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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: https://authenticmaths.co.uk/the-authentic-maths-story/
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.

Regards

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 contests 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.

Commentary on the “Fascinating Little Life Hack for Percentages”

07 May 19
Rebecca Hanson
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This tweet has had many views and shares and has been much discussed

“x% of y = y% of x. So, for example, if you needed to work out 4% of 75 in your head, just flip it….”

Jen Rogers of Oxford University and the Royal Statistical Society was asked to comment on it on ‘More or Less’ (https://www.bbc.co.uk/sounds/play/m0004md0 at 17:25).  It had come as a big shock to her and her fellow mathematicians. 

This was certainly well known in my classrooms.  I remembered being startled when a student first came up with it and, at first, I came up with the same explanation Jan gives.

But over time I found a much simpler and more elegant proof which is simply that ‘of’ is the same as multiplied by. So if you accept the commutativity of multiplication (so elegantly demonstrated through array – arranging objects in rectangles) then this is just obvious…….

If it doesn’t sound obvious then please be reassured that it did take me many long online discussions over several years to completely convince myself that ‘of is multiply’ throughout primary maths and well beyond and that array explains all multiplication and division at that level. 

This understanding of multiplication and division was to form the basis of my PhD in maths education. But when it became clear that no research into maths education would be taken into consideration in the development of policy it seemed wiser to devote my time to political campaigning rather than on pushing back the frontiers of knowledge. Fortunately the former has not come at the expense of the latter, but sadly it has denied me my doctorate.

Maths with Play Dough

28 Mar 19
Rebecca Hanson
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The First4Maths team who have invited me to run a workshop at their Warrington Conference on 24th April.

Come and enjoy some maths with play dough! This hugely enjoyable cross-curricular maths session is designed for all primary teachers from nursery to year 6.

You can book to attend the First4Maths Conference here.

Maths with Play Dough can also be booked as a whole primary school INSET workshop (and can be combined with other Authentic Maths training). Please contact Authentic Maths to find out more.

Summer 2019 Training – Booking now live

27 Feb 19
Rebecca Hanson
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Booking for courses in Cumbria and Liverpool is now live.

Early booking – 10% off until Friday March 8th. Use code EarlyBird10.

Book here: https://bookeo.com/authenticmathsmastery

Detailed teachers course information: https://authenticmaths.co.uk/primary-teachers/

Detailed TAs course information: https://authenticmaths.co.uk/ks2-3-teaching-assistants/


Major News

17 Feb 19
Rebecca Hanson
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Coming soon: 1-day conference-style primary maths CPD in Cumbria and Liverpool.

Following the success of recent courses I am investing in the administration infrastructure needed for this substantial business expansion.

Watch this space for news of courses in Cumbria and the Liverpool area which will be coming shortly after half term.

Now far more teachers and teaching assistants will be able to access primary mastery maths training that really works and which builds from their current practice.

Mixed-year mastery courses

14 Jan 19
Rebecca Hanson
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NW Maths Hub 3 would like to invite all schools from across the NW region to the following:

Mixed age group Mastery Training

Outcome of the training:

Know how to teach every maths concept on your part of the curriculum effectively for mastery to your mixed-year class.

Rationale:

Teachers of mixed year classes struggle to implement the same approaches to teaching mathematics for mastery that work in single year classes, however some teachers of mixed-year classes achieve stunning outcomes with their children including teaching all their part of the maths curriculum effectively, for mastery, to all their children. This training shares what they know and do.

During this hands-on workshop you will be shown how to teach each maths concept on your part of the curriculum for mastery, with a simple concrete, visual, abstract (CVA) approach. You will also be taught how expert teachers use advanced questioning techniques.  The training builds from what you already know (no good practice is replaced), ensuring any gaps in your pedagogical knowledge are identified and filled, and that you are better able to explain and defend good practice you already use. Particular attention is paid to ensuring that you understand the key insights some children fail to acquire and that you know how to teach in ways that ensure all children overcome their barriers to learning.  All other aspects of teaching for mastery are also explored and teachers are encouraged to raise questions about their particular context so that all their concerns can be properly addressed.

What the session will look like:

  • What does mathematics mastery look like in mixed year classes?
  • Why is a CVA approach more efficient and powerful than a textbook-led approach?
  • Which apparatus do I need and what should I do with it?
  • What else is involved in teaching maths for mastery?
  • What about my children who are miles behind?
  • How do I deal with the particular issues I’m facing in my classroom?

Training details:

Y5-6 training: Wednesday 16th Jan 2019- 9-3.30pm at 4 Piele Rd, Saint Helens WA11 0GR

Y3-4 training: Wednesday 23rd Jan 2019- 9-3.30pm at 4 Piele Rd, Saint Helens WA11 0GR

Y1-2 training: Monday 21st  Jan 2019- 9-3.30pm at 4 Piele Rd, Saint Helens WA11 0GR

If you wish to book on any of the following sessions please email or call:

Sarah Makin (Senior Administrator): sarah.makin@three-saints.org.uk

Paula Foster (Administrator): paula.foster@three-saints.org.uk

Multiplication Tables Check Assessment Framework Correspondence

04 Dec 18
Rebecca Hanson
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Dear Standards and Testing Agency.

I wish to reopen my enquiry reference number 181119-000054 because you have not responded to my concern.  The purpose of the rest of this email is to explain my concern about the assessment framework for the Multiplication Tables Check more clearly.

Best practice for teaching tables in primary schools is to start by teaching children to understand the concept of multiplication so they can reliably answer tables questions correctly. Children then practice their tables many times so that they learn to recall answers with an increasing degree of certainty and to check their knowledge with gradually more efficient methods. A child who can recall their tables and quickly check them using efficient methods has achieved fluency.  Over time children can come to know most, or all, of their multiplication facts so well that they no longer need to check them and reach the level of automaticity (recall from long-term memory without checking).  However, their memories for some results may fade and they may return to fluency.

This test is deliberately designed to assess automaticity (recall from long-term memory without checking) and to give no credit for fluency.

The problem we have is that there is no evidence to suggest that it is realistic for all 8-year-old to achieve automaticity as an extension to fluency.  Experience shows, and experts think, that it not realistic to expect that they will.  Research evidence shows that girls (in particular) are reluctant to drop the process of checking their answers – especially in a test situation.  Nobody has ever created a case to suggest that is wise to force children to drop the checking process by the age of eight.

The problem we then have is what happens to the children who are fluent with their tables but have not yet achieved automaticity?  What happens to the girls (in particular) who still desperately want to check their answers – especially in a test situation?  Many of them simply will not cope with the 6 second guillotine on every question. They will find it tremendously stressful and will experience repeated failure.  They will panic and will achieve few marks.

Teachers will want to ensure their students avoid this stressful experience of repeated failure.  The most obvious way they can do this is by ensuring tables are taught to be rote learned from the beginning.  Children who’d experienced this learning journey would do well on this test and should not find it particularly stressful.  But they will not understand their maths so they will be unable to puzzle out answers when they start to forget them and they will not have key elements of mathematical understanding in place to support their future learning.

So by specifying the assessment framework for the Multiplication Tables Check in this way the Standards & Testing Agency are putting colossal pressure on schools to use bad practice.

You should remember that the key reason we are introducing this test in year 4 because it is assessing a skill that is taught in year 4 in the current primary curriculum.  But the currently curriculum was created by politicians, not experts. Only a tiny amount of consultation happened after the court case against the DFE for not consulting was won. This happened too late to influence the curriculum content. But a key concession that was won was the replacement of references to rote learning with references to teaching for fluency towards the point of children being able to recall results.

If you had created a specification for the multiplication test which timed how long it took for children to complete it (with full marks) with more credit being given to children who took less time overall (and a gold standard which is consistent with automaticity/recall), you would have designed a meaningful and relevant test. What you have instead is a test that will encourage schools to focus on discredited teaching practices which will do the education of many children.

Please explain how you will address this concern.

Yours sincerely,

Rebecca Hanson (MA Cantab., MEd.)
Authentic Maths

Multiplication tables check (MTC) assessment framework

14 Nov 18
Rebecca Hanson
3 comments

The specification for the MultiplicationTables Check (MTC) (which will be statutory from 2020 – i.e. for the current year 3) was released yesterday and can be found here.

Key headlines:

What’s in the test?

  • Multiplication will be tested, division will not.
  • 0 x and 1 x tables will not be tested – so 121 multiplications from 2×2 to 12×12 will be tested (or 66 multiplications if you assume children use the commutative law).
  • There will be a bias towards harder (KS2) tables questions.

How will it be administrated?

  • The test will be delivered and marked online.
  • Tests must be taken during a 3-week window in June by all year 4 students (some pupils may be withdrawn – further details will be provided in the ARA which will be published in autumn 2019).
  • A maxim of 6 seconds will be allowed per question.
  • Once the question has been answered the pupil can press enter to proceed or wait for the time to expire.
  • There will then be a 3 second pause before the next question appears.
  • There will be 25 questions in the test so it will take a maximum of 3 minutes 45 seconds.

How will results be reported?

  • Results will be made available to schools at the end of the assessment window.
  • Results will also be shared with the DFE and Ofsted.
  • Results/league tables will not be published.
  • There is no pass or fail mark; however the ‘standard of interest’ is the number and percentage of pupils who achieve full marks.

Commentary:

This publication is deeply worrying because it fails to meet most of its own requirements:

1. The MTC should test for fluency (but it has been carefully designed to test for rote learning instead).

The stated intention (which was hard fought for) was always to test fluency.  Children who have mastery of their tables have an instinctive feel for what the result of a question is but they also check it (for example from a near result), with some results being more known and less checked and others being less confidently known and more checked.  This enables automaticity and understanding to complement each other.

This natural state of fluency is explicitly stripped out of this test format which is designed, instead, to measure only recall from long term memory.  This aim is enforced by the time guillotine on every question which has been deliberately designed to prevent children rapidly calculating answers.  Therefore schools are being pushed very hard to teach tables as rote learned fact instead for mastery (fluency with deep, structural understanding).  Removing the division facts for tables (which were widely expected to be included) from the check is a further push in this direction.

So the MTC has not been designed to test fluency.  It has been designed specifically to test rote learning and has used research to set question times that research shows will ensure only rote learning is tested.  It therefore fails in its own purpose.

2. The MTC should not be detrimental to pupils’ self-esteem or confidence (but it has been designed in a way which will ensure it is deeply damaging to the self-esteem and confidence of many pupils).

By having a time guillotine on every question this test will ensure than many pupils experience failure many times in a short space of time.  Children naturally want to get things right.  A much better way to administrate the test would be to have it time de-limited (but timed) and to give children credit for achieving full marks and then bronze, silver and gold certificates for achieving full marks in shorter times, allowing them several attempts.

If children are not achieving the target standard it is far better that they are getting the answers correct slightly more slowly than is desired than that they get a proportion of the answers wrong.  This insight also complements the learning journey they should be taking.  Children should, at first, be able to work out their tables and they should gradually become more fluent in them and approach, but never completely rely on, automaticity.  The tables check should assess their progress on this journey.  It should not assume that schools should force children to rote learn tables from a very young age and that children gradually make fewer mistakes, as it currently does.

3. The MTC should allow all pupils to demonstrate their knowledge of multiplications tables (but it will not achieve this aim because children who can answer all questions correctly slowly will get no credit at all).

Children who can answer multiplications tables correctly but take seven seconds to answer each question have a good knowledge of their tables which this test will not allow them to demonstrate.

4. The MTC should provide opportunities for all pupils to achieve, irrespective of gender

It is well known that, in general, girls like to check their answers before declaring them while boys are happier guessing and are more resilient if they make mistakes.  This test will therefore be biased against girls.

The specification claims to have overcome other aspects of bias through consultation and the development of access arrangements.  No evidence is provided to support this claim.

Why is this specification so bad?

This is an atrocious specification which catastrophically fails to meet its own requirements because it has not been trialled and has clearly not been influenced by people who understand how children learn mathematics effectively.

Formal action should therefore be taken against the DFE to prevent this test being implemented without modification.  In particular the six second time limit per question must go.

 

 

 

 

 

Update – Exciting Times

29 Oct 18
Rebecca Hanson
No Comments

Over the last four years I’ve discovered many unique insights into primary maths teaching from (and with) the wonderful teachers I’ve worked with in Cumbria.

It’s now time to feed this new understanding of primary maths teaching back into the mainstream world of maths education.  I’ll therefore be running courses outside of Cumbria (starting with courses for teachers of mixed year classes for the St. Helen’s Hub in January 2019). I’ll also be presenting a double session at the conference of the Association of Teachers of Mathematics (ATM) in April.

I’ve also been seriously considering returning to academia and studying for my PhD.  I was developing a PhD application in 2011 but I put it on hold to campaign on policy issues instead (as there seemed to be no point in pushing back the boundaries of knowledge when all knowledge and expertise were being persecuted).

As part of my thinking I’ve met with many potential PhD supervisors.  Their response has been fascinating I can’t thank them enough for their time.  The essence of it is that they all agree that I cannot do a PhD on what I already know – i.e. the aspects of expert primary maths teaching that I’ve discovered with the teachers of Cumbria.  I just need to get on and write that up in a series of books. So I’ve been working with Dr Naomi Norman to put together book proposals.

But a seriously exciting insight appeared when one of my mentors (Yvette Solomon at MMU) suggested that I study for a PhD on the co-production of primary maths CPD.  She had spotted a key aspect of what’s different about the professional development I run.  It’s not about me rolling out a big idea or a product.  It’s all about starting from, gathering, co-developing and sharing the professional skills of teachers.  The more I thought about this and talked about it with different mentors the more it made sense.  Co-production is at the heart of everything I’ve done as a teacher, for the Royal Society of Arts, (where I’ve worked on the capacity of discussion forums to generate 21st Century Enlightenment) and in politics and policy work – where I’ve been working on (and have written a book about) the co-production of healthcare. I can’t think of anything more professionally exhilerating than working on this topic. My next step is to develop my PhD proposal.