Visual Models in Arithmetic Operations - Draft 1

It's well established that good mathematics teaching helps students to connect concrete, visual (or pictorial) models and abstract models.

What are the fundamental visual models for the four operations in calculation?

To help understand the answer to this question I think it's first necessary to say what they are not.  Consider this excellent poster by Maria Droujkova.  It provides a lovely insight into the kind of ways in which multiplication appears in nature.  But it does not explain how people 'see' multiplication in their heads.  There are clearly two separate steps.  In the first they decode that a situation requires multiplication by recognising a multiplicative structure.  In the second they carry out the multiplication.  They may complete this second step using known facts or an algorithm they cannot explain.  But if they are confident and have been well taught they should be able to draw a picture which explains their thinking.  And except in very simple cases for multiplication this is most likely to be a picture/diagram of a repeated addition process.  Repeated addition is the most widely understood and used mental model for addition.  


I think that the visual models used for the four key operations with real numbers are as follows.  In every case students benefit from being able to express these models with real objects, a number line or equivalent thinking and with base 10 materials.

Addition

Count all

Subtraction 

Take away
Difference
Inverse of addition

Multiplication

Repeated addition (the use of array/multiplication through areas of rectangles is powerful for scaffolding variety of thinking and future work in alebra)
Scaling

Division

Splitting/How many each(for 1)
Chunking
Inverse of multiplication
Reciprocals 


Notes on models (in italics) which are generally not taught and/or clearly understood.

I've shown two models in italics because they are currently weakly defined in Western teaching however I've listed them for completeness because students may be using them and if we do not try to accept and acknowledge what they are already doing complications often arise.  Also there's no harm in being aware of what others do.

The scaling model for multiplication requires that if any general quantity (such as a length or a weight) is considered to be 1, another number (such as 7) can be estimated.  Cuisenaire rods have been used to explicitly develop students' skills in scaling.  It seems to be very well developed as a strategy in non-literate cultures (see for example Nuhnes' work with street traders).  It also seems to bear some resemblance to the teaching of music through doh ray me rather than absolute note names.  To work properly each interval needs to be drilled and many results are learned.

The model of reciprocals for division (and multiplication) uses the awareness that multiplying by a number is the same as dividing by its reciprocal and vice versa.  e.g. multiplying by 1/3 is the same as dividing by 3.  Dividing by 2/3 is the same as multiplying by 3/2 (or 1.5) and so on.  This is demonstrated in LiPing Ma's comparative study of mathematics teaching in China and the US as being an active strategy used in China.



These are the models which emerged in my classroom when I used the SDPQ activities decribed in my 8-part blog - How do the Chinese do it?  They also fit with my extensive reading of the current literature in mathematics education and my discussions with other enthusiasts.  But if your perception differs please do say.  None of this is set in stone.  Different people may have different models and there may be things I've missed.

Special Measures

Here's a link to the radio 4 drama Special Measures which tells it as it is for many schools.

ACCOUNTABILITY OF THE OFFICE FOR STANDARDS IN EDUCATION [OFSTED] Motion to be discussed at the Liberal Democrat NW Conference Sat 13th Oct 2012

Proposed by: Rebecca Hanson                                             Summator:    TBA

Conference notes that:

      Ofsted was created in by the Conservative government in 1992 by the Education (Schools) Act and that when it was created efforts to give schools the power to hold their regulator to account if they believed it to be behaving unfairly were rejected and not incorporated into law.  It is believed that this was done because the government believed that the HMIs who came from the previous system of inspection were of a sufficiently high caliber to regulate their own behaviour.

          

      In 2004 the Labour government commissioned a general review to consider the scope for reducing administrative burdens by promoting more efficient approaches to regulatory inspection and enforcement, without compromising regulatory standards or outcomes. This review led to the establishment of the ‘Hampton Principles’ of best practice in achieving the aims of inspection and regulation which are generally agreed to be; improving practice, protecting against dangerous practice and correctly reporting to government regarding the state of the organisations regulated.

      The Legislative and Regulatory Reform Act (2006) created a legal framework within which regulated organisations could challenge their regulators and force them to improve their practice if they interfered unnecessarily with their activities or behaved unfairly (within the context that regulators who adhered to the Regulators’ Compliance Code which is based on the Hampton Principles would be considered to be acting within the law).  

      In 2009 the Labour Government carried out a Consultation to establish which private and third sector (charitable) organisations should be protected by the Legislative and Regulatory Reform Act (2006) which led to all regulators, including Ofsted, being obligated to this law for all their activities with private and third sector organisations from 1^st October 2009.

            

Conference further notes  that:             

      During this 2009 consultation Ofsted expressed the concern that it could be required to introduce different inspection and regulatory requirements for private/third sector providers operating in the same sector as state providers who are legally required to provide the same levels of service.

      The government responded by noting that Ofsted could voluntarily apply the required standards to its activities with state funded organisations.     

      However the government did not obligate Ofsted to the law regarding its action with state funded schools, leaving open the possibility that Ofsted could fail to apply best practice to its activities and that if it did so state funded schools would have no legal mechanism to use to require Ofsted to improve its conduct.

Conference is gravely concerned that:

     There has been a recent significant rise in reports of state funded schools having serious concerns regarding the behaviour of Ofsted.

     In cases where schools have attempted to challenge Ofsted’s behaviour, which appears to seriously contravene best practice, they have been unable to obtain judicial reviews of Ofsted because they have no legal framework to use.

Conference is greatly alarmed that:

      This inconsistency seriously undermines the objective of increasing professional competencies and freedom for those working in education and that Ofsted is being used to put pressure on certain schools to opt out of Local Authority control.

Conference calls on Liberal Democrat Ministers and Parliamentarians to:
       Press for an order to the Legislative and Regulatory Reform Act (2006) to be rapidly passed obligating Ofsted to this Act for all its activities, in order to give state funded schools the same protection as private and third sector schools.

References:

General information about Ofsted including the date of creation:

http://en.wikipedia.org/wiki/Ofsted

The commissioning of a review to “consider the scope for reducing administrative burdens by promoting more efficient approaches to regulatory inspection and enforcement, without compromising regulatory standards or outcomes”

http://www.berr.gov.uk/files/file22988.pdf

The Legislative and Regulatory Reform Act (2006) with a direct link to the salient point

http://www.legislation.gov.uk/ukpga/2006/51/section/21

The Regulators’ Compliance Code

http://www.berr.gov.uk/files/file45019.pdf

The 1^st October 2009 Order to the Legislative and Regulatory Reform Act is here

http://www.legislation.gov.uk/ukdsi/2009/9780111481080

and the salient point re Ofsted is at (21) (blue numbers).

Government Response to the Consultation on Extending the Coverage of the Regulators’ Compliance Code and the Principles of Good Regulation (May 2009)

http://www.bis.gov.uk/files/file51591.pdf

The key points are 4.8 and 4.13

Downhills

http://www.bbc.co.uk/news/uk-england-london-19271143

http://www.whatdotheyknow.com/request/107850/response/268894/attach/3/Downhills%20Correspondence.pdf

Furness Academy and Other Cases

http://www.guardian.co.uk/education/2012/jun/25/ofsted-inspection-upset-headteachers-schools

http://www.bbc.co.uk/iplayer/episode/b01k1nk6/File_on_4_School_Inspections/

The Coming of Age of Ofspare

Ricky Mauve took up the reins as SoS for Parenting with great enthusiasm.  He’d arrived in power on the back of his promises to increase freedom in parenting and to properly reform Ofspare.  A recent journalist with the Jeremy Mogul empire, his close friendship with Mr Mogul himself ensured he had all the freedom he needed to describe how wonderful his ideas were in all the major papers.  The uninitiated were enthusiastic (or at least they were according to the papers – and enthusiasm breeds enthusiasm in these situations).  Those who had children reserved their judgement.  Some had heard Mr Mauve speak and were concerned that his slick rhetoric served to effectively conceal deeply ignorant views.  Others had read all his articles and had noticed that in one of them he had declared that he was going to run a cultural revolution like the one in China.  Because, unlike Mr Mauve, they were aware of that particular era of Chinese history they and were also concerned.  

What happened next took those who watched it by surprise. Of course most people didn’t see what happened because they were reading the newspapers which reported only Mr Mauve’s brilliance.  During his fist few weeks in power Mr Mauve forced through legislation to create freedom in parenting.  However the unexpected twist was that this freedom in parenting was offered only to children, who were invited to select their own parents.  Birth parents were stripped of all their rights, as were all other bodies who had traditionally overseen parenting.  All other bodies, that is, apart from Ofspare.  Mauve effectively created a free market in parenting so that professional parents who made a profit from what they did could thrive.

The media gushed in admiration (usually in Mr Mauve’s own words) at these tough policies designed to strip the incompetent, amateur parents out of parenting.  The papers paraded the triumphs of the children who had moved from low scoring parents to high scoring ones in the past.   They waxed lyrical about how Mr Mauve’s increased emphasis on parenting ability would drive up the standards of the behaviour of children in society. Mr Mauve’s brilliance in shutting down all the government’s advisory bodies on parenting was also lauded (as these bodies were clearly responsible for the slow rate of progress in the past) and the press enthused about the discipline he showed in systematically clearing out the enemies of the state who worked in the department for parenting and didn’t entirely share his views, replacing them all with young people who knew nothing about parenting.

There were riots, which of course confirmed timeliness of and the need for the inspiration leadership skills of Ricky Mauve and the public were extensively reminded.  Mr Mauve cranked up the energy of his reforms, establishing plans to shut down all university departments in parenting and instead to ensure that parents received their training directly from parents who were highly rated by Ofspare.  Mauve’s deputy, Nichola Glibb, proclaimed that she would rather her children were raised by young parents of many children than by older parents who were raising only his child, no matter how good they were.  The fact that, of course, she’d never been a mother went without saying as no self respecting person over 30 who had not completed the NPQOP (the National Professional Qualification in passing Ofspare tests in Parenting) would dream of attempting to inflict their deeply flawed parenting skills on a child.  

Mr Mauve was found guilty in court of not consulting on his policies, so he set up sham consultations with remits which prevented relevant discussion.  Freedom of information requests were a source of embarrassment but his decision to replace all those around him at the Department for Children proved wise as the replacements were so passionate about his policy that they had no qualms about deleting the evidence of his illegal behaviour wherever necessary.  

Mr Mauve persuaded his idol Sir Jack Monterey to deliver his dream of driving up standards with the help of Ofspare. A grade 3 rating by Ofspare which meant that there was no cause for concern about the progress of the children was reclassified as being an unsatisfactory rating requiring intervention. All parenting which responded to the needs of children rather than proactively parenting them in all the Ofspare approved ways which was now being classified as grade 3 was therefore eliminated in a stroke aside, of course, from the fact that it had only existed with the support of the university departments in parenting which were now being shut down anyway.  Many parents operating in very difficult circumstances, such as them having children with special needs or little money slipped from achieving satisfactory rating to being failing parents.  On of Sir Jack’s key initiatives was to ensure contextual circumstances were not examined as part of the test.  There were to be no ‘excuses’ for poor parenting.  

The image of the wise HMI inspector was much publicised but in reality hardly any existed now as the original inspectors were gone and the new ones had been trained in an era where they’d have few or no failing families to inspect so had learned only to tick appropriate grading boxes.  Blessed with the image of credibility their predecessors had created for them most had little awareness of their own limitations or of the stark contrast between their own methods of operation and those of other regulators. 

Some HMIs who were still far more capable than the system which had produced them, and occasionally one such individual would be tasked with coming up with proposals to reform Ofspare in order to appease the voices of complaint.  But while changes were rapidly and frequently made, they did not address the issue associated with finding the increased numbers of parents to be designated as being failing parents which Gove and Monterey demanded. In practice these changes served to ensure that all complainants were deflected with the response that the system had changed since the issues they had observed had taken place (or was about to change) so their concerns had already been addressed.  The chaos of the constant changes created a fog in which parents could be labelled as being failing parents for not having adjusted sufficiently rapidly to the new standards and this helped towards achieving the target number for failing parents.  The shutting down of Parents TV which had previously informed parents about changes in standards and best practice thickened this fog, as did the sudden change in the behaviour of the state parent discussion forums (the non-state forums had withered as they had been the poor relation to the well funded and run state forums under the previous government).

Ofspare were arriving at inspections with the results of those inspections having been pre-determined based on the outcomes of the tests the children had sat which were designed to test how well they knew the skills their parents should have taught them.  Their job was simply to adjust words in a pre-written text to make it sound like it related to the particular situation.  Other inspectorate bodies looked on in horror.  Ofspare inspectors didn't notice.

Mr Mauve then took personal responsibility for appointing those deemed fit to be parents.  It was suggested that he was using his position to allow his personal friends to be parents.  Given the pattern of inspections it was clear that he was telling Sir Jack which parents to inspect and fail directly to create a supply of children to give to his professional parent friends.  In response to these accusations the Mogul press turned up the volume of its proactive denunciation of all those who raised any objections to Mauve’s improvements in parenting who found not only that they had no voice and no rights, but that if they raised objections they know that not only would they be punished but all their friends and family would be too.

In a committee room in parliament one night the head of parenting in Neighbourland came to speak to anyone who would listen.  Given that Neighbourland was topping all the international comparison tables in parenting he spoke to a packed room.  He spoke about how he'd been inspired by the parents he'd met here 25 years earlier when he'd done his PhD in parenting.  He explained how the principles of developing parents and children together had been applied in his country as it was considered important that children had excellent role models.  He emphasised the importance of tailoring parenting to the needs of the particular child and of parents (rather than politicians) determining policy in parenting.  He was asked about Neighbourland's inspectorate body in parenting and he explained that he had been appointed into the role of Chief inspector and that his only action in that role had been to shut down that central inspectorate body - replacing it with a system where parents could select from accredited inspectors.  At this point Sir Jack Monterey walked out.  But everyone else stayed and when the two hours was up the applause went on and on.  Nobody wanted this brief moment of sanity to end.  Nobody wanted to return to a world they couldn't control and to madness they couldn't stop.

Ofspare – The Decades of Attrition.

When it was created Ofspare’s clear key strength was its HMIs.  These had come from the old service which used to assess only children who were clearly in very vulnerable situations.  They were determined that parents from disadvantaged backgrounds should be sensitively and properly assessed and that the full variety of parenting should be valued.   They had a substantial input into the assessment framework and they were confident and independent minded.  Some of them had been critics of the concept of Ofspare and now they were in place they were determined to ensure that Ofspare operated to a high professional standard which raised it above the flawed foundations on which it was built.  They took tremendous care to ensure that the government delivered on its promise to ensure that children who were removed from their parents received substantial funding and high quality love and care.  The government was able to use this reality to convince the public that the criticisms of Ofspare had been unjustified and it used its links with the media to ram home this message.  But of course the HMIs who has worked only in the cases of clear need could not possibly cover the job of inspecting all parents as was no required so many new ‘additional’ inspectors were brought in.

The data collected from all these inspections generated some interesting insights.  Parents with several young children generally scored more highly.  Younger parents scored well, as did wealthy parents.  Older parents of one only one child generally did not to score well.  It was suggested that this indicated that younger parents with more children tended to use more explicit parenting strategies with plenty of rules and boundaries which were more easy for Ofspare to accredit highly than less dictatorial methods of parenting but such insights were too complex to make good headlines in the mass media where ‘Over 40, Over the Hill for Parenting’ and ‘Only Children Suffer’ generated more sales.

The number of children being taken away from their parents went up.  Where people saw friends, family and neighbours who they trusted and respected losing their children they assumed that they were witnessing a rare mistake and they bought into the media message that it was worth it for the bigger picture.  The parents affected saw their children being taken in by exceptionally able parents and given the very best of everything.  This and the very narrow window of time they had to object (which seemed to hit them at a particular point when their confidence and spirits were broken and had not yet had a chance to recover) and the fact that Ofspare was its own judge and jury of its decisions not only meant that there were very few complaints, it meant that assumptions of guilt and poor conduct on the part of the parents who had lost their children were endorsed because they did not win their children back.  Parents who had lost their children often suffered breakdowns and descended into substance abuse, further confirming their guilt in the eyes of society.

Aware of the electoral popularity of Ofspare and with an election looming, some members of the government created development plans for Ofspare which were entirely to do with electoral popularity rather than to do with the quality of the service Ofspare provided.  Horrified by this some of the original HMIs resigned.  Others found themselves sidelined as it was perceived that they were blocking the government’s will.  At best those who were promoted instead did not have the wealth and depth of experience of dealing with children in serious need that the original HMIs had had.  At worst they were people who sought their positions so that they could remove children from particular parents or categories of parents they disliked.

Aware of the issues arising with Ofspare and securely in power following its re-election, the government did three things.  Firstly it invested heavily in intervention strategies designed to ensure that children were not removed from their parents.  Secondly it set up online networks so that parents could support each other in developing and defending the full variety of styles of parenting and thirdly it set up a nationwide review to analyse best practice and the law in inspection and regulation.

But the variety of parenting styles had gone, with the exceptions which proved the rule surviving only where they had close contact with and the support of university departments in parenting.  The fact that only the outstanding rating recognised the styles of parenting which responded to the needs of the individual child (rather than proactively parenting using all the strategies a child might need) meant that it was only parents who could explicitly define what they were doing and why it was justified who were now parenting in this way.  However even they found that Ofspare often did not credit their skills.  In fact Ofspare had taken to testing children on what they had been taught by their parents and what they knew about life and society.  Children parented in this way tended to score highly on the second test about life and society and this prevented their low scores on the first test putting them into the lowest category where intervention was  not required.  So when the definition of outstanding practice was rewritten to make it as prescriptive as all the other gradings no-one bothered to object.  Few could remember why it had ever been otherwise. Ofspare’s inspectors set up personal businesses in advising parents on how to tutor their children so that they would pass Ofspare’s tests and it became standard practice for all parents who could afford such support to get it and to use it as their guide for how to parent. Hence the divide in the results achieved by rich and poor parents widened.  

The general review of inspection and regulation generated some important insights.  Firstly it was clearly expressed that regulator must behave in ways which were transparent and consistent and it was concluded those inspected must have the legal right to hold their regulator accountable if this was not the case.  Secondly it was found that regulators had a duty to clearly define unacceptable practice and to intervene only in cases where such unacceptable practice was identified and then only with measures which were targeted at those issues and which were proportional to those issues.  Thirdy, the practice of rating the quality of services in cases where there was no cause for concern was roundly condemned both because it had been shown to prevent healthy variety and innovation and also because it had been proved that inspectors who were rating services in this way consistently failed in their duty to report to government regarding what was actually going on in the areas of society they regulated (as they were too busy assessing them according to predefined categories  so were not forensically investigating what those organisation were actually doing).  Laws were defined which gave organisations the power to hold inspectors accountable for adhering to these standards.  Modes of best practice for effectively driving improvement were defined so that regulators could defend high quality practice.  Most regulators requested some time to work on redefining their cultures and modifying their practice so that they were properly complying with the law before it was introduced and the government accepted their point. 

However wider events determined that the government would fall and be replaced.  Aware of its impending end it scrabbled to pass an order to the law on inspection and regulation which would obligate all inspectors to it.  Five of the seven national inspectorate bodies welcomed it with no reservations, understanding that it would give them the freedom they wanted to reject inappropriate government intervention in their business of improving practice in the organisations they regulated for the benefit of society. Ofspare raised objections and was clearly not ready to conform to it.  Worried about the chaos which would be created by forcing a regulator to be obliged to laws it was clearly violating the government obligated Ofspare to the law only with regard to its inspection of parents with high incomes and clearly directed it to conform to it, accepting its assertion that it could only run one system of inspection for all.  But this left Ofspare subject to it’s original legal framework for most of its activities and meant that poorer parents were now alone in being inspected and regulated by an authority which was accountable only to itself and to the secretary of state who had oversight of it.

Ofspare

In response to last summer’s riots, the government has decided to create Ofspare (the Office for Standards in Parenting).

Parents will be regularly inspected with their standard of parenting being graded on a 7 point scale. Any parent who scores 1 will have their children immediately removed from them.  A score of 2 will result in them being placed on ‘notice to improve’ with their parenting being inspected every four weeks and their children being taken away from them if they do not rapidly improve their scores.

The strongest and most convincing complaints have come from those parents who allow their children a lot of freedom.  They are worried that while the skills of strict parents are obvious, their skills are more subtle and less easy to identify and correctly grade.  They say that they like to watch their children and allow them to make mistakes and explore the world as much as possible, intervening only when necessary and usually through subtle methods of encouraging their children to reflect on the consequences of their behaviour which a stranger would be unlikely to spot and may confuse with poor parenting.  They are arguing that the purpose of inspection should be to eliminate unacceptable behaviour and some of them think that this is best done through support rather than the immediate punishment of the confiscation of children.  They think that acceptable parenting should not be graded as the grade definitions proposed will reduce diversity of practice, freedom and innovation and enhance the likelihood of parents moving towards stricter, more overt and excessively interventionist styles of parenting which are easier to accredit.  They are also concerned that parents who do not understand the challenges associated with raising children with specific needs or raising children in difficult economic and social circumstances will negatively judge good parents who are coping with very challenging circumstances.

Parents have also complained that the schedule of high stakes inspections will force them to focus on passing those inspections rather than on their other activities which contribute to society which they feel that ultimately their children will benefit from seeing them participate in.

In response to their criticisms two concessions were made.  The first was that the definition of the highest rating has been loosened to allow it to encompass excellent parenting which allows significant freedom.  The protestors say this is not good enough as parents who allow more freedom need to progress as well (they don’t suddenly emerge as being outstanding parents) and the issue whereby not all inspectors may have they experience to assess this type of parenting has not been properly addressed. They are, however, more positive about the provision that parents should be allowed to select from accredited inspection bodies – allowing them to reject those which do not have the relevant expertise to assess their practice.

However in a last minute unexpected twist the second decision to allow parents to select their own inspection body has been reversed.  A couple of proponents of strict parenting who had been defeated during the consultation processes quietly submitted an amendment to force all parents to be assessed by one regulator.  They managed to get that amendment scheduled for debate at midnight on the night before Ascot so that it went through without anyone noticing soon enough to object.

So now Ofspare exists.  What do you think will happen next?

Twinning Schools

Does anyone else remember the post war European twinning program which saw communities making arduous bus journeys and arriving exhausted to enjoy the hospitality of families they could barely communicate with?

Cockermouth, where I live, still has a thriving partnershipwith Marvejols, a rural town in the south of France.  My favourite memory of this twinning would be the time my first husband (then my boyfriend) and his brother were eagerly awaiting their duty of entertaining the two teenage ballet dancers (guaranteed to be fluent in English) who were coming to stay with them.  Suffice to say it was their mother who cuddled the eight and nine-year-old girls who arrived and struggled to communicate with them with the aid of heavily Cumbrian accented phonetic French from a phrasebook.

I came to believe then and do still firmly believe in the importance our learning to build direct relationships with people overseas which bypass the mass media and government.  I also think our children benefit greatly from having the opportunity to stay with another family.  But I believe it’s time we explicitly decoupled these two ambitions and incorporated them in different experiences and in this blog I will explain why.

Between 2000 and 2002 I had the wonderful privilege of leading the maths teaching component of a British Council aid project in Jordan.  The Jordanian government had requested that UK teachers support their teachers as computer rooms were introduced into pilot schools for the first time. 

The Jordanian teachers and Jordanian Department for Education workers we met were razor sharp in demanding we justify in precise detail the benefits of introducing computers into schools and it was in the climate of the highly stimulating dialogue that we realised that we were at a transition point between stand alone computer technology and the internet, and the benefits that each brought to education were very different.   

Over the two years of the project I came to believe that it was time to re-launch the European twinning project as a global project with a bigger emphasis on students studying the social, political and geographical context of their twinned school in collaboration with students at that school using the magic bullet the internet promised to be.  When I travelled to Jordan in late 2002 to celebrate the conclusion of the initial project the Middle East was preparing for imminent war and it seemed everyone was gone.  But as is often the case in these dark hours the people of quality were left and in this rarefied company my colleague Steve Moss and I were able to have long conversations with many inspiration people. We listened to their hopes and fears for the future and guided them towards the twinning vision we had come to be so passionate about.  And then we went home and the bombs fell and it seemed nothing would come of it.

But we had reckoned without Dr Khalid Toukan who listened to his ministerial department and went on to request that the British Council’s next project be a trial link between schools in Cumbria and in Jordan.  In 2003 and 2004 top studentsfrom Jordan and Cumbria traveled with teachers to each other’s schools, taking assemblies they had prepared with their friends at home and inspiring their communities to think deeply about each other’s cultures through their excellent use of the latest audio visual technologies.

The British Council went on to make Connecting Classrooms a flagship project and last year I had the wonderful experience of watching my son’s year 3 assembly about his school's link with a school in Ghana (created within the British Council infrastructure) which was empowered by real insight and resources from his teacher’s visit there.  I hope my children will also benefit at secondary school from further new links which are supported by Connecting Classrooms.  You may remember a TV advertising campaign last year which encouraged schools to link up in the run up to the Olympics under the patronage of athletes and teams who would be coming to Britain for the Olympics.  This project is also supported by the British Council twinning infrastructure as are many more.

Now the internet is delivering all we dreamed of and more the potential of these links to benefit student learning across their curriculums have greatly increased.   At present most links are with developing countries but it was my original intention that each of our secondary schools would link with a variety of partner schools including some in developed countries and I still hope this will be possible in the long term.

However what’s missing is the other big benefit of the European twinning program - the experiences children have when they leave their own families and go to stay with another family.  Very few children actually get to visit their partner schools.   

In a recent blog Matthew Taylor suggested that we should link contrasting schools in the UK.  I would like to strongly endorse this idea.  We could build strong and lasting links between pairs of UK schools with contrasting contexts, nurturing a culture which believes that children benefit from coming to understand the lives of other people, receiving love and invitation of another family and exploring parts of society they would not normally be able to access.  With care and support we could link schools in contrasting areas.  Parents and host parents could chat freely to ensure children are better supported in their exchange than was possible in the early days of European twining and friendships could be made this way. 

We’ve become very good at teaching our primary children to travel away with their classes.  Now I’d like to see children embark in low cost family to family exchanges during Key Stage 3.  Here in Cumbria we have tremendous problems persuading children to leave home to go to university and we have little ethnic diversity so it would be nice to see our schools linking with schools in cities so that an exchange could be combined with exposure to university life and exercises to build students’ confidence in seeing university (or moving away from home in another context) as being a possible futures for them, as well as giving them real opportunities to properly experience the variety of British minority cultures.  In return we can offer both our farming and rural culture and our energy coast to inspire children who have had access to neither.

As with ‘Connecting Classrooms’ the benefits of teachers having the opportunity to travel and explore the lives of others up close are multiple and substantial.

I believe that by decoupling the objective of having most children travelling and staying with other families at a young age from the objective of children coming to understand life in other countries we can create two schemes which would both be more robust and viable in the long term than their wonderful and inspirational parent – the European twinning project. 

Footnote:

Dr Toukan was awarded the Gandhi Peace Medal in 2003.  He is a key architect of projects like Sesame  , the Middle East synchrotron project which founded jointly by Bahrain, Cyprus, Egypt, Iran, Israel, Jordan, Pakistan, the Palestinian Authority and Turkey.  Looking back now it is difficult to describe how impossible the idea of British and Jordanian children taking each other’s assemblies seemed to so many people in 2002 and the psychological barriers which had to be overcome.  I have not met Dr Toukan since 2002 but I am deeply indebted to him for his patronage of our trial link project and I would like to publicly offer my thanks to him, his staff at the department for Education in Jordan, Tim Gore and his staff at the British Council in Jordan and all involved in Cumbria for bringing this project to life and demonstrating its incredible potential.

Ten Hours with Erica - Recommendations

Some recommendations for schools, teachers, parents and students who are struggling with maths at KS2 and beyond.

1.  Don’t give up.

Erica had been offered interventions and support in maths before but they hadn’t worked.  There are two reasons why previous interventions may not have worked but a future one might.  Firstly it may be because the student has too much else to cope with or isn’t in the right frame of mind at the time the intervention is offered so they can’t take advantage of it.  Secondly it may be because the intervention offered is not the right type of intervention (the next points should offer some insights into why this might be the case).

2. Go right back to basics.

Does the student actually know their numbers?  Do they know and understand their number bonds to 10 and to 100?  Do they have the core vocabulary for mathematics?  Do they understand base 10?  Do they properly understand what addition, subtraction, multiplication and division are?  There are many more questions than these which need to be carefully asked and explored.  ‘The Dyscalculia Assessment’ by Jane Emerson is an excellent step-by-step guide which explains how to assess a student’s grasp of the fundamental structures in mathematics so that the precise difficulties they have can be identified and addressed.

3. Build the confidence bubble.

Sometimes an intervention is offered which gives the student confidence with their maths when and only when they are working with the adult who provides the intervention.  It is crucial that from the very beginning I expected Erica to work on her maths when I was not with her.  Having established that expectation with a single topic I then built it across wider topics before carefully managing the step where she started to do math in her classroom with her usual class teacher that she clearly understood.  Once I was confident a new norm has been established in school Erica stopped needing me.  I hope to stay in touch with her and will offer her support again if she needs it but it is important to notice that I did not withdraw when I felt I had covered all the topics Erica needs, I withdrew when I felt her confidence with maths was fixed and that she was ready to make full and effective use of her normal lesson time again. 

4.  Challenge the student.

Even though we went back to basics in maths I didn’t spoon feed Erica.  I listened to her and helped her express what she was thinking and explained how her thinking linked to other ideas in maths.  After the first couple of sessions I relentlessly told her silly wrong answers to try to force her to challenge me and to recognise and defend her own point of view.  I told her precisely what I was doing and why (because her confidence had been so damaged she’d stopped trusting her own opinion and we needed to sort that out) but she still found it incredibly hard to think that she might be right and I might be wrong.

5. Use real objects and visual structures.

We usually had cubes to count, fraction pizzas to build, flat or solid shapes and so on in front of us and if we didn’t then we would draw sketches to help us ‘see’ what we were doing.  These visual aids are extremely important tools for communication.  Erica was used to struggling and failing to explain what she was thinking and having her own thought suffocated by an explanation from someone who was thinking through the same problem differently.  With real objects to play with I was able to build her confidence and her belief that she could explain her own thoughts and be understood and that she would be able to follow explanations offered by others which she’d failed to follow when they’d been abstract.

Ten hours with Erica

This is a true story about how a student in year 6 (Erica is not her real name) who was experiencing very serious difficulties in maths became confident and happy in her work.  I’ve written it down so that other teachers, parents and students can read it and see if there’s anything in it that might help them.

On average each session with Erica lasted about 45 minutes.  So although this article is called 10 hours with Erica in reality I’ve probably only spent about 8 hours with her so far altogether.  I'm keeping a couple in reserve in case she ever needs them in the future.

Preamble

One day as I saw a girl I didn’t know come running out the front door of my son’s primary school crying her heart out.   She sat down in the stone garden sobbing violently.  While my own children played I went and sat beside her with my arm around her.

After a little while her mum appeared from school and shouted for her.  They left together.

A week or so later I spotted the mother and went to chat to her to check that it had been okay that I’d put my arm around her daughter.  A very sad tale of how miserable Erica (her daughter) was in maths came tumbling out.   Erica had severe hearing difficulties until she was 7 and when she began to hear she had so much to catch up on she simply refused to engage with maths at all.  Now, in year 6 and with SATS approaching, her inability with maths was overwhelming her and dominating her life.  Mum was looking for a tutor.  I offered to tutor Erica if her mum would look after my children while I did so, an offer which was readily accepted.

Session 1: Exploring shape

I opened a box of ATM mats, which are regular polygons all with the same side length manufactured like beer mats.  I simply asked Erica to create patterns.  She created a tessellation, so we discussed tessellations and what they were.  Then she created a picture with mirror symmetry so we discussed and explored mirror symmetry.

We found that although she knew the names triangle and square Erica did not know pentagon, hexagon, octagon or decagon.  We learned those names by linking octagon to octopus, decagon to decimal and hex to six (both 3 letters end in x).

Each time Erica created a pattern I got her mum to come and look at it and to cherish and understand what she had done.   The atmosphere was happy and very positive.

Erica asked if she could draw her patterns so I got some wallpaper and she drew them by drawing round the shapes. 

For homework I asked her to learn the shape names and create more patterns on wallpaper – including at least one tessellation and one symmetrical picture.

Erica was highly literate and very clearly someone who would benefit from teaching which was always based around things she could see.  I explicitly reassured her and her mum that that was what she was going to get from me and that it would overcome her problems. 

Session 2: Ways of adding and base 10.

Erica had completed her homework beautifully and had made some observations about which shapes tessellate and which don’t which she was keen to share.  We put her drawings away so that we would be able to come back to them as an introduction to talking about angle at some time in the future.

I gave Erica some piles of blocks to count and after letting her do that for a while we explored how building them into sticks of 10 could help her ‘see’ how many there were more easily.

I then gave her two piles of blocks at a time to add.  Erica was not comfortable working in base 10.  She wanted to count all and had a preference for grouping the blocks into fives to help her do that.  I let her do that for a while and then showed her how grouping the blocks into 10s (as earlier) gave us a way of finding the sum more rapidly.  We took time to talk about the difference between her preferred method and the method her teacher would have been trying to teach her and to show her that they weren’t very different.  I reassured her that by using visual aids such as multilink blocks she would be able to communicate much more easily with me and her teacher and that would help her teacher understand her methods and her understand her teachers methods much more easily than had happened before.

For homework I set her some simple sums and asked her to use blocks to help her do them.  I asked her to tick the answers she was confident with, mark the ones she was not so sure with and write some sums of her own.

Session 3: Reviewing adding in base 10 and clip together shapes

We reviewed Erica’s sums.  She’d marked which she thought were right and which she was confused about.  We just explored them, using the base 10 blocks and puzzling out how to work through them.

Then we got out the clicksy polygons and made some 3D shapes, talking about the names of the flat shapes and starting to look at the properties of the solids.  I tried to talk about edges and corners but the way the bits fit together confused that as the parts of the edges which pop inside each other look like extra corners.

Homework was to build interesting solids from the clip together shapes.

Erica talked about how she’d been doing averages that day at school and hadn’t had a clue what was going on but it hadn’t mattered because her teacher had taught a ‘cheats method’ to help her find the answer with a calculator.

At this stage I started to try to find some teaching materials Erica could constructively be working with in class at times when she couldn’t follow the main lesson.

Session 4: exploring nets and solid shapes

Erica brought her shapes she’d made (mainly irregular).  I asked her to choose her favourite shape and she chose a double length triangular prism she’d made.   We talked about each shape. 

This week we used an exercise I’d already introduced in previous sessions, where I tap around the walls of the room with a stick to get Erica to count up and down (I would name some numbers and then stay silent while I tapped backwards and forwards to get her to count up and down).  When she was confident I would focusing make the exercise more challenging by moving into negative and large numbers and making difficult jumps like ‘down one from 10000’.

This time I tried tapping down for doubles but Erica really struggled with this change. 

Then we explored a box of solid shapes – describing them and naming them.  We talked about nets and made them on wallpaper by drawing round the faces of a square-based-pyramid, cutting it out and exploring the use of flaps. 

We talked about nets in general and opened out the triangular prism from earlier to turn it into a net in different ways.  Erica can clearly manipulate nets in her head.

Homework: By drawing round the faces of the 3D solid shapes, create nets for them. Name each net with the help of the lists of the names of the solid shapes.

Session 5: Introducing the open number line

Erica brought with her the beautiful nets of 3D shapes she had made.  I asked her to choose which was her favourite and talk about it.  She chose the ‘tent prison’ and we laughed about that – clearly contrasting the spellings prison and prism.  She spoke about each shape in turn.  I helped her notice that on prisms the faces which are not ends are all rectangles and on pyramids the faces which are not the base are triangles.

Then we started work on addition with an open number line.  We started with the first number and Erica added the second by breaking it into easy bits.  We used units, tens and hundreds generally but Erica did start to group them.  We moved on as soon as she was confident from 38 + 25 to 134+33 to 326 + 107 and so on.  We looked at adding 199 by adding 200 and taking off 1 – talking more about the strategy and the route than the specific number.

For homework I lent Erica a pizza game and asked her to play it with her family to help her build her confidence with fractions.

I’m working hard on telling Erica very silly answers as if they are right and checking she pulls me up on that which she is beginning to do.  The extent to which she will accept and agree with silly answer I tell her is startling but this is beginning to change with the help of a lot of good humour.  I’m still involving her mother in her progress, both to cherish the positive progress which is being made and to involve her and Erica together in understanding precisely what I am doing and why I am doing it.

Session 6

We explored the pizzas Erica had been playing with, looking at different ways of making a whole and some equivalencies of fractions.  In each case I wrote the sum that we had made with pizza parts on paper and ensured Erica could follow what it represented but had no expectation she could work in this abstract on her own yet.

I asked her how many halves in a whole and she could see it was 2 but for thirds and quarters and fifths she had to make them.  Then it clicked and she knew 1/10ths would be 10 and so on.  We linked that to the names of fractions (1/10ths are called 1/10ths because they come from splitting 1 into 10 parts).

We left the fractions and moved onto creating a 2 dimensional number wall (based on the number tapping exercise in session 4) with blocks.  We used the language three fives and so on – looking at the variety of ways of counting up the totals and in particular looking at why three fives are five threes (you just turn the block of cubes round) and so on. 

I discovered that Erica could count in 2s by rote but couldn’t really puzzle out 4 twos and so on, so I set her a homework of learning to say the two times table which is written out for her with squares to count for the answers.

Erica commented that she’s being forced to do SATS preparation every day and that she got 6 in one test but then today she only got 2.  Her mum says she isn’t sleeping because she’s stressed.  I think this is the right time to talk to school about letting Erica do different work in class and I’m going to suggest they allow her to work through the year 2 workbook as I think this will give her confidence in her ability to do maths she really understands in school while also highlighting points she still does not understand from KS1.

Sessions 7-9

At this point I was able to get Erica, her parents, her class teacher, her numeracy coordinator and her head teacher all to agree to take Erica off SATS preparation in class and to give her a year 2 workbook which she should work on both in class and with me.  In her sessions with me we talked ‘around topics’ – exploring them in wider contexts and with a clear focus on visual structures.  I found it useful to have the year 2 workbook to prompt me to explore gaps in Erica’s knowledge I might not otherwise have spotted.

This helped me identify that Erica’s had a lack of perceptual awareness of perpendicular lines and that she struggled to visualise clockwise vs anti-clockwise motion.  I’ve started to work on this with Erica focusing in particular on kinaesthetic activities but more work is needed.

As we introduced multiplication, I gave Erica visual times tables (3 fours are with a picture of 3 rows of four squares, 4 fours are with a picture of four rows of four squares and so on) which helped her properly ‘see multiplication’ as being repeated addition.

Erica rapidly completed the year 2 work book and we moved on to the year 4 resources.  When we introduced division I set it up as a splitting structure for her which she could confidently use – e.g. for 21 divided by 3 she would draw 3 people and share out 21 things between them.  But we also repeatedly discussed that there was also a chunking structure – drawing the matrix layout which links the two results.  They aim was that if a teacher used chunking or the reverse of multiplication to solve a division problem Erica would not be confused – she would simply know there are other methods and that she only needs to engage with them as far as she feels able because she can return to the structure she is confident with.

Changing Erica’s work in school led to a step-change in her engagement with and enjoyment of maths which her teachers noticed and responded to enthusiastically.   Her attitude to maths away from school also changed and she began to actively look for and obviously enjoy opportunities to calculate.

Published with the permission of Erica and her mum both of whom I would like to publicly thank.


My recommendations on how to intervene to help students who are experiencing severe difficulties with maths are available here.  They are particularly appropriate for students who have had a disrupted early education.

Ofsted: File on 4: School Inspections

Just a quick post to draw attention to this excellent program on radio 4 which is currently available on iPlayer.

Ofsted - A level deeper

The underlying purpose of a regulator is to protect the public interest.
The duty of politicians is to make sure there is a regulator in place.  Politicians also have a duty and a right to scrutinise the behaviour of regulators on behalf of the public.

When the Legislative and Regulatory Reform Act (2006) was consulted with regulators, 5 out of 7 welcomed it as they knew it would empower them in fulfilling their duties to a high standard.

Only Ofsted opposed it and they did this not only with the arguments which are recorded, there also seems to have been substantial obfuscation and a continual supply of misinformation.  This is consistent with my personal experience of trying to engage in discussion with Ofsted.

Ofsted have shown no interest in adopting best practice in the interests of the public.  They have instead chosen to be Gove's puppets for destruction - employing without complaint  or objection procedures which is clearly established to be bad practice.  The disproportionate level of punishment of schools which is taking place, the recategorisation of satisfactory as being unsatisfactory, the processes used by regulators to judge without forensic investigation, - these are all practices which other regulators cannot by law and would not wish to engage in.

Ofsted - Clearing the Fog

This post provides specific detail relevant to my previous blog: Ofsted - Clarifying the State of Affairs.

It seems that whenever the issue of improving Ofsted is raised, a substantial volume of points are raised to confuse the issue.  The purpose of this blog is to list points most commonly raised and appropriate responses to them to help to 'clear the fog' of confusion.  If anyone hears of any other points being made which create the impression that it would be unwise for Ofsted to be obligated to the Legislative and Regulatory Reform Act (2006) please do post them in the comments to this blog so that they can be discussed.

Point 1 - That the Legislative and Regulatory Reform Act conflicts with Ofsted's prior statutes.

The Legislative and Regulatory Reform Act was created to oblige regulators to apply best practice when fulfilling their duties to:

- drive improvement

- protect against bad practice and

- report to the government regarding the state of the organisations they regulate.

It challenged regulators to improve the quality of their practice as they fulfill these duties which are, of course, Ofsted's duties.

Ofsted's previous statutes allowed them to behave in ways which are now recognised and accepted as being bad practice.  Their obligation to the Legislative and Regulatory Reform Act (2006) should clearly override any previous legal obligations which contradict this law.  

Point 2 - The Hampton principles include references to economic progress and are therefore not suitable for the state sector

While the Hampton principles contain references to economic progress, the Legislative and Regulatory Reform Act (2006) does not, it only obliges regulators to act in ways which are transparent, accountable, proportionate, consistent and targeted only at cases where action is needed.  The Hampton principles sit behind this law in that they provide explanations of what good practice is which regulators can use to defend their actions but the law has been written with no reference to economic progress so that it can apply to all organisations. 

Point 3 - That obligating Ofsted to the Legislative and Regulatory Reform Act (2006) will lead to an avalanche of legal cases with which our legal system will not be able to cope.

This was a point made with great energy and conviction on a discussion forum (see comment by Ricky Tarr 07/06/12 7:29pm).  I'm not sure why the poster feels this will happen.  Private schools, public schools and (virtually?) all other regulated organisations already have the protection of this law.  Is it currently leading to lots of spurious claims?  

Applying for a Judicial Review (which is what you do if you're using this law - you are saying that the regulator is behaving illegally and their conduct needs to be challenged) is an expensive process and schools would need to be accountable to their governing bodies and other stakeholders for hat expenditure so I can't see it happening unless there is a clear breach of the law by the regulator, in which case surely it should be happening?

If the regulator is behaving consistently outside the law and several Judicial Reviews are granted, the legal system is configured to cope with this situation because instead of running several separate Judicial Reviews it convenes an 'Independent Commission' which investigates the behaviour of the regulator and examines the interpretation of the law by others who are obliged to it in order to rule definitively regarding what is and isn't legal behaviour for the regulator.  And then the issue should be concluded - unless the regulator continues to defy the law which is not a circumstance I would expect.

Point 4 - This has been previously consulted and the conclusion was that Ofsted should not be obligated to this law

This appears to be untrue.  This document shows that it was the clear conclusion of the last government that Ofsted should be obligated to this law for all its activities (see point 4.11).  Graham Stuart (Conservative MP and Chair of the Education Select Committee) recommended that the Ofsted directorate meet with me to discuss the salient points of my concerns during their consultations regarding their activities last year however despite agreeing readily in public, I was told firmly and absolutely that my concerns would not be discussed by Richard Brooks (Ofsted Director of Strategy).  I can't find any indication that there has been a consultation which has concluded that Ofsted should not be obliged to the Legislative and Regulatory Reform  Act (2006) for all its activities.

Point 5 - We don't need to obligate Ofsted to this law because they are already following it.

No they aren't.  Under this law the areas in which a school is behaving in an unacceptable way must be clearly and specifically identified and any action taken must be proportionate to and specific to the issue identified.  This is not what is happening at present. 

The phrase 'satisfactory is the new unsatisfactory' is deeply at odd with Hampton.  Satisfactory means there is no issue to be addressed.  Unsatisfactory means there is an issue to be addressed.  You can't say that 'satisfactory' is 'unsatisfactory'.  

There's plenty more I could write - please do feel free to get in touch or ask questions through the comments to this blog.  Thank you for reading this.

Ofsted - Clarifying the State of Affairs

In 2005 the government completed a review (the Hampton Review) of inspection and regulation with the purpose of establishing and embedding in law best practice in regulators fulfilling their duties to:

- drive improvement

- protect against bad practice

- report to the government regarding the state of the organisations they regulate.

The Hampton Principles which were established from this review were embedded in law in the Legislative and Regulatory Reform Act (2006), the salient point of which is point 21 which legally obliges regulators to act in ways which are transparant, accountable, proportionate, consistent and targeted only at cases where action is needed. The Hampton Principles sit behind that law to provide explanations of the types of regulatory activity which meets these standards.

I have, for the last couple of years, been exploring why Ofsted uses methodologies which directly contradict best practice as defined by Hampton (see for example blogs her for August and September last year).  I was very shocked by the way in which those in authority refused point blank to engage in intelligent discussion about the component issues.  

In January this year I came to believe that Ofsted have in fact been obliged to these standards.   I knew that the last government had intended to get them under it as can clearly be seen in this document (see point 4.11 and onwards), I knew it made sense for them to be under it, I knew that public and private schools were under it (part 1A point 21) and Ofsted themselves had said it didn't feel it could/should run different systems for different types of school (point 4.8) and then I heard on the BBC TV news that Ofsted were subject to judicial review due to a judgement related to their behaviour at Furness Academy.  This couldn't be the case unless that academy was also covered by the Legislative and Regulatory Reform Act as without this law Ofsted remain unaccountable to everyone but themselves and the SoS for Education.  However it turned out that the BBC report was incorrect.

So while all other regulators are required to the principles of the Legislative and Regulatory Reform Act (shown in green above), Ofsted have a special exemption from it in the case of State Schools.

The main consequence of this exemption from the law is that it allows Ofsted to operate in ways which serve the interests of politicians and itself rather than requiring that it works to the benefit of society and the customers of the organisations it regulates.  The Legislative and Regulatory Reform Act (2006) was the mechanism by which organisations can hold their regulators accountable if they are failing to implement good practice in their own activities.  While all other organisations have the power to hold their regulator accountable, state schools do not.  They have no power at all.  This means that when the regulator behaves in ways which are clearly detrimental to education nobody can stop them.

The consequences of this on the ground are horrific.  When inappropriate regulatory behaviour occurs scapegoats have to be created in and around the school affected because everyone knows the regulator cannot be held to account.  For those of you who haven't seen what it's like when that happens and how good schools, teachers and high quality education are destroyed - all I can say is - lucky you.  Far too many people in education have experienced firsthand the extreme behaviour which is required to try to do everything possible avoid such a situation occurring and have direct experience of how ludicrous and counterproductive much of this behaviour is. 

This could be corrected so easily.  All that's needed is an order to the Legislative and Regulatory Reform Act which clearly makes Ofsted accountable to it for all its activities.  It could be done in just a few weeks.

Ofsted and those associated with them put forward many objections to them being obligated to the Legislative and Regulatory Reform Act.  They are all just smokescreen.  As soon a I get the time I will write a blog which lists them and counters each so that those who wish to pursue this issue can do so effectively and efficiently.

Pasi Sahlberg's Talk and Discussion in the Houses of Parliament: Thursday 17th May 2012

Pasi Sahlberg came to the Houses of Parliament to try to explain how the incredible standards demonstrated by Finnish students in PISA tests have been achieved.

He spoke in committee room 14 which as packed with about 150 people. Two hours flew by and the applause was long when we were reluctantly forced to stop. This blog is an attempt to capture what was said as I remember it. My thanks to Janet Downs for her contributions to these combined notes. Others who were there are welcome to add their memories in the comments section where questions are also welcome.

Five Key Points:

1 Increase co-operation/collaboration, decrease competition.
2 Increase personalised education, decrease standardisation. Recognise that pupils are different and tailor teaching appropriately.
3 Trust professionals, decrease external accountability measures. Don’t use standardised tests judged against the average but increase formative assessment.
4 Focus on pedagogy. Regard technology as a tool not as an end in itself. Pupils need time away from technology to connect with humans not machines.
5 Increase professionalism and reduce bureaucracy. Only professionally-trained teachers should be allowed to work in schools and all should acquire masters status.

The critical emphasis was on increasing equity. The Finnish Government allocates resources to increase equity – this means that money is targeted where it is most needed. 30% of Finnish children are assessed as needing some kind of special education at some time during their school lives. There is no stigma attached to special education because so many pupils receive it and in 22% of cases it is not permanent. Pasi claims that the Finnish government never pursued excellence - they pursued equity instead.

When asked what he would choose if he could advise one thing to English education Pasi said that we should be letting our children play more. School starts at 7 in Finland with children having the option to go half time from the age of 6. Even when they are full time they spend about an hour less in class each day and have much longer play times instead. The teachers spend the time in collaboration, student assessment, school imrovent, welfare issues and planning. Gladwell’s law of 10,000 hours has its most important application to children and play. Little homework is set – especially for young children.

Setting by ability is illegal in Finland and private schools became state schools.

He showed the picture of the different animals in the classroom where the test (to be sat at 10am) was to climb the tree to illustrate points 2 and 3 above.

Pasi got himself appointed as the chief inspector and his only action in that role was to abolish the inspectorate. Areas now appoint their own inspectors/advisers. (There were people at this meeting who remembered the night Ofsted was created - it had been intended to adopt the structure Finland now had but by moving the vote to midnight on the night before Ascot someone managed to get an amendment through to make it a central and compulsory authority).

Some substantial aspects of the reforms have been achieved at times of crisis and/or economic collapse. They have been opportunistic, so for example measures of accountability have been shut down at the same time school budgets have been cut.

He contrasted Finnish culture in education with the culture in many other countries which he called the GERM culture

GERM culture / Finnish Culture
Competition / Collaboration
Standardisation/ Personalisation
School Choice / Equity
Test-based accountability / Trust-based professionalism

Here is an explanation of GERM culture:
Diane Ravitch, New York Review of Books, reviewed Sahlberg’s book and wrote: ‘Sahlberg recognizes that Finland stands outside what he refers to as the “Global Education Reform Movement,” to which he appends the apt acronym “GERM.” GERM, he notes, is a virus that has infected not only the United States, but the United Kingdom, Australia, and many other nations. President George W. Bush’s No Child Left Behind law and President Barack Obama’s Race to the Top program are examples of the global education reform movement. Both promote standardized testing as the most reliable measure of success for students, teachers, and schools; privatization in the form of schools being transferred to private management; standardization of curriculum; and test-based accountability such as merit pay for high scores, closing schools with low scores, and firing educators for low scores.’

Pasi paid tribute to the people in UK maths education who inspired him when he was doing his PhD research in London 20 years ago.

(On a personal note I know those people and they inspire me still – for insight into the culture Pasi would have been experiencing then I would recommend Jo Boaler's book 'Experiencing School Mathematics')

Pasi strongly recommended we read the OECD report: Equity and Quality in Education.

Here is Pasi Sahlberg’s website.

Here is his recent book about Finnish Education.

Assessing students up to age 14 - A better future. Part 10 - At what age should this type of tracking begin? (& tracking inputs)

This blog is subject to these protocols

Young children need to have access to a curriculum which allows them to develop different skills at different times.  Thus during the EYFS and KS1 the emphasis on tracking progress should be placed not on the outcomes in the child but on the child having access to well structured and appropriate learning opportunities.  I think it's reasonable to argue that such an approach could also apply to year 3, creating more space within which a focus on students engaging with the formative concrete tasks which will give students a secure foundation for the later abstraction of insights can be cherished.

So it would be more appropriate for a school to use a tracking system based on an ICT framework like this to share information with parents regarding a child's progress through a reading scheme and their engagement with wider schemes of activities than it would be to share information about the particular attainment targets a child has reached. The focus should be on progress with formative rather than summative activities.

I would hope that a criteria based tracking system for older children would retain a component strand which creates space for each child's engagement with activities which  are intended for formative rather than summative purposes to be shared.  For example if a class is engaging with a practical investigation in mathematics for a single lesson, it should be possible for the teacher to record in a couple of sentences what took place during the lessons and export that comment instantly to the record of every child who was there.  If students took part in an investigation which lasted for several lessons it might be appropriate for a teacher to record individual comments regarding what they achieved (the teacher may also want to store photos of work).  Older students or teachers may then wish to refer to these comments when they are reviewing their progress against criteria which are not so easily assessed, such as their ability to select which pieces of knowledge to use in practical contexts, their confidence in finding strategies to move on when they are stuck and their skills in co-operating with other students.

I would suggest that designers of such systems take care to pay separate attention to the needs of students, parents and teacher up to the age of 8 and their needs from ages 8-14 and should then look to merge the systems on to a single framework.  Ideally I would have completely separate teams working on the designs for the two systems - bringing them together to design an product which includes both systems only when they are well advanced in their thinking.

Assessing students up to the age of 14 – A better future  QUICK LINKS

Part 1: key components of the way forward

Part 2: protocols for this series of blogs

Part 3: integrating formative (APP) and summative (SATS) assessment

Part 4: being allowed to test what is testable

Part 5: more about online testing

Part 6: central tracking of progress

Part 7: supporting diversity

Part 8: student behaviour management

Part 9: bridging the primary/secondary divide

Part 10: at what age should this type of tracking begin? (and tracking inputs)

Assessing students up to age 14 - A better future. Part 9 - Bridging the Primary/Secondary Divide

This blog is subject to these protocols

At present students generally transfer from primary school to secondary school with just three grades - their SATS results in English, Maths and Science.

These grades bring with them two main problems:
- Firstly they are too broad-brush and give little insight into what each child can and can't do.  For example one child may achieve a particular level in maths without answering a single question with content at that level or higher.  However another may achieve the same level by answering questions at harder levels but losing marks at lower levels through carelessness or through them having gaps in their knowledge which it is important to fill.  A system of integrated formative and summative assessment could provide far more detailed and useful information at the time when a child transfers between schools.

- Secondly they are too high stakes and are based on just a few exams.
The pressure on primary schools to cram students so that grades are artificially inflated and knowledge is not retained is intense.  The grade they achieve represents only what they could do under exam conditions during one week.  A system of integrated formative and summative assessment would remove the need for students to engage in high stakes exams and could far more accurately  record what they can and can't do by accumulating data over time which can include multiple perspectives on each criterion.

It is therefore essential that those designing systems of integrated formative and summative assessment plan for how data can be transferred between schools whether or not the school a child moves to is using the same tracking system as their previous school.

Assessing students up to the age of 14 – A better future  QUICK LINKS

Part 1: key components of the way forward

Part 2: protocols for this series of blogs

Part 3: integrating formative (APP) and summative (SATS) assessment

Part 4: being allowed to test what is testable

Part 5: more about online testing

Part 6: central tracking of progress

Part 7: supporting diversity

Part 8: student behaviour management

Part 9: bridging the primary/secondary divide

Part 10: at what age should this type of tracking begin? (and tracking inputs)

Assessing students up to age 14 - A better future. Part 8 - Student Behaviour Mangament

This blog is subject to these protocols

When designing a system of integrated formative and summative assessment, it is worth considering how such a system will link to any systems a school may already have in place for tracking student behaviour.

It seems appropriate that a system of integrated formative and summative assessment should be proactively designed to work well with any systems of behaviour tracking a school may use as the two issues impact so closely on each other.

Edward Whittaker at IRIS was very helpful in helping me to understand some of the issues involved in behaviour tracking.

Assessing students up to the age of 14 – A better future  QUICK LINKS

Part 1: key components of the way forward

Part 2: protocols for this series of blogs

Part 3: integrating formative (APP) and summative (SATS) assessment

Part 4: being allowed to test what is testable

Part 5: more about online testing

Part 6: central tracking of progress

Part 7: supporting diversity

Part 8: student behaviour management

Part 9: bridging the primary/secondary divide

Part 10: at what age should this type of tracking begin? (and tracking inputs)