The Challenges of Implementing the New Primary Mathematics National Curriculum

I've written a report on the challenges of implementing the new primary national curriculum for maths.

It's available as a free download here:
http://authenticmaths.co.uk/report-primary-schools-new-national-curriculum/

Tax Policy, Financial Literacy and Education

Comment regarding the guiding principle of ‘simplicity’ on page 20, Tax Consultation Paper 114

It is important to clearly describe the difference between:
‘simplicity for the benefits administrators’ (i.e. implementability) and
‘simplicity for tax payers’ (i.e. transparency).

Implementability must  be considered as a limiting factor.  However transparency is a complex and very important principle for many reasons.  It is not about the numbers being simple.  It is about individuals properly understanding the numbers.  The numbers can actually be quite complicated if they make sense graphically.

An individual wants to know three things about their own income:
1. How much tax will I pay if I earn/receive different amounts of money?
(This can be shown with a graph.  There should also be a graph for the amount of money which they will get for different income levels given effects of national insurance and benefits.  There also needs to be a clear logical statement which would allow people to reconstruct the graph if they didn’t have it)
2. What is the %tax I pay as I earn different amounts of money?
(I.e. if my income goes up by £2k a year what proportion of that will I see?)
3. What are the implications of proposed tax changes for my income?

Here are two examples of graph 2 – overlaid to compare policy:

Here is an example of graph 3:

Health warning.  I am not confident these graphs are correct even though I have a degree in maths and management and have tried hard to research this topic.  Hence the need for this policy focus!

(Sincere apologies to readers for the current malfunctioning of the graphs. Please don't hesitate to contact me if you'd like the originals through a different route.  I'll try to fix this problem when I get time.).

Beyond understanding their own income people want to know how their graphs differ from other people and why those differences exist.  It should be possible to rapidly overlay the graphs of people in different 

circumstances and to clearly see and comment on the different.  At present it isn’t. 

When tax is considered in this way things like earnings from investments, income from inheritance tax and so on are considered as part of the income of the individual receiving them.  It may be that only a proportion or an amount after a threshold of these should be considered.  If so this should be openly and transparently discussed.

This policy principle should be clearly linked to the introduction of the teaching of financial literacy into schools.

One of the drawbacks of the £10k threshold is that it means that many young people will not pay tax and will therefore not learn to cope confidently with the tax system.  One thing we could do to address this would be to say that from the ages of 16-25 you pay 10% tax on your income if you are still living at home (expense on education could be deductable?).  The purpose of this would be to actively link the teaching of financial literacy training all our young people to engage with the tax system and their state.  If they engage actively at this age they will not forget that experience.

We should not forget the Jimmy Carr case.  Lots of honest tax-payers pointed the finger.  We pay our fair share and so should you.  Most people want to be honest tax-payers who pay their fair share.   The kind of thinking I’m describing would make it very clear to all what everyone’s fair share was and therefore it would be blindingly obvious to the individuals concerned and those scrutinising them whether they were tax avoiding or not.  There will always be some people who seek to tax avoid at all costs but they are actually few and far between.  There are a heck of a lot of people who will tax avoid if they think it’s the done thing and are unaware of what they should be doing.  We should not neglect to capitalise on the things which peer pressure can achieve that complex legislation never has.

About the contributor:

Rebecca Hanson is a lecturer in mathematics education.  She became a mathematics teacher not because she loves maths but because she loves people and is inspired by the positive changes in them when they become confident mathematicians.  She is on the committee of the LDEA and will be standing for election to Cumbria County Council in May.

She became involved in this consultation by taking part in the session run by Lisa Smart at NW conference and then in the session run by Jeremy Hargreaves in Brighton.

Letter to Graham Stuart MP 12 March 2013

The Rt. Hon. Graham Stuart MP
Chair of the Education Select Committee

                                                                            12^th March 2013

Dear Graham,

As you prepare for your discussions with Michael Gove tomorrow you might find the insights contained in this letter useful.  I’m a specialist in online discussion forums (I run workshops and give advice on how to make them work well and I’m an FRSA researching and writing on mass online discussion and 21^st century enlightenment). I’m also a lecturer in education and have particular expertise in education discussion forums.

You may remember that I first contacted you in the early days of this government during the Ofsted enquiry because I had been trying to explore positive ways forward for Ofsted on the TES discussion forum.  I had been very shocked to find that when I did this I was immediately subjected to severe cyberbullying, the systematic deletion of my posts, other inappropriate moderator intervention and substantial personal attacks which went beyond that forum and were clearly designed to discredit me so to a level where my opinion would be meaningless.  I was concerned that your enquiry would struggle to reach the quality of conclusion it should have attained as constructive debate appeared to be being actively prevented.  My MP, Tony Cunningham, persuaded you to view some of the issues on the forum with him.  TES rejected my offers to help them improve their discussion forums and have instead chosen to threaten me with legal action and ban me from their sites.

You may also remember that I raised specific concerns about Ofsted at the Westminster Education Forum you spoke at after that review.  You advised me to speak to the Ofsted directorate about these issues.  Richard Brooks (the director present) readily accepted this request in  public, however his attitude was completely different when I followed this up.  I found that there was no place where I could have intelligent discussion about the future of Ofsted.  

In response to this I started to work hard on developing small education discussion forums which were run by individuals for the purpose of free speech.  The first major progress was made on linkedin.com where there are many such forums and there is no anonymity.  It was, for example, possible to systematically explore the intellectual foundations and the practical rationale for Michael Gove’s reforms and to discover that they were not robust.  Eventually it became possible to transfer this quality of discussion onto a forum where anonymity was allowed.  That forum was the ‘Local Schools Network’ which is lightly and impartially moderated by four labour campaigners. 

It was interesting to see key characters around Gove participating in this forum.  They simply couldn’t cope with the quality of discussion and found their ignorance exposed by the high quality participants and impartial moderation.   

During Easter Recess last year a new character suddenly appeared on the Local Schools Network forum under the pseudonym of ‘Ricky Tarr’.  Ricky Tarr could access any information on education at lightning speed.  He always knew Michael Gove’s views precisely and thought them entirely rational.  He never had to qualify his descriptions of them with caveats such as ‘I think’ he means.  This was a very different behaviour pattern to all other posters.  Despite careful observation I never found any reason to suspect that this was anyone other than Michael Gove.  We chatted at length for many months before he posted that he somebody called ‘Rick’ from the DFE and disappeared.  His posts were at first abusive and derogatory but they rapidly improved because on a properly moderated forum such behaviour only discredits the poster.  Here is a link to just one of the many conversations I and others had with ‘Ricky Tarr’ on the Local Schools Network. 

I was eventually able to properly explore the issues associated with Ofsted in the properly moderated forums and, together with expert regulators from outside education and the Liberal Democrats, have been able to develop the policy insights I’d been unable to attain while conversation was prevented.  

It became much more difficult to ‘manage’ cyberspace during 2011, the year of the Arab Spring.  This happened because ordinary people became hyperconnected and were able to converse in real time through multiple devices.  They also became empowered with platforms which enabled them to set up and moderate their own discussions. 

The world is changing very rapidly.  At present I can’t see it changing in favour of those who wish to control the thoughts and views of others.  We seem, thankfully, to be moving rapidly in the other direction.  We need to prepare to positively manage the consequences of this.  In state education there is further to move than in many areas of society.

I hope this letter is of some use to you and you committee.  Please don’t hesitate to contact me if you have any further questions or if I can help you in any other way.

Yours sincerely,

Rebecca Hanson  MA(cantab.), MEd, FRSA

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.