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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
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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.

 

 

Why Cumbrian primary teachers are world-leading in teaching maths for mastery

24 May 18
Rebecca Hanson
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Videos from the Teacher Inquiry Conference at the University of Cumbria yesterday:

 

 

 

 

University of Cumbria Teacher Inquiry Conference Wed 23rd May 2018

17 May 18
Rebecca Hanson
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I will be presenting at this conference and look forward to catching up with many of you then.

The title of my workshop is “What is the role of simple apparatus within Cumbrian Mastery Approaches to Primary Mathematics?”

The link to the conference is here: https://www.cumbria.ac.uk/about/events/university-events/carlisle—fusehill-street/led-research-centre-teacher-inquiry-conference-.php

Authentic Maths News May 2018

17 May 18
Rebecca Hanson
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Authentic Maths primary maths training has thrived.  The first thing I must do here is to express my deepest and most sincere thanks to every headteacher who has invested their money and time in this training and every teacher and teaching assistant who has contributed to it.  I don’t know how to put into words my gratitude to you all.  Together we have captured essence of what brilliant Cumbrian maths teachers do and how they do it and we’ve been able to share this understanding so that all teachers can teach all their students the current primary curriculum ‘for mastery’ in a way that starts from the good practice they already have.

Crucial aspects of the training we have developed are unique, in particular the idea of ‘fundamental representations’ which underpins the efficacy of the training.  Earlier this year I reached the conclusion that it is time to share our work with the wider world of maths education.  Seven years on from when I dropped my plans to write a PhD in order to ‘do politics with that part of my life’ I decided it was time to pick up those plans again.

So far I’ve met with nine potential PhD supervisors.  They’ve been absolutely amazing and have given me their time and attention and wise advice for free.  The conclusion of these meetings has been that I should write a PhD but it should be about analysing and understanding how teacher professional development is co-created with teachers and is designed to start from teacher’s current knowledge rather than to teaching them a new system.  This is incredibly exciting for me because my wonderful mentors have correctly identified the essence of what motivates me and this PhD domain will bring together my experiences from education, politics, healthcare and as an FRSA working on 21st Century Enlightment.  But it does not solve the problem of how to share the practical content of our Authentic Maths training.

At present I think the most likely way forward is that I will write up Authentic Maths year specific training as short books (‘How to Teach Year 1 Maths for Mastery’, ‘How to teach Year 2 Maths for Mastery) etc in 2018/19 and look to start my PhD in the second half of 2019.

But I’ve learned to expect the unexpected in life!

In the meantime I’m continuing to run training and I’m working with hubs to prepare to run day courses from 2018/19.  I’ve little time or need to do marketing so if you’d like training please do contact me and I will do my best to fit you in.

Cumbrian Schools Ready for the Statutory Tables Check

26 Jan 18
Rebecca Hanson
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Staff from St. Mary’s Harrington preparing to ‘Nail the Table Check’.

 

 

 

 

 

Robert Ferguson Primary Carlisle, St. Patrick’s RC Primary Workington and St. Mary’s RC Primary Harrington have completed training and have action plans in place to ensure their children nail the new ‘Tables Check’ when it becomes compulary for year 4 in 2020.

“I wouldn’t have changed anything about this Inset.  It was really appropriate for a twilight session.  no-one ‘switched off’!”   Sheryl Slack (Headteacher – St. Patrick’s Workington).

Sessions are selling fast.  To secure a slot for your school contact Authentic Maths now.  More information about cost and content is available here.

 

Primary Mathematics Curriculum and Assessment Changes

08 Nov 17
Rebecca Hanson
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Primary Numeracy Co-ordinators Update – Winter 2017/18

The government report ‘Primary assessment in England’ September 2017 lays out the following changes to primary mathematics:

At EYFS:

Curriculum:

The Early Learning Goals will be aligned with the KS1 curriculum – particularly in literacy and mathematics.  Work will be undertaken to improve the teaching of numeracy.

The government intends to explore further whether it is feasible to reduce the ELGs to 3 areas; mathematics, literacy and ‘communication and language development, physical development and personal, social and emotional development’.

Any changes to the ELGs will come into effect from the 2020 to 2021 academic year.

Assessment:

There will be a new assessment early in the reception year.  In mathematics this is expected to involve counting, basic number operations and simple 2d shapes.  This assessment will only be used to generate a whole-school progress measure and for analysis of national data.  The assessment is due to be introduced in autumn 2020 following large scale piloting in 2019.  It will be provided by a single supplier.   It will not be an observational assessment which is carried out over time but it should not feel like a ‘test’ or be different from many of the existing on-entry assessments that schools already undertake with their pupils.

Authentic Maths EYFS course (designed for teachers and teaching assistants working in the final year of nursery and reception class) strengthens EYFS mathematics teaching without compromising other areas of teaching. It achieves this up-skilling teachers to use more powerful and efficient teaching methods and to quickly recognise and implement the specific interventions children need.

At KS1:

The curriculum will remain the same.

The first children to be assessed in reception class will reach the end of KS2 in the summer of 2023.  The end of KS1 test will not be statutory for these children if they are in all-through primary schools from 2023.  It is not yet clear whether this test will be statutory for children in infant schools, first schools and other schools which are not all-through primary schools.  Clarity on this issue is expected by January 2018.

The requirement for schools to report on pupil performance and attainment to parents in more detail at the end of KS1 will remain.  Optional end-of-KS1 tests will be available for schools to use as they see fit.

Meanwhile the interim teacher assessment frameworks for mathematics at KS1, together with the guidance and exemplification materials will be updated and published in due course for first use in 2018/19 (with the current year 1).

Authentic Maths Y1 and Y2 courses teach KS1 teachers and teaching assistants the key representation of number and powerful teaching techniques that will help them ensure all children fully understand KS1 mathematics. 

At KS2:

The curriculum will remain the same.  KS2 SATs will still be statutory.  However the statutory requirement for schools to report teacher assessment judgements in English, reading and mathematics will be abolished. The current year 6 (with KS2 SATs in 2018) will be the last group for which teacher assessment judgements will be required.

Authentic Maths Y3, Y4, Y5 and Y6 courses teach KS2 teachers the key representation of number that help all children fully understand their maths.  A separate course is available for KS2 TAs.  All courses are delivered in your school and take 2 hours (+ 1 hour preparation for teachers) 

The new tables check:

The substantial change in KS2 will be the introduction of the multiplication tables check.  This will take place at the end of year 4 and will become statutory in 2020 (for the current year 2) following extensive trialling in 2019 (with the current year 3).  Schools will have a window in which to administer the assessment and there will be no requirement for a class to take the check at the same time.  The check will be brief, and will be administered online, with an off-line option available for schools without suitable internet connectivity.  Results will be available to teachers instantly and there will be no additional data submission burdens.

No information is available on whether the test will include division as well as multiplication and nobody seems able to answer this question or know when it is likely to be answered at present.

Authentic Maths tables INSET prepares schools to nail the tables check.  The INSET focuses on ensuring teachers from Reception class to Year 4 teach all the relevant skills in ways which will make sure every child understands, enjoys and is fluent with their tables.  Year 5&6 teachers should also attend to ensure their teaching builds from the new practice and standards.   Paired infant and junior schools should book joint training where possible.

For more information about Authentic Maths courses and recommendations for them please see the accompanying sheet, visit www.authenticmaths.co.uk or contact rebecca@authenticmaths.co.uk

September 2017 Local and National News

30 Sep 17
Rebecca Hanson
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I’ve been busy!

Please accept my apologies for the lack of posts recently.   I’ve been lucky enough to have work come my way without having to chase it so I’ve been concentrating on working rather than blogging and marketing.  I’ve been working with teachers and students in Cumbria but I’ve also been further afield running courses in the Liverpool area.

National News:

On 14th September the Government published important information about the future of primary assessment in England:

There are two essential pieces of information for maths.

  1. A tables test in year 4 will be extensively trialled in 2019 (for the current year 3) and will become statutory in 2020 (for the current year 2). This is going to present substantial challenges for many schools. I’m currently developing whole school INSET which is designed to help schools face this challenge head on.
  2. KS1 SATS are to become non-statutory in 2023 as the official baseline will become a new reception class baseline which will be trialled in 2019 and will become statutory in 2020.

More detail is in my summary of the report which is here.

Meanwhile:

I’ve been updating Authentic Maths courses to fit seamlessly with the training being provided by the National Centre for Excellence in the Teaching of Mathematics (NCETM).  All Authentic Maths courses securely teach the ‘Representation and Structure’ aspect of mathematics mastery.  They also help teachers develop their understanding of the other aspects of mastery in ways that complement what their schools are already doing in these areas.

Politics

17 Mar 17
Rebecca Hanson
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Radio CumbriaOne of the best things about running your own business is that sometimes you can take time out do do other things you really care about, something that’s just not possible when you’re teaching.

In November & December last year I took 2 days out each week to campaign for our NHS services which are facing closure.  The campaign team needed a mathematician with political experience of and the ability to change the minds of experts.

Then I was asked if I would stand in the Copeland by-election.  I did this to try to get our local issues on the agenda.

I have substantial political experience from my years during the coalition government when I worked hard to challenge poor education policy.  I’m also an experienced local councillor.

Politics is not an easy thing to get involved with when you’re a teacher.  It can affect your employment and it can have a substantial impact on your family.   And its difficult too.  Learning to influence policy is a bit like learning to program machine code because simple programs like Word aren’t working – it’s frustrating at first, it takes time to learn how to do it and it’s annoying becuase you feel it shouldn’t be necessary. But it’s essential that experienced people from education do get involved if we’re going to connect policy with our world and, ultimately (hopefully), devolve most policy decisions in education to professionals again.  If you are thinking about getting involved and you would like my help to understand the world of politics please do contact me – I would like to help you if I can.  I don’t care which party you’re interested in joining.  All our parties need people with real experience in education.

Politics is tough but you can do a great deal of good.  And it can be liberating, exhilerating and exciting.  You get to see more of the world as it really is and some of the people you’ll meet will inspire you.  And if you’re at ease taking the flack challenging kids give you every day you’ll probably really enjoy the rough and tumble.

I’m back at work now and loving that.

Rebecca.  March 2017.

Picture: Recording the Radio Cumbria Debate for the Copeland By-Election.