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Authentic Maths in 2020

02 Jan 20
Rebecca Hanson
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Authentic Maths exists to provide support for primary school teachers to help them become expert maths teachers.

Teachers and schools are under extreme pressure to follow detailed pre-written stepwise schemes of work. Expert maths teachers do not need these schemes – they are able to work directly from the national curriculum. Although some expert teachers may choose to use part or all of a pre-written stepwise scheme of work or any other maths teaching method that matches the needs of their students well, many choose to use more efficient teaching strategies which pivot around the teaching of fundamental structures and low-threshold high-ceiling teaching methods instead of using stepwise approaches.  The observational, creative, responsive and inclusive nature of low-threshold high-ceiling teaching strategies, in combination with the time gained through the efficiencies they bring, allow teachers to spend much more time responding to the needs and interests of their students. This usually leads to significant gains not just in maths learning but also in cross-curricular learning and in student and teacher mental health. In Finland, where expert teaching is the norm, there is no youth mental health crisis and education standards are exceptionally high.

Expert teaching is currently under existential threat in England because of the very substantial pressures on it which have been applied by government policy.  Expert teaching has only ever thrived in communities where teachers have been resourced to share and reflect on their practice with highly skilled mentors. Over recent years schools have been swamped with free training on adopting stepwise schemes of work and no resource has been provided to support expert teaching or low-threshold high-ceiling teaching methods. Although stepwise schemes clearly help our least able teachers improve their teaching, they generally de-skill our most expert teachers. 

Since 2014 Authentic Maths has been working hard to try to support our expert primary maths teachers by mentoring them and trying to capture and share the essence of what they do.  Two-hour year-specific training sessions and have been developed and improved over four generations of re-writes. They now share the fundamental insights teachers need to be able to become expert maths teachers and to understand low-threshold high-ceiling teaching so they can use it if they feel it’s the best approach for their students.  In late 2019 I made an initial attempt to start Freesharing this training on YouTube and the reception class course which resulted from this effort is available here:

Teachers and other experts are invited to criticise and add to Authentic Maths training.  This is leading to collaborative videos such as this one on motor sensory integration:

So what’s next?

In 2020 my aims are to:
1. Share the core training for years 1-4 in four more professionally produced series of videos, each of which are time-limited to 2 hours. Years 5 and 6 will follow in 2021 and series for parents and teaching assistants will hopefully follow in the future.

2. Continue to create collaborative videos with other experts who add more insights into maths teaching beyond those I offer.
(cost for aims 1&2 will be approx. £1000 for travel and resources. I will record the videos on my iphone and edit them myself at the rate of approximately one per week).

3. Promote these videos so that teachers become aware of them and can find them if they are looking for them.  To do this I need the support of a distributor (cost approx. £500/year for 2 years for distribution across forums), a marketing advisor (cost approx. £1000) and an SEO promotion company (cost approx. £2000).

The total cost of this plan is therefore around £5000 and I will try to raise funds for it. I do not have this money myself and it is not realistic that these videos will ever generate enough income to cover these costs (they’d need about 2-3 million views!). Sponsors can be credited but no editorial control is offered.  If I do not manage to raise this money. I will just carry on regardless and do what I can.  With more than £5000 I could provide more than one video per week and I could do much more to promote the videos and the general concept of expert teaching.

I’ve now created a JustGiving page where anyone can donate to help raise this money. It’s here.

Motor Sensory Integration and Maths

28 Dec 19
Rebecca Hanson
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Rebecca Hanson interviews Charlotte Davies about Motor Sensory Integration

I’ve often written about the challenges associated with teaching maths to children who are only 4 years old (that most countries teach when they are 7). These include lack of short-term memory (to manipulate information), lack of long-term memory (to retain information) and lack of foundational skills (such as having an understanding of what number is).

Charlotte Davies has identified another substantial issue, which is that children young children simply can’t take in information through their senses because their sensory inputs are not properly linked up. In this interview she explains these barriers and what can be done about them to help our children learn maths despite these challenges.

Reception Maths Training Complete

30 Nov 19
Rebecca Hanson

The core series which explains the essence of the maths children need to learn in reception class is now complete and available to view on YouTube here.

This series makes no judgement on how teachers should teach (whether they should facilitate independent learning through continuous provision, whether learning should be teacher directed, whether it should be indoors or outdoors and so on). Instead it recognises that in order to make the best decisions for their children, there are basic things teachers need to know about the mathematics learning journey children need to take. If teachers don’t know these things, they will rightly feel the need to rely on detailed plans which have been written for them and will therefore have much less choice in what they do.

These core videos (total series run time is less than 2 hours) distil out the underlying knowledge our most expert teachers have and present it to teachers in very short episodes. Some of the insights provided are mainstream, others are unique to this series. The whole series deeply understands that the learning journey children need to take is age-dependent (i.e. you have to take into account that these children are 4 years old – you can’t just assume that what works for 7-year olds will still work). This series is very thoroughly grounded in the experiences of expert teachers who are meeting the challenges of our current curriculum and it is also pays very thorough respect to the established research into the teaching of early years maths.

No expensive resources are needed for teachers to teach reception class maths brilliantly, however some recommendations for particular pieces of apparatus are made (with a typical one-off cost of around £30 or less). All recommendations are entirely genuine, and no payment has been taken for any recommendations made in this series.

Teachers who have taken the face-to-face version of this training have often chosen to move on to more sophisticated and sometimes unique pedagogical approaches. Training on pedagogy is not provided by Authentic Maths, but as part of the next phase of this video series I am inviting teachers and teacher trainers with expertise in different pedagogical approaches to contact me if they would be interested in showcasing what they do. They are warmly invited to describe aspects of reception class maths teaching they are passionate about, promote any training services they offer and comment on the core course (especially if they would like to challenge elements of it or suggest improvements to it – I love challenge!). I can incorporate pieces of video shot with iPhones. Consent forms for participants must be provided. Interviews will generally take place in Cumbria or the North West.

While the core series is meant to be universal (all teachers need to know this), these pedagogical episodes are intended for teachers to pick and choose from as they puzzle out the best way forward for their school.

I am now also moving on to filming the core series for the teaching of year 1 maths and aim to continue to release these videos every Thursday at 3pm.

All Planning guides now live

02 Sep 19
Rebecca Hanson

Authentic Maths term-per-page maths planning guides are now all available for free download in the Expert Primary Maths Teachers Facebook group.

Guides are available for Reception, Y1, Y2, Y3, Y4, Y5, Y6, mixed Y1/2, mixed Y3/4 and mixed Y5/6

A new social purpose for Authentic Maths

26 Aug 19
Rebecca Hanson

Since 2010, the world of English maths education has become more and more dysfunctional.  Most teachers and schools now feel forced to slavishly follow government-endorsed detailed schemes of work because they cannot take the risk of being blamed for failure. What else would you expect to happen if you introduce a curriculum which teaches maths to children younger than anywhere else in the world without trialling or consulting it?  What else would you expect if you abolish consultation and ignore all expert advice?

Across the UK there are still innovative private providers of education CPD which support the teachers who think outside of the box and who try to do more than just follow detailed maths lesson planning written for them by someone else.  But is it very hard for these providers to survive because;

  • all schools are being avalanched with free government-backed training and resources at the same time as they are being hit by very serious cuts.
  • the DfE will only support initiatives that preach the deeply-flawed government line
  • the government-backed resources and schemes are ‘all consuming’ because they are inefficient, so teachers have little or no free time to innovate around them.  
  • In stark contrast to 10 years ago – government-backed providers now appear to have no duty to work collaboratively with other providers.

And so, as part of the way forward, I’ve found it’s necessary to develop a unique social purpose for Authentic Maths which is this:

  • To provide (freesharing wherever possible) core resources and training that enable schools to take the journey from relying on detailed planning which is written for them to having professional oversight of their teaching and being able to teach in more efficient and effective ways.
  • To stick to this unique work and not to stray into the domains of other independent providers – instead to recommend their work, resources and services.
  • To provide whatever support I can on a personal level to other independent providers of services, whether this is recommendations, mentoring, promotion on LinkedIn, training, or listening to their concerns about national maths education policy.

Any UK provider of maths education resources or services who feels this applies to them is warmly invited to contact me.

post script – noticing some of the comments of and conversations between other private providers – I would also like them to know that I can offer them support to enter politics should they wish to do so. I support people across all parties. Being involved in politics has given me access to journeys of professional development which have trained me to work at very senior levels, had enabled me to do extremely valuable things for the children and for the world of education in many ways and also brings me an income which supports my business. These days it’s practically impossible for those working in schools to engage with politics in this way. But it’s perfectly possible for private providers too. It actually fits really well for many.

More term-to-page maths planning guides now available

14 Aug 19
Rebecca Hanson
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Mixed Year 1/2, Mixed Year 3/4, Mixed Year 5/6, Reception Class and Year 1 term-to-page maths planning guides are now available for free download in the Expert Primary Maths Teacher Planning group on Facebook.

Year 2 will be uploaded tomorrow (Thurs 15th August) and Years 3, 4, 5 & 6 will follow in the next few weeks.

Free Reception and Mixed Year 1&2 Maths Year Planning now live

15 Jul 19
Rebecca Hanson

From September 2019 All Authentic Maths Training will come with free, complete year planning guides. These are available for free download from the Facebook Group: Expert Primary Maths Teacher Planning.

At the time of writing this post Reception and Mixed Year 1&2 plans are available. Mixed Year 3&4 and Mixed Year 5&6 will be shared this week. Single year plans for Years 1-6 will follow during the summer break.

I’ve posted them in Facebook because it’s so easy to updated them and for people to share their comments about them together. If you’re not on Facebook and would like copies please contact Authentic Maths.

Sept 19 Cumbria Course – Booking now live

15 Jul 19
Rebecca Hanson
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Authentic Maths training courses are now live to book here:

Use code Early50 for a £50 discount if you book before the summer holidays.

Apologies for the delay in getting these live and advertised. I’ve been working on the Maternity result and trying to sort out the CAMHs crisis….. among other things. #sometimesitjustcomesatyou

A good response from Ofsted on the new inspection framework.

17 Jun 19
Rebecca Hanson
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I raised a concern about the new inspection framework with Ofsted and they have now sent me an appropriate response.

My enquiry (send May 23rd 2019) was as follows:

Dear Ofsted,
Through my business (Authentic Maths), I provide exceptionally high quality CPD for primary teachers which supports their teaching of mathematics.

The CPD I provide nurtures teachers’ high-level professional skills. I encourage them to teach low-threshold high-ceiling lessons which pivot around the fundamental representations of mathematics.  This is a different approach to East Asian Mastery because it does not require teachers to carefully sequence knowledge lesson by lesson.  This is particularly helpful in schools which face the most challenges, including those working with children with very substantial gaps in their education, established psychological barriers to learning and mixed year classes.  

This approach is thoroughly grounded in research and has been forensically developed with schools with exceptional practice.  It is profoundly age-appropriate for younger children.  You can read the history of how this training has been developed here:
Children who are taught using this method make more rapid and efficient progress, and acquire deeper learning, than those using the East Asian step-wise mastery approach.  As well as enabling teachers to cope with the issues listed in the second paragraph of this email, the efficiently of low-threshold high-ceiling teaching also provides them with plenty of classroom time to focus on ensuring that all children have achieve all the demands of their curriculum towards the end of their time in a class, as well as plenty of time for extended problem solving activities (in addition to the regular use of problem solving activities during lessons).

Given that the definition of outstanding teaching (which fitted teachers using this practice very well) has been removed and replaced with section 294 of the new inspection handbook, I am contacting you to ask you to provide me with written assurance, which I can publish and show to schools, that the exceptional teaching in schools I work with will be recognised and not penalised by inspectors?

The particular points from section 294 which I am concerned about are:
– the school’s curriculum planning for mathematics carefully sequences knowledge, concepts and procedures to build mathematical knowledge and skills systematically
– the curriculum divides new material into manageable steps lesson by lesson.

I am worried that these points are specifically describing the East Asian Mastery approach being promoted by the NCETM and do not understand more effective methods.  I am concerned that inspectors will not be trained to understand low-threshold high-ceiling teaching in mathematics. I am also worried that headteachers may be dissuaded from using more effective methods because they may share these concerns. I have experienced the extinction of this type of teaching from secondary schools in Cumbria because headteachers have been afraid that Ofsted would not understand it.

I would be delighted to provide you with any further information and evidence you may require to assess and respond to this request.

Yours sincerely,

Rebecca Hanson

Their response (sent 16th June 2019) was as follows:

Dear Rebecca 

Thank you for your enquiry. Inspectors carrying out their work under the new Education Inspection Framework will look at the extent to which pupils understand and remember the mathematical knowledge, concepts and procedures appropriate for their starting points, including knowledge of efficient algorithms. Teaching should ensure that pupils are ready for the next stage, whether that is the next lesson, unit of work, year or key stage, including post-16 mathematics.

The handbook, including section 294 on mathematics draws carefully upon research. Inspectors will judge schools taking radically different approaches to the curriculum fairly, as Ofsted recognise the importance of schools’ autonomy to choose their own curriculum approaches.

If leaders are able to show that they have thought carefully, that they have built a curriculum with appropriate coverage, content, structure and sequencing, and that it has been implemented effectively, then inspectors will assess a school’s curriculum favourably.

Please note that the evaluation schedule in the new school inspection handbook is not exhaustive and does not replace the professional judgement of inspectors.


Jonathan Tryhuba
Ofsted – Applications, Regulatory and Contact team
Telephone: 0300 123 4666

Improving Primary Maths SATs Draft 1

31 May 19
Rebecca Hanson
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What should done during a 5-year parliamentary term to improve primary maths SATs?

This document is not formal set of proposal.  It is a ‘work in progress’ which captures some apparently sensible suggestions, so that discussions and comments can start from what’s already been suggested rather than from scratch.  I expect that there will be further versions of this document.

Planning two stages to reform:

It is essential to minimise change and to ensure that changes which are implemented have a clear rationale. It therefore seems appropriate to plan to work in 2 stages during a 5-year parliamentary term.

The first stagewould assume that the curriculum is fixed, and only minimal changes are possible or desirable.  Each change must be fully justified.  Consultation would be immediate and short with ACME being fully involve and with changes being implemented 18-24 months into a term of office.  

The second stagecould involve curriculum changes (which should be kept as minimal as possible with each one being thoroughly justified) and could involve substantial changes in assessment.  These changes should be thoroughly consulted and trialled over 3-4 years.  Time should be taken to build a consultation infrastructure which is fit for the 21stCentury and care should be taken to understand and address the vulnerabilities created by those in positions of leadership in maths education not having been upskilled in this area since 2010.

Suggestions for first stage changes:

KS1 (recommendations 1 to7). KS2 (recommendations 5-11).

Recommendation 1 (KS1)
Children should be allowed to use 1-100 counting beads and/or Dienes blocksduring SATs if they want/need them.

Rationale: Many children completing KS1 SATs are still only six when then take them. At six they may not yet have the level of neurological development that enables them to remember and manipulate abstract information.  Mathematical apparatus will allow them to complete calculations and express what they can do.  Children using apparatus to complete calculations at this age will not need apparatus when their working and long-term memory develop further.  Removing apparatus from very young children who need it causes substantial unnecessary stress.  Knowing that apparatus will not be available in tests influences teaching in, negative ways. Using 1-100 counting beads helps children learn to subordinate the partitioning of small numbers in more complex calculations – an essential skill most are in the process of acquiring at the end of KS1.

Recommendation 2 (KS1)
Explore whether SATS can happen at a later date in the year.

Rationale. Children are extremely young when they take these tests (many are only 6).  KS1 SATs take place very early (in early May).  If it is possible to have these tests later this should be done.

Recommendation 3 (KS1)
Ensure all answer boxes are blank.  

Rationale: At present some answer boxes are blank and some have squares in them.  This is confusing for children.  If choosing one or the other, blank is better as it doesn’t get in the way of children using methods that don’t fit on grids.

Recommendation 4 (KS1)
Ensure there are no blank pages labelled ‘blank page’ 

Rationale: This confuses young children.

Recommendation 5 (KS1&2)
Further simplify the use of language – especially names.
  Reduce the reading age of the language further and consider each question carefully to ensure that the least amount of language and simplest possible language is used (except in questions at the end of the tests, where dealing with redundant information is part of the challenge).  Names should be short and should follow simple phonetic rules.  Better still, create characters who are featured in the tests for a particular year and allow teachers to introduce them and ensure all children can read their names and recognise them before the test. 

Rationale: Many children in the UK are E2L.  Language is tested separately and should not be a barrier to achievement in maths.

Recommendation 6 (KS1&2)
Allow a soft end to tests (children can stay longer than the allowed time if they want to).

Rationale:  Many young children do not yet have the capacity to manage timings during exams.  Negative experiences such as running out of time can cause them to rush and panic. Timing issues cause serious stress for some children.  Some children have neurological issues with processing speeds that are not yet diagnosed. Allowing extra time would facilitate rather than inhibit diagnosis (because children with these issues are observed to need time to perform well and would not be incorrectly labelled as being lower achievers giving teachers incorrectly low expectations of them).

Recommendation 7 (KS1&2)
Improve the relevance of the contexts used.  Ensure teachers who work with children of the appropriate age (especially in KS1) are consulted on contexts to be used for problems so that they are always relevant, engaging and age-appropriate.

Rationale: Use of inappropriate contexts has been reported as being a barrier to children demonstrating what they can do and having a positive experience of maths by teachers.

Recommendation 8 (KS2)
Have two papers instead of 3. 

Rationale: This would allow more time (with extra time if needed) for each paper.  No clear rationale has been presented for there being three short papers instead of two slightly longer ones.  

Recommendation 9 (KS2)
Ensure the reasoning paper is progressiveby requiring all early questions to be simple to decode, and ensuring the questions which are very different to anything children will have seen before, or which contain redundant information, are placed at the end of the paper.

Rationale: Young children do not yet have well developed exam ‘coping-strategies’ which enable them to prioritise questions.  Many will stay on a question they are stuck on for a very long time.  It’s essential they meet the questions they should be able to answer before they meet the questions, they are expected to find very challenging and spend substantial time on.

Recommendation 10 (KS2)
The third method of short division presented on page 47 of the primary maths national curriculum should be explicitly allowed as an acceptable method for division by a two-digit number.

Rationale: This is the most efficient method to use in some circumstances.  It was the intention of the national curriculum that it would be allowed.  

Recommendation 11 (KS2)
Specify more tightly the type of pie chart questions that will appear,
e.g. by specifying that all sections in pie charts will be 1/2, 1/3, 1/4, 1/6 and 1/8 (180o, 120o, 90o, 60oand 45o).

Rationale:  This topic is too large and is therefore overwhelming for many teachers and students. Tightening it in this way would help to ensure that a basic understanding of pie charts and circular representations of fractions are both thoroughly taught while work on fractions and angles are consolidated and children learning to recognise the size of key angles.

Suggestions for second stage changes:

1. Carefully review the National Curriculum, aiming to improve it with minimum change.  Each change must be fully justified with a rationale (i.e. as above).

2. Develop component-led assessment where summative grades come directly from the component parts rather than from exams.  Written and online tests should be created to allow substantial parts of this assessment process to be automated for teachers so that they can generate most of their results rapidly and in ways transparently objective.  However, teachers should be allowed to provide alternative evidence to accredit children with achieving component objectives.

Particular attention should be paid to the innovations in assessment being developed in Australia (known as NAPLAN).

Update 1: Mon 3 June

Feedback so far:

1. Clarify the state of play regarding making KS1 SATs non-statutory. This DFE publication indicates that this will probably happen for students in primary schools (R-Y6) in 2023. It states that an announcement will be made regarding infant schools will be made in Jan 2018 but I cannot find any evidence of this announcement having been made. I have contacted the DFE for clarification.

If assessment is concept-led and is meaningful and efficient for schools to implement, the issues explored in the DFE publication above suggest that it might be sensible to have assessment in years 2, 4, 6 and possibly in year 8 as well. This should certainly not be considered if the assessments are summative and are disconnected from concept-led assessment as they currently are.

2. Proactively engage with the Standards and Testing Agency before deciding which of the recommendations on the development of SATs questions go to consultation.

3. add:
Recommendation 12: KS2
Restrict questions on angles in polynomials to that it is only assumed that children will know the sums of angles in triangles and quadrilaterals. Scaffolding must be provided to help children work on angle problems for regular polygons with five or more sides if these appear.