is deemed to be acceptable behaviour by these young people, who are our future educators, what hope is there for those who emerge from the secondary school system barely literate and numerate with a disaffected attitude towards society?

In addition, the government’s QTS tests in English and Maths, taken towards the end of their undergraduate (and postgraduate) teacher training, are proving a really difficult hurdle for many, to the extent that Michael Gove has announced that a Conservative government would limit the number of times that they can be re-taken by trainee teachers. What is this saying about the level of education of our young people, if those with fairly decent A levels are struggling with literacy and numeracy?”

I’m reminded of a recent cartoon in which an excited sixth-former had just opened a letter offering him a place on a teacher-training course. “All I need” he is announcing to his parents ” is an A, a B and a C. And they’ll teach me the rest of the alphabet when I get there…”

So any suggestions as to how this situation needs to be changed that don’t involve the traditional reaction of  the need to get back to the good old days of formal academic education? As always I look forward to your comments…

Going for Gold

Did you see this recent news item?

2012 Olympic Games Medal Shock!


‘The Olympic Games Committee made a surprise announcement today in which it stated that in future Gold medals will only be awarded to the winners of the 100 metres, which it considers to be the only true test of an athlete. Winners of other track events that involve at least some competitive speed running will only be awarded Silver medals, while other, so called ‘soft sports’ such as pole-vaulting or horse-riding will only gain winners Bronze medals. Team games, in which it is impossible to identify a single winner, and sports that can be played professionally, such as football and boxing, will still be offered as recreational fringe events, but no medals will be awarded. A spokesperson said ‘It’s essential not to further devalue the gold standard, and we hope that this action will encourage more athletes to train for and compete in the 100 metres’.

Crazy, and of course quite untrue. Except that in the UK that’s exactly how we view the current education system – we prepare everyone for success in one event that only a small proportion of entrants are capable of succeeding in. What makes it worse is that the one event is, by definition, ‘academic’ – theoretical rather than practical. An academic is ‘a person who works as a researcher (and usually teacher) at a university, college, or similar institution in post-secondary (tertiary) education’. Why is it that we all want our children to be brilliant academics, but are quick in a discussion to dismiss an idea as being ‘academic’, i.e. of theoretical rather than any practical relevance? As a result we have a nation full of trained 100 metre runners, the vast majority of whom have no chance of ever achieving Gold, and frequently see themselves, and are also seen by potential employers, as failures and as such un-equipped  for any other event, such as work in the outside work. And how much longer will the ‘essay’ and the multiple choice question remain the main format for assessment, given that few jobs involve a great deal of essay writing or answering mcqs.

This attitude is by no means new, and has been something that as a society we have been dearly clinging on to for centuries, while other countries seem to have been able to move on and value technical and vocational education in a far more positive way. Somehow we need to bring about a major shift in the way we perceive and value education in the UK, and re-naming schools as ‘academies’, making A levels more difficult and getting more people to study subjects such as English and History to degree level is not the direction we should be going in. In just about every area of business, commerce, health, defence, housing, farming, etc., there have been changes during the past 60 years on a scale that make them unrecognisable from the way they were in the 1950s. The single exception is education where, apart from the largely inappropriate use of computers, little has altered except in name. If the UK is to remain, or even become, in any way competitive in the global market place, it’s much too late therefore for a slow, evolutionary incremental shift in public opinion and institutional structures, curriculum and teaching method. We need to think the unthinkable. Nothing less than a short, sharp revolution in needed.

I have no grand plan or costed strategy for development, but here are a few of the sort of things we ought to be currently considering:

• We need a shift away from the idea that we all attend compulsory full-time schooling between 4 and 16. It’s always struck me that the single most inappropriate environment for a 14 year old is to be required to sit still in silence for hours on end listening to adults who think they know everything.

• The traditional school structure and organisation is entirely outmoded for the modern age. We need to develop institutions that facilitate a more effective daily mix of exposure to teaching styles and learning experiences, essentially including independent learning.

• Students need to be given and take more responsibility for their own learning, utilising the innovative possibilities of innovative computer technology, rather than simply using IT to reinforce and automate traditional approaches.

• The use of the slogan “What have you learnt today?’ could be used to prompt a genuine approach to lifelong learning for all in which the act of learning something new everyday is recognised and valued by individuals and employers.

• How can all intelligences and abilities come to be seen as being equal, and none more equal than others? The emphasis on academic education is only appropriate for the roughly 5% of the population who are suited to it. We need some sort of single national award system that recognises a relevant comparative ‘gold’ standard across all courses.

• In this day and age are we really still unable to teach every child how to achieve basic standards in literacy and numeracy? Standards have improved slightly over recent years, but there’s clearly something badly wrong here that needs sorting out.

• We need to introduce of a valued certificate or ‘qualification’ of basic achievement that recognises the practical application of reading, writing and arithmetic in daily use, alongside a similarly valued certificate of personal learning and creative thinking/problem-solving skills, both taken at any age when the learner is ready.

• Currently teachers have five training days a year which are mostly spent on being introduced to new administrative procedures. There needs to be a major investment in effective and compulsory in-service training / CPD (Continuing Professional Development) for teachers to enable them to keep up-to-date with their rapidly changing subject knowledge and with the new substantially different methods of teaching and learning afforded by developments in IT.

• By narrowing the range of knowledge and understanding that is now examined we have successfully raised the number of students gaining A level passes and going into Higher Education. We have steadily improved the number of children who get five GCSE A* to C grades. But when are we going to start doing something for the other 50% of learners who have limited qualifications and remain alienated by an education system that has little to offer them?

• In terms of a quick fix, one of the problems is that children’s attitudes towards school and learning is heavily influenced by their parents’ experiences. Most of today’s parents were at failing comprehensive schools in the 1970s and 1980s and remain unconvinced of the value of education. Today’s children, who have grown up in a narrow assessment-led National Curriculum culture, will become parents in the next two decades. How do we ensure that they will have a different, more enlightened view of education to pass on to their children?

Ironically, sadly all these things are probably somewhat ‘academic’. It’s difficult to see future governments or administrative organisations initiating or welcoming change on this level. Somehow we need to find a way to take control of our own future learning and growth.