DfE Annouces Times Table Test Trials

The government announcement of times table testing trials to begin in schools this spring might have caught a few people by surprise - whilst the statutory check has been on the cards for a few years now, it was put on hold in 2016 following the appointment of Justine Greening as education secretary.

As the BBC report, some 7,250 pupils in 290 primaries are expected to take part in the trials which the DfE note will "last no longer than five minutes and is similar to the checks many schools use already." Given our understanding of using Number.fy in schools, we would expect that to equate to 20 questions, probably randomly generated.

As we have noted before, a good understanding of pupil level times table knowledge requires at least 100 questions. The government's test will therefore give a good understanding of knowledge at the Local Authority and National level - it is unlikely to do so at the school level. Small schools are more likely to suffer from misleading results so it will be interesting to see how Ofsted view these outcomes.

Our recommendation would be to baseline test your children termly from Year 2 and practice for 15 minutes a day (40 questions each). Schools that implement this have seem dramatic changes in times table knowledge.


Why Flurrish?

Eleven marks a passage of rite for many - at this age you can legally choose your own religion, have your ears pierced and be convicted of a criminal offence (Oxme). In school it usually marks the age at which you transfer from Primary to Secondary. Key Stage 2 SATs are the educational marker which the government uses to measure the effectiveness of Primary education, but SATs are also significant for the child as they are now aware of their own capabilities. Exams matter no matter how much they might be wrapped up otherwise.

Erin was ten - born in July she was a summer baby and come March her class was full steam ahead in preparation for SATs. I helped where I could, feeding back on numeracy questions, spelling worksheets and writing exercises. She found spellings difficult as the order of letters never seemed to stick for long. Numeracy questions she understood more easily, however there was one area she struggled with - finishing the question with sufficient time to spare. It was actually the calculation in the mental maths questions that burned time.

Watching her one day, I could see she understood the mechanics but just needed enough time to complete the problem. On the spur of the moment I fired a few times table questions at her - I started with a couple of easy ones (10x5, 4x4) and then progressed onto harder ones (9x7, 7x8, 8x4). Instead of reciting them, she began calculating the sums in her head - she didn't know her times tables. No wonder she was struggling to complete the maths questions!

My thoughts instantly shifted to getting her to answer rapid fire questions - an app, there had to be an app! A quick search on the Google Play store showed there were plenty of them. I tried a few and then settled on one which simply fired banks of 20 questions, timing you along the way, showing what you got right and wrong. Erin started playing - not all the time and not every day. But several times a week, 60, 80 or 100 questions at a time. Week by week she just kept answering questions and gradually, noticeably, she got faster on the timed clock and also faster at answering the SATs questions.

For Erin, the rote memorisation of times tables worked. There is nothing new in the idea - regular practice, repetition, is all that was needed. But the app provided a rapid way to practice and a yard stick to measure yourself by. How fast and which ones were correct. That suddenly made me think - if we log all the answers we are able to record performance over time, provide feedback to teachers and, more importantly, learners.

And so Flurrish was born - out of Erin's SATs came our unique vision for empowering teachers and enabling pupils.

Just 20 Random Questions...

Numberfy is just a tool in your mathematical teaching arsenal, an aid to helping children master the number foundations. By design, we've tried to replicate the way times tables are taught in the classroom, but really it's about slotting in to teachers' needs and the way they deliver the curriculum. However we do get asked about "preferred" methods that both engages and maximises learning - in this context there is one game that we push above all the others: the random 20 (20 randomised questions across the 1-12x tables or the question mark on your game screen). And that's for FOUR great reasons:

  1. Real Life: in the real world we rarely need to perform calculations in a pre-defined order.
  2. Better Learning: in our whitepaper we highlight interleaving as a major technique in more effective and longer lasting memorisation. Randomising questions taps into this aspect heavily - with demonstrable success.
  3. Baseline Testing: do you want to know how well your children are learning? Then baseline test them regularly - low stakes, little and often. You will understand in detail what they know and don't know.
  4. Statutory Testing: no one knows what the government testing will involve, but it would be a good bet that randomised questions will be in there. If your students can do this in Numberfy well, then they will ace the government test, with no stress.

How did you do? 2017-18 school data

Pupils played a mammoth 12.2 MILLION questions last year! Yup, we enjoyed crunching and reviewing a vast amount of data - showing a staggering amount of play and a whole lot of learning. These are the top results for a single day:

  • 111,000 questions
  • 93 classes
  • 1324 pupils
  • 194 questions per pupil

That is some impressive times table play and we are hugely proud of the achievements of the pupils across our schools. This year is looking to trump this by some margin. So far, over 3.5 MILLION questions have been played which means, at this rate, pupils could end up playing over 20 MILLION questions this year. So far this year the top results are:

  • 159,000 questions
  • 101 classes
  • 1752 pupils
  • 108 questions per pupil

Last year we looked at the top 10 hardest times table questions... has this changed? This year we have a data bank of 3.5 MILLION answers where pupils played 20 randomised questions. This is a great basis on which to assess the hardest (greatest error rate) questions. This year it is:

8x6 6x8 7x8 8x7 4x8 8x4 7x6 6x7 7x7

And our firm favourites are in there - it is again the centre of the times table square that is causing the problems with 8x6 and 6x8 taking the top spots with 28% of questions answered incorrectly. These are the gaps in learning for pupils as they try to remember number facts. So, what are your best strategies for their memorisation? We look forward to hearing from you.

One number to rule them all... MASTERY

One number to rule them all... that is Mastery! Here at Flurrish HQ we have been trying to make reviewing and understanding your pupil data both simple and informative, something that pupils can use to guide their learning, teachers can use to personalise learning and Senior Leaders can use to make strategic decisions.

In the last blog we discussed how summary gameplay for each individual pupil can provide vital baseline data for the year ahead so that it is easy to demonstrate progress and identify where this is above or below expectations.

However we wondered if we could summarise this in a single number to incentivise learners - Mastery is our answer. We started by thinking about the two things pupils have been most competitive about…

(1) Speed

(2) Accuracy

Quite simply, Mastery calculates the number of questions answered per minute, then multiplies this by the percentage of answers that were correct. The faster you go and the more questions you get correct, the higher your score.

If learners are looking for a single number to measure themselves against or compete with friends, then Mastery conveys it simply. To push your score higher you must go faster, yet still get as many questions correct as possible. This taps into one of the key tenets of Number Fact learning (see our Whitepaper Learning Number Facts) - really push yourself "at the edge" in order to improve ("purposeful practise"). Work at getting your Mastery scores higher and you really will commit number facts to memory.

With the imminent release of the new version of Number.fy to the Play and App stores, we are excited to announce that Mastery is one of the game stats that pupils can access from the NEW pull-out tab. Tap on the icon and see all your Mastery scores for the current session.

Watch this space for our release announcement!

Baseline Testing

The effectiveness of any kind of teaching intervention is knowing the impact it has had - in short, you need to know what your children were like before and after. This is no different for learning number facts and something we strongly encourage at Flurrish - in fact, schools that use our software are at a significant advantage in this regard given that we record all questions answered by each and every child. This is evidence for the child (to help them improve), evidence for the teacher (to focus learning strategies), evidence for senior leaders (to determine progress of each child), evidence for governors (to hold senior leaders to account) and evidence for Ofsted (to clearly demonstrate good practice).

Baseline testing is something we have assisted Caddington Village School in developing and we now strongly advocate. So, what should you do and how should you do it?

  1. Test Type: unequivocally, randomised testing across all 12x tables should be used. This is your knowledge standard and should be measured against. Within our Number.fy app this means using the "random 20" game.

  2. Number of Questions: the more questions children answer, the better your estimate of their knowledge. This then determines how long testing will take - children that have poor number fact knowledge will take ~2 minutes per blocks of 20 (the "game" has a built-in maximum length of 5 mins). That means about 10 minutes for testing which would fit within a 30 minute lesson.

  3. When: testing should be undertaken as soon as is practical at the start of the school year so you have a real understanding of their knowledge at the beginning.

  4. Data: this takes the form of the percentage correct per child. This is currently not available as a direct download from our results website (although it's top of our 'to-do' feature list!). Some schools calculate this for themselves or ask us to do it - we are more than happy to send you the results for your pupils pre-calculated. Just contact us.

  5. Reporting: results can be reported in tabular or graphical form. For anonymised presentation, class data can be aggregated and used to produce summary statistics (mean, minimum, maximum) and box-and-whisker plots - the latter are particularly effective as they visually show the distribution of number fact knowledge, highlighting where the class is and any children that are significantly different from this.

Baseline Testing is an essential part of developing a teaching culture of measuring the impact of interventions (and selecting the ones that work), but also being able to understand the progress of each and every child, producing a nuanced knowledge of how they learn. The charts below are an effective starting point as you can see how many children have played (n), how many questions they answered (Qs) and how many questions per pupil (QpP). At a glance you can see that both classes are similar in terms of cohort and performance, although the top class has a pupil with very low achievement scores. Valuable knowledge at the start of the year.

Example box plot for two classes

Example box plot for two classes

SATs scrapped (but times table testing lives to on)

The big news for schools last week was the axing of statutory SATs in Year 2 (age 7) which have proved devisive and a replacement with baseline testing in Reception (age 5). Performance metrics are designed to measure achievement at any one point in time, but achievement is a coarse metric and in terms of determining the "quality of education", improvement over time (progress) goes hand-in-hand. As a result, there must be a baseline at some point. It will be interesting to see whast this is and how meaningful it will be.

However, the interesting news was the confirmation of times table testing from 2018/19 (next year) - for year 4 (age 9) children (something Nick Gibb had noted earlier this year). Yes, year 4. From our experience and data, we know that those children that don't regularly practise their times tables have poor number fact knowledge. In fact, many children who leave Primary School at age 11 don't have confident number fact knowledge, yet the National Curriculum specified times table knolwedge upto 12x by year 4 (age 9) - testing will now take place at that point.

Using traditional techniques, times table knowledge takes several years to acquire - our whitepaper "Learning Number Facts" outlines best practise - time that many schools don't have before testing begins. As a reminder, that means current year 3 children are expected to know all 12x tables by the end of the next school year.

Watch this space as we wait for confirmation of the testing and the form it will take.

2017 Number.bee: All School Times Table Championship

We are very proud to be working with Caddington Village School to bring you the Second Annual Number.Bee Competition.

  • enter your best times tabling pupil
  • compete against other schools in the area
  • learning activities between rounds of game-play
  • teams of four pupils (up to Year 6)
  • prizes of FIVE 7" Android tablets

This is a no cost event that will bring together staff and pupils who avidly teach and practise their times tables!

Put the date in your diary - FRIDAY 7th JULY 2017

Register by emailing numberbee@caddington.cbeds.co.uk

We look forward to seeing you there!!

Partnership Education Learning

We'll be presenting at Parnership Education's Teaching Tools and Technology Learning Event next week so if you are interested in a technology event focused on teaching then look at the programme below. The event is free to attend (with a free lunch!) so just register here.

Hope to see you there!


10.00 -10.30 – Registration & Introductions

10.30 – 10.50 – ESET – GDPR: Changes in Data Protection Legislation

10.50 – 11.10 – ESET - Crypto Virus: How to protect yourself

11.30 – 11.50 – iPads - Impacting on learning with iPads - 5 Key Apps

11.50 – 12.10 – iPads - iCoding - teaching computing with iPad

12.40 – 13.00 - Clevertouch – Effectively utilising classroom technology

13.00 -13.40 - Flurrish – App to Support Numeracy

13.50 – 14.10 - Arbor – Analysing Pupil Data

14.10 – 14.30 - InVentry – Fire Safety Procedures

14.40 – 15.00 - Impero – Safeguarding and the PREVENT Duty

15.00 – 15.20 - Wizkidz - Going Google

Flurrish User Group 2017

Earlier this month we ran the 2017 Flurrish User Group at Caddington Village School, organised through Central Bedfordshire CPD.

The day kicked off with a keynote by Dr Tom Mitchell from Liverpool Hope University titled the "Learning Imperative" looking at the psychology of the growth mindset (see Carol Dweck's work). As part of this, he reviewed attribution theory and how this can explain part of how an individual responds to learning (in terms of motivation and so achievement) and so the notion of growth. Modelling correct behaviours-attributions is key to making progress. This is about building praise into feedback, developing resilience in learners and so a positive psychological cycle. This can link closely to maths anxiety and, by using the notion of growth mindset, improve performance and move towards mastery. Flurrish's Number.fy can form part of a successful intervention strategy to achieve this.

Richard Kingham (Caddington), then talked about "The Home Straight" - using Number.fy with year 6 in preparation for Key Stage 2 SATs. This was very much "front of house" from a teacher with extensive experience of incorporating Number.fy in to delivery of the curriculum. Outlining when it's used in class, how it's used as a strategy for improving number fact knowledge and his experience of the sorts of outcomes achieved by pupils. This included a summary of the extent of current number fact knowledge and performance on a weekly maths skills test.

Mike Smith (Flurrish) then followed Richard, outlining how data recorded by Number.fy can be used by teachers to underpin their classroom practice. That is, how do individual pupils perform, what do they know/not know and how can they improve? This included a review of the Cupid statistic (Questions per Pupil per Day; QpPpD) to ensure that everyone is getting enough daily practice. However, not just daily practice but QUALITY practice. Are they playing randomised questions across all 12x tables? And what proportion are correctly answered? Once you know that, the SPEED with which they can achieve that is a good measure of mastery. And the results? Well we presented a plot of Richard's class' maths skills against number fact knowledge - whilst only representative of one week, it shows a strong correlation.

Jeni Houghton (Headteacher, Hawthon Park) then outlined their approach (using assertive mentoring) to improve curriculum outcomes at Hawthorn Park. Number.fy forms one of a number of strategies for this with the data helping teachers understand misconceptions and so target appropriate interventions. She concluded with quotes from staff and pupils which included:

"The impact of more secure times table recall is really being seen across all areas of the Maths curriculum."

"Flurrish trains your brain to do times tables. It's fun when we hold competitions."

After lunch Sue Teague (Headteacher, Caddington) then reminded everyone that DATA is NOT INFORMATION, which is NOT KNOWLEDGE, which is NOT WISDOM. As educators we have a responsibility and duty to best use the data we have and make wise decisions based upon it. So... use headteacher's report from Flurrish to review Cupid, percentage correct and proportion of randomised questions. Do this at school, class and individual level to use granular, detailed and useful data and make decisions based upon it.

The day finished with the exciting launch of our whitepaper "Learning Number Facts" with delegates receiving their own printed copy - if you haven't got your copy yet, then download it today. We concluded by outlining a roadmap for continued development of the Number.fy app and results website - watch this space, but just to let users know that v2 (aka "Nero") will be available for update shortly with v3 currently in development. More news next term!

We were proud to be able to participate in such a productive user group day and grateful to Caddington Village School (and Central Bedfordshire) for organising it. Those who presented provided thought provoking and inspirational talks. We look forward to next year's FUG!!


The Learning Imperative, Dr Tom Mitchell-Gallagher, Liverpool Hope University

The Home Straight (part 1), Richard Kingham, Caddington Village School

The Home Straight (part 2), Mike Smith, Flurrish

Gap Filling and Number Crunching, Jeni Houghton (Hawthorn Park School)

Demonstrating Progress, Sue Teague, Caddington Village School

FREE Whitepaper: Learning Number Facts

Number facts are one of the “essentials” for succeeding in life as they underpin the way we understand mathematics and progress in the subject. As adults, we use them daily for calculating shopping totals or estimating building quantities. Memorising number facts allows us to focus our mental energy on the core task and not get bogged down in calculation, yet many children and adults don’t “know” them

Flurrish is proud to announce the publication of it's whitepaper "Learning Number Facts." This has come through working closely with educators at Caddington Village School and researchers at Liverpool Hope University. It is intended for teachers, senior leaders, parents, learners - all those who have a interest in the learning of number facts.

We present an outline of how memory works and how schools use this in traditional methods for learning number facts. But, given recent research on memory, what might optimum strategies for learning use and, if we implemented them, what might they look like?

We believe this will provide an invaluable synthesis for all those who want to impact upon number fact learning and the benefits this can have upon numeracy during later learning.

Please goto our download page if you would like a FREE PDF copy.

Using School Performance Data

Following on from the previous blog about Flurrish’s headteacher report, this is a guest post from Sue Teague, headteacher at Caddingon Village School.

So, what did you do with YOUR data? These were my actions as soon as the e-mail landed...

  • Shared the e-mail with key staff in briefing and forwarded them the flurrish e-mail (Time: 2 minutes)
  • Sent the mail to admin and technical staff and asked that they check the correct number of children are registered with the app and playing; in short, do the mumbers/names tally? (Time: 5 minutes)
  • Made sure the app is being played at an appropriate level (i.e. the 'Goldilocks Factor'). Too little could mean pupils won't learn and progress, too much might mean they are being given the devices instead of high quality teaching and learning. (Time: 5 minutes)
  • I saved the data, ready to use at the next Teaching and Learning committee meeting of the Governing Body to provide feedback to governors. It directly demonstrates how we are using the app and shows value for money (Time: 2 minutes)

The data provided is too valuable to just sit in your inbox - share it, use it, learn from it.

Times Table Testing Back on the Agenda

The BBC reported yesterday that statutory times table testing is now back on the agenda for schools following Nick Gibb's comments at the Commons Education Select Committee. We commented on this in an earlier blog and it was notable at the time for increasing the stakes in Year 6 (as part of SATs) as well as being mooted as the first computer-based testing. As we noted then:

"This is part of Nicky Morgan's "non-negotiables" that aim to ensure all children have a floor standard in terms of competencies."

Justine Greening then put all new testing on hold (although no news on how the actual trials went), but these look set to go ahead. As we noted back then:

  1. Testing is a fact of education, a fact of life. Once it is routine it becomes easier and is therefore a positive benefit for pupils. We wouldn't agree with testing for the sake of it or where (beyond reasonableness) testing becomes the goal, rather than learning.

  2. Schools have a responsibility to ensure a good education for all pupils. Responsibility without oversight leads to abuses in the system - this is one potential solution to ensuring delivery of non-negotiables.

But that's where the rub is for many teachers - they don't know what their kids don't know. And our original work reporting the hardest times table question showed just how poor times table knowledge can be - for schools using Number.fy, this won't be an issue but expect some suprise when the initial league tables are produced.

The Headteacher's Report

Following on from the previous blog (about our QpDpD, known as Cupid, stat), one of the services we provide at Flurrish is a half-termly summary performance report that is sent to the headteacher. This provides a detailed class breakdown. Here’s an example of one:

What can the head immediately see from this? Over the half-term (5 weeks) the 2-class intake primary school has

  • a total of 106,596 times tables questions answered
  • Class 5A have answered a large number of questions per pupil over this period, but the percentage correct is relatively low.
  • Class 5B have answered far fewer questions (Cupid=16.6) , more slowly but their accuracy is better
  • 6A have a large number of questions answered per pupil, rapidly with a high percentage correct
  • 6B have played very few questions (Cupid=6.6) although are accurate

The headteacher can also see how they have performed (in bold) against other 10 other schools in the area (ordered by Cupid):


Some further points to draw out:

  • they are in the top three for Cupid (38)
  • however this masks the two low Cupid scores for 5B and 6B
  • the accuracy is broadly similar between schools, but masks variability between classes

Remember that these classes should be able to complete 40 questions in a 10 minute starter session. If a 30 pupil class plays every day, then (30 pupils x 5 days x 40 questions) they’ll answer 6,000 questions per week.

Next blog is about actions you might take following a report like this.

Flurrish User Group 2017

A quick half-term note to say that, in collaboration with Central Bedfordshire and the Acorn Teaching School, Caddington Village School are hosting the Flurrish User Group (FUG) on Friday 24th March 2017.

Keynote: The Learning Imperative: psychology of the growth mindset (Dr Tom Gallagher-Mitchell, Liverpool Hope University)

See the attached flyer for the full programme

Book now at http://www.centralbedscpd.co.uk

We look forward to welcoming you!

Cupid - what are you pupils doing?

At Flurrish we provide reports to our schools on a regular basis with summary gameplay on a daily/weekly basis by class and half-termly monitoring of classes within schools (which we send to the headteacher) and of schools which we anonymise so that schools can see how they are doing comparatively (and we'll be outlining this in a follow-on blog).

But Cupid? Well, just a reminder from our webpage outlinig "why Flurrish":

MASSIVE practice: a 10-min starter, 30 children and 40 questions a day. That's 6000 questions a week!!

If times table learning is embedded in the classroom it should take an age 8 pupil who knows their times tables about 1 minute to answer 20 questions. Achieving 40 questions per day is a realistic goal and one that leads, as we say, to 6000 questions per week.

So, that's our statistic - Questions per Pupil per Day (QpPpD) or Cupid!!

It's helpful as it summarises how much a child, class or school is playing over a period of time and allows you to investigate anomalies further.

Why 40? Well experience has suggested that this leads to effective repetitive practice, but it's an area we are working with schools on to see what is effective. At this stage we would suggest this is a minimum, but any comments based upon classroom experience would be welcomed!

The Home Straight

As we approach half-term we are closing in on halfway through the year and whilst for some this might seem like a “glass half empty” scenario (another half to go!), we are fully aware that for those taking Key Stage 2 SATs, it really is very much the “home straight”. With the mathematics papers timetabled for Wednesday 10 May 2017, it’s only a few weeks after the summer term starts back up following the Easter break. Now that mocks are out of the way, staff are focusing upon targeting key gaps in knowledge for groups and individuals, practising taking tests and enabling the children to achieve the best possible results. Think of Usain Bolt easing ahead over a 200m race – he comes off the bend and has the 100m straight to go. He ups the gear, puts his head down and powers through to the finish.

Times tables obviously only forms a part of numeracy at KS2, but it is fundamental to rapid mental maths, accessing more complex manipulations of numbers and overall confidence. Pupils enter the realm of “can do”. So what have our classes actually been doing over this period? In terms of raw questions answered, these are the top 5 classes (all Year 6):

211904 (yes, that’s over 200k!), 144020, 121656, 117360, 113792

OK, but how many is that per pupil?

6836, 4801, 4055, 4347, 3924

Now, heck, that’s a lot of practice! The top class are nearing 7,000 questions (on average) for each pupil in their class, with what we’d consider a good class doing around 4,000. Now that sounds a lot – it is a lot!! But what does that equate to per day? Well, here are the figures (based upon 82 statutory school days up to last week):

83, 59, 49, 53, 48

Seriously! That is 50+ per day – pupils who know their 12x tables can do 20 questions in less than 1 minute. So, as a starter activity this is 10 minutes. Net result, 100,000+ questions answered by the time you get to mock SATs. This is such a strong motivator for the power of practice.

If you aren’t quite at the 100,000 question mark yet (and you can check exactly how many there are for your class on our results website simply by changing the date range) then you may well be doing some or all of the following already (and trying to avoid doing the Grannies and eggs thing!) over the next 61 days:

  • use the results website to 'download dataset' for your class and identify those pupils who do NOT yet know their times tables properly (e.g. are scoring less than 90% in random 20s). Ensure these pupils have specialist intervention by a teacher, HLTA or other mentor
  • Identify the 'tricky' times tables using the interactive results site or weekly summary headteacher reports. Get pupils to write them down – use black pen on a yellow post-it note (to aid memory recall) – then stick them around the classroom and home (by the toilet or bathroom mirror are prime places!)
  • Convince pupils that they have made real progress by showing them a few examples of class results and individual pupils’ results from the results website. Compare a week in September to a week now - reward them as appropriate, build confidence!
  • Make sure pupils use their mathematical agility by applying what they have learned. For example, tell them they can “buy one, get three free” - if they know 8 x 4 is 32, then the know 4 X 8 is 32, 32 divided by 8 is 4, 32 divided by 4 is 8. What a bargain!!
  • Issue certificates in assembly – "I know my times tables"
  • Have a mini competition at lunchtime to promote an ethos of rapid recall - give small prizes for the fastest and most accurate times tables/number bonds to 20 for the top 3 pupils
  • Loan devices out (with an agreement form) to pupils who may benefit from extra practise over the weekend or holidays - even if they cannot connect to wifi they can play in guest mode and so keep their daily practise going
  • Praise, praise and more praise - confidence is key to pupil success - cultivate a can do attitude. When a pupil says they can't do something - say "you can’t do it yet!!"

(with thanks to the staff at Caddington Village School!)

Top 11 Hardest Times Table Questions

Just following on from our earlier blog updating the hardest times table questions, we wanted to flag the top 11 in the times table hall of shame!! These are:

  1. 8x6
  2. 6x8
  3. 7x8
  4. 8x7
  5. 4x8
  6. 6x7
  7. 8x4
  8. 7x9
  9. 7x7
  10. 7x6
  11. 9x7

And that's an interesting group - a classic mistake for Stephen Byers (who famously answered 8x7 incorrectly), but (as we noted at the time) shameful of George Osbourne to dodge the question. However there is nothing like being put on the spot (by Sky News) to make the heart race.

As we see in the graphic below, it's that central area that causes the problems and thats the reason for the top 11. Of that central area of 16 questions running from 6-9 by 6-9, 9 of them are the hardest questions. That top 11 also includes 4x8 and 8x4 (notable outliers) and after that we see some of the 11x and 12x creeping in. This is core critical to number fact mastery and, given that they are hard to compute, storing them in long-term memory is important for success.

Are there better ways we can focus on this area??


Redux: What is the hardest times table question?

Way back in 2013 we reported on a research project at Caddington Village School on the hardest times table questions where

we logged a total of 60,000 questions across 232 children in years 5-8 using our intuitive smartphone/tablet app. Each child logged in to a centralised server using a fast graphical routine (no tricky passwords!) and played games that were batches of 20 random questions across the 12 times tables. All the answers (and the time they took) were then returned to the server

Sue Teague (the Headteacher at Caddingon Village School) and I followed this up with a published paper in Mathematics Teaching called Why is 48 so hard to remember?.

Well, we thought it was about time we updated some of the data on this area using all of the results we recorded for 433 children across 10 of our schools for the 2015-16 school year (encompassing years 2-8). All results recorded were from playing games of 20 randomised questions giving a total of 1,303,260 answers.

From these data (and with a little data wrangling in R) we have produced the visualisation below (left) which shows the percentage incorrect and can be directly compared to the original 2013 data (right). Some initial things worth pointing out:

  • there are alot more questions
  • there are alot more children
  • it's not a snapshot in time, but represents all games over the whole year. The children will have memorised more answers as time went on
  • whilst not the purpose of this post, ongoing research is looking at the impact of using Number.fy to memorise times tables. This would utilise a snapshot approach at the start and end of the year (similar to the startling year trial at Caddington Village School)

OK, so what are the takaways here:

  • the number of errors has reduced from 20% to 15%!! And it's worth noting that this dataset is year 2-8 (with very few year 7-8), whereas the origial trial was year 5-8. The improvement is therefore far more significant.
  • the hardest 21 questions in 2013 had a range of error rates from 40-62.5%. That extended "tail" of very high error rates now no longer exists with a maximum error rate in 2015 of 36%.
  • the order of hardest question has changed, although is very similar. The top two hardest questions remain the same: 6x8 and 8x6.
  • perhaps not surprisingly, those questions that are the hardest occupy the "middle" of the chart on the left and are shown by the distinctly red hot spots!!
  • and the 12x questions are being answered correctly more often.
  • after practise, this data probably represents the best estimate of the times tables children find the hardest and that the 12x is perhaps not as cognitively difficult as adults might think (or maybe it simply represents greater practise?)
  • those 6s, 7s, 8s, and 9s still remain dang hard!




Times tables tests put on hold... for now

The TES reported that the government have put times tables tests put on hold which is suspiciously or coincidentally close to the appointment of new Education Secretary Justine Greening. That said, it really is too close judging that the news release came from the Standards and Testing Agency and said:

Multiplication tables check and year 7 resits update

Following previous announcements about the multiplication tables check and year 7 resits we are re-confirming that there will be no statutory requirement on schools to administer these tests in the 2016 to 2017 academic year.

We will engage with the sector as we introduce the tests and will provide further details in due course.

For me the crucial part is the last sentence. I actually read this as the tests in our trial schools didn't work as we expected so we're postponing them until they do. Would be very interesting to find out how the trials did actually go - that said, those pupils who know their times tables accelerate rapidly in the further maths schools, something born out in KS2 SATs.