Monthly Archives:May 2019

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.

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.