2104 Primary National Curriculum Not Fit for Purpose

Since writing my previous report, I've corresponded with the key people involved in the creation of our 2014 primary mathematics curriculum.  They've consistently claimed that our curriculum is most like the Singapore Curriculum.

This is such utter nonsense that I've written a brief report which summarises some of the key differences between our new curriculum and the Singapore curriculum and which calls for the implementation of our curriculum to be immediately suspended.

It's available as a free download here.

It's already had some useful coverage in the press.  In this excellent article (if you read 'multiplication tables' in the headline rather than 'multiplication') the reporter has caught a DfE spokeswoman still claiming that our curriculum is like the Singapore curriculum!!!!  Liz Truss MP has had this report for nearly two weeks and I've discussed these issues with the key person at the DfE with relevant responsibility.  The rumours that people at the DfE are trained just to stick their fingers in their ears and sing 'la, la, la' very loudly when anybody discusses evidence must be true.  Sigh.

Special Measures

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

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 - 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.

Cyberrhetoric

I now devote part of my time to developing the academic discipline of analysing the processes and outputs of mass online discussion (that's conversations in forums and the comments threads to blogs, news articles and so on).

My passion for this subject started in maths education - see for example this article:
http://www.scribd.com/doc/55142332/Exploring-Discussion-Forums
And I am delighted to have been asked to manage and moderate the inspirational group:
Math, Math Education, Math Culture on linkedin.com, a role which I love and I would warmly invite any enthusiast of maths education to join this warm and vibrant group.

But my interest in forums has now grown beyond education and so I've started a separate blog specifically for it.  The first post in my new blog (which I shall run in parallel with this one) contains my notes on cyberrhetoric - which is the ways in which participants in forums can post to help conversations which are stuck or abusive become productive and respectful -from the session I ran at the Mozilla Festival in Grenwich on Sunday.  As well as developing this study further, I will also post on the analysis of the ways in which mass online discussion can enhance democracy and generate intellectual capital and I hope to link to other articles about mass online discussion.  Here's the link:
http://cyberrhetoricbyrebeccahanson.blogspot.com/

I shall keep this blog for maths education and related issues in education.