Why You Should Welcome Times Tables Tests: Part 2

Continued from Part 1.

The most likely reason that the importance of fluency in times tables has been downplayed is due to ideology. While plenty of primary teachers discover the benefits of fluency in times tables while teaching (particularly if they have to prepare students for SATs), the majority of blogs I read by primary teachers, and 100% of those I read by trainees, have the bizarre idea that maths is divided into discrete categories: “facts”, “methods” and “conceptual understanding” and that it is the last of these that is most important. Unfortunately, the “conceptual understanding” category tends to be code for “relevance”, “group work”, “games” and learning multiple strategies for arriving at answers rather than actually learning the best methods to fluency. In times tables this means that students are taught the most trivial aspects of times tables (that multiplication is equivalent to repeated addition, that multiplication is commutative, and division being the inverse of multiplication) without learning off by heart that 3 lots of 7 is 21. Worse, people talk as if facts and methods are in opposition to understanding; as if learning the times tables will somehow undermine, rather than illustrate, those trivial aspects of times tables.

A further objection to times tables testing is the idea that it will cause “stress” or “anxiety” for students to have to recall basic facts under time constraints. Of course, recalling times tables in an unlimited amount of time is actually pointless, as it would undermine recall completely if students were given enough time to calculate answers. It would be like handing out dictionaries in a spelling test. I think the low expectations here need to be challenged directly. Answering questions on something you know fluently is one of the least stressful tests there is. That’s one of the main advantages of fluency. Can you imagine an art teacher arguing that students shouldn’t have to know what yellow is because the effort of remembering might cause stress? Or a PE teacher saying that students cannot be expected to know any of the rules of football while under the pressure of playing a game? Remembering the basics is not stressful unless you don’t know them well. To be tested on times tables 2 years after the curriculum says you should know them fluently is not stressful unless your teachers have failed you and it is that type of failure that is being challenged by the introduction of the tests.

And finally, one objection that’s come up is the idea that tables beyond 10 are pointless. To be honest, the 11s are not terribly useful, but they are so easy to learn that the opportunity cost of learning them is insignificant. As for the 12s, I have seen it argued that this is some hold-over from pounds shillings and pence that is no longer relevant. If you think that, kick yourself now; you have just accepted uncritically one of the most ludicrous claims on the internet. The 12 times table is one of the most useful. There are 12 months in a year. There are 12 inches in a foot. The number of degrees in a half or full rotation is a multiple of 12, as is the number of seconds in a minute, minutes in an hour and hours in a day. The fact that 12 is a multiple of 1,2,3,4,6 and 12 has made 12 and its multiples extremely useful for dividing up units of measurement for thousands of years. It’s also why we often refer to “dozens” when grouping objects or indicating magnitude. And that’s without the advantage knowledge of the 12 times tables gives in the many mathematical questions that will make use of the number 12 precisely because it has so many factors. If we weren’t biased by the number of fingers on our hands, we would probably have a number system built around the number 12. Seriously, how could any numerate person have missed the importance of 12s?

I’ll leave it there. If we want students to be good at maths, then it should not be too much for them to learn a few dozen basic number facts fluently after more than half a dozen years of education.

Why You Should Welcome Times Tables Tests: Part 1

I promised I’d write about this last weekend, and then ran out of time, so apologies for the delay.

I support the introduction of times tables tests at the end of Key Stage 2. The main reason is that I am a secondary maths teacher and I see so many students arrive at secondary school not knowing their times tables. The complacency of those who say “primary schools already do this” amazes me. There are some primary schools that are good at this, but to be honest, since the end of the original NNS I can’t think of any year 7 class (other than when covering at a top grammar school) I’ve had that turned up to secondary fluent in their times tables. And this includes top sets and classes at independent schools. Very often the only students who know their times tables were educated overseas, taught by their parents or had private tuition (particularly Kumon maths). Worse though, is how often students think they know their times tables properly but don’t. It’s common for me to ask a class who knows their times tables and get 50% of hands up, then to ask “What’s 7 times 8?” to a student with their hand up, only for them to start counting on their fingers. Often students arrive at secondary not only not knowing their times tables, but convinced that as they could work through a table by repeated addition, then they have mastered the skill. Often they know virtually nothing of the 12 times table. Some students are not even fluent in their 2 or 3 times table after 7 years of daily maths lessons.

The reason the lack of fluency makes a difference is something that should be obvious to anyone who has followed the debates about cognitive psychology and education in recent years. Our working memories are limited. The way we cope with more complicated calculations is to fluently recall helpful information from long term memory. We also learn better if we do not overload our working memories by thinking about too much at once. In practice, this means it is much easier to grasp the idea of simplifying fractions, and remember it in the future, if every time you think about simplifying fractions you do not have to think hard about times tables calculations at the same time. It takes a second to simplify 49/84 if you realise at a glance that both numbers are in the 7 times table, and know exactly how many times 7 goes into both numbers without thinking about it and the idea of simplification is easily remembered if you didn’t get distracted by the need to work out times tables. Every maths teacher has experienced the student who thinks all simplifying of fractions should involve division by 2, because those are the only questions on simplifying they have ever mastered. Also common is the student who loses track of what they are doing part way through simplifying a fraction, and writes down the common factor in the simplified fraction rather than dividing by it. These are failures that occur because of a lack of times tables knowledge. And all fraction calculations tend to involve similar considerations of times tables. As do the methods for dividing and multiplying larger numbers, negative numbers or decimals. Multiplication and division are also fundamental for accessing proportional reasoning and much of algebra. Even topics in geometry (eg. angles in regular polygon) and statistics (eg. pie charts), are often easier if you can divide fluently. If you don’t get how fundamental times tables are to learning maths, I am prepared to argue that you don’t understand how to learn maths. Maths is cumulative and fluency at one level leads to understanding (and more fluency) at the next.

Continued in part 2.

 

What education bloggers have said about times tables tests

I thought it might be worth seeing if it’s possible to write 500 words summarising the views in the education blogosphere about one topical issue. Let me know what you think. Also, I’d be very interested to know if I missed any blogposts debating the issue. I will probably add my own views in a post later this weekend.

3 weeks ago, there was an announcement from the government that students should be tested on their times tables at the end of KS2. How did the blogging world respond?

Some parts of the blogging world reached an immediate consense. The teaching union blogs were against.  The ATL‘s blog claimed that times tables are too narrow to be concerned about, objecting to the timed element, and raising practical concerns. The Voice blog published a statement opposing testing on principle. The NAHT site featured a blogpost describing the announcement as “spin” and suggesting it was a criticism of schools.

There was a similar consensus from most blogs providing political commentary on education. Roger Titcombe, at the Local Schools Network claimed that the tests “conjured up Gradgrindian classroom scenarios”. Michael Rosen preferred Alice In Wonderland to Hard Times, but seemed to object. Education commentator, Owen Hathway also opposed the tests, claiming that tables tests were unnecessary and interfering, and that:

…the world has moved on.  Children learn in different ways in the digital age and using a calculator, or phone, is a simple way of looking up times tables. … we must …. be mindful of the modern world and make sure that children and young people use the computing ability on their mobile phones so they can get that at their fingertips.

Jules Darby, on the Labour teachers blog, suggested that the tests would impact on those with SEN and existing difficulties. However, two other Labour Teacher commentators had a more mixed perspective, with Michael Tidd analysing the Labour Party’s response and Lisa Harford discussing both the importance of knowing times tables, and the limitations of tables tests as in indicator.

That Labour Teachers were less hostile than political commentators who don’t teach, might be explained by the differences of opinion among teacher bloggers generally. Two secondary maths teachers wrote positively about the idea of times tables tests. Jeff, from the “A Maths Teacher Writes” blog, argued that times table knowledge is important for further progress in maths,  and that tables were not difficult to learn. Tom Bennison also wrote to criticise the objections to the tests, particularly complaints that testing is bad for children: “Of course I realise that some children may not particularly enjoy tests, but the ‘children hate tests and they make them hate maths’ talk that is common is a massive stereotype and not universally backed up with any evidence.” One secondary maths teacher did object; Mr Chadburn argued that “Rapid recall is only of use in the future in a pub quiz”. Two primary teachers, Gawain Little and Mr Teacher wrote posts contrasting mathematical understanding and reasoning with the recall of times tables facts. The strongest objections were made by home educator Ross Mountney who argued that the tests “…will inevitably change teachers’ behaviour towards pupils, possibly towards a more coercive style if they feel that there is a real threat to their status as a result of their children’s performance”.

My post for @LabourTeachers : Why I’m not convinced about local authority control in education

I wrote a post for Labour Teachers earlier in the week. As it was about education, I thought I’d share it here.

I was reminded the other day of this blogpost “Let’s stop eulogising democratic accountability” by Jonathan Simons of Policy Exchange. The post argues that the political accountability for education provided by control by local authorities is so weak that parties who oversee a worsening in local education provision are more likely to have gained electorally than lost. This is not a surprise. No single issue dominates local elections, and education is one where local politicians often have the least to say. But it is rare to have any discussion in the Labour Party of education without somebody suggesting that local authority control is more democratic and that Academies are “privatisation” or “undemocratic”.

What follows are my main experiences of local authority control of schools. Utterly anecdotal, but I hope they highlight issues.

1. When I was training to be a teacher, my local constituency party invited in the councillor responsible for education. (I think it would have been in the days of “committee chairs” rather than “lead members”). Despite having schools in the area that supply teachers would run a mile from, and a lot of schools with low exam results in the area, he told us the council were doing really well because no schools were currently in special measures.
2. When I was an NQT, the director of education (or probably the deputy director of education) visited my school and told all staff that there would be no permanent exclusions from now on because figures were too high. In the months that followed teachers were sworn at, spat on and terrorised in the school.
3. I worked at a school that had once been branded the worst in the country. It became part of a federation with another more successful school. Its results went from terrible to just bad. It started attracting a different intake. The leaders I saw (provided from that other school) were incredibly effective. Then, before the school had a chance to really improve, the funding for the federation was withdrawn by the local authority; most of the good managers went; an emergency replacement head was drafted in who didn’t seem to have a clue, and the school became something of a nightmare to work at.
4. During the time when “inclusion” was still fashionable, the education spokesperson of the Labour opposition group came to speak to members at a policy forum organised by the district party. When I raised the issue of inclusion, (i.e. the deliberate policy of running down special schools and forcing kids with special needs or appalling behaviour into mainstream classrooms) she simply said that all the experts were agreed that it was for the best, so we had to support it. Other party members at the meeting also disagreed with her, but even in opposition, it was not considered possible for the party to oppose what council officers had advised was best.
5. Two of the authorities I worked in changed control between Labour and the Tories or back again, while I was working there. I cannot tell you a single policy change that resulted from the changes that I was aware of as a teacher.
6. I experienced local authority trainers and consultants. Back in the days of local authority control, my NQT training was given by the local authority. They taught me about thinking hats.  Other LA advisors taught me about thinking skills. And card sorts. And interventions. And all sorts of nonsense. And this does not seem to have been unusual. LA consultancy was the place that failed middle managers tended to end up.

I don’t think anything I describe above is particularly unusual. LAs were bureaucracies whose main priority often seemed to be keeping a lid on the worst schools while trying to keep the best schools from attracting too many students from their neighbours. No doubt, for every anecdote above about LAs an equivalent one can be found about academy trusts. But then I’m not arguing for compulsory academisation. All I’m arguing for is an acceptance that sometimes, for some schools, the influence of the LA can be harmful and an escape route is needed. All I’m arguing is that LA control was never a model of democracy. All I’m arguing is that Labour should stop speaking up for the idea that council officers know best.

I’d sooner have the status quo than a return to the days of LA interference. Turning the clock back to LA control is a policy with little to recommend it. If we are not happy with the current situation, and I accept it is fragmented, then we should at least come up with something new, perhaps something genuinely democratic.

The #OFSTEDMyths Videos

A post to the OFSTED blog about myths yesterday, included three videos in which OFSTED luminaries sought to set the record straight about inspections. I thought I’d publicise them and, just in case you can’t be bothered to watch them, or your school blocks Youtube but not my blog (what are you thinking?), there is a transcript below each one.

London Director of Schools, Mike Sheridan on preparing for inspections:

When we go into great schools, we tend to see that they are focused on the young people that they serve. They’re not looking to see what Ofsted wants. They’re looking to see what their children need and this is really refreshing and inspectors are very capable of really recognising the difference that those processes and systems make for the young. It’s rare that we go into a school and we find that superficial and so we don’t want schools to be worrying about the process of want schools to be going through ‘Mocksteds’. Of course you want schools to understand where they are. We want them to be able to evaluate where they are. We want them to be able to use this evaluation to be able to improve further. There’s no one way of doing things and it’s really important that teachers and leaders find the best way for the communities that they serve.

Deputy Director for Schools, Joanna Hall on feedback:

There’s no particular expectation about seeing written records from oral feedback. The most important thing is, do the pupils understand the feedback, do they act on the feedback, and how does that have an impact on their learning?

Deputy Director for Schools, Joanna Hall on grades:

Ofsted doesn’t grade lessons anymore. We might visit a whole range of lessons, talk to leaders about the quality of teaching, talk to staff and talk to pupils. The most important thing is: what’s the impact of teaching, learning and assessment on pupils’ progress.

The blog post and youtube pages also link to the updated OFSTED myth-busting document.

I think most of this is stuff that schools need to get the message about. There’s still too much nonsense imposed on schools on the basis that OFSTED will want to see it (some recent examples here and here). However, there is one bit of these videos that worries me: the part in the second video where Joanna Hall asks “do they [students] act on the feedback…?”. While, technically, students improving and not repeating mistakes is evidence of acting on feedback, schools now seem utterly convinced that the only way to demonstrate student response to feedback is to have “interactive” marking policies that involve students responding to teachers. I don’t think that OFSTED require this sort of “triple marking” or the multi-coloured pens it so often involves (see here) but that comment in the video is only going to encourage schools to introduce such policies. I think greater clarity about how OFSTED will look for evidence of students acting on feedback would be useful.

Update:

A twitter response from OFSTED national director, Sean Harford, which will hopefully come as a relief to a lot of teachers:

Top Blogs of the Week : Schools Week (January 2016)

Schools Week have published my review of the best blogs of the week.

The sinner who repents

By ijstock.wordpress.com

A geography teacher recalls his PGCE training back in the 80s and considers how biased it was to one particular set of values and to certain opinions that were not to be questioned. In particular, he decides that recent experience does not support the advice from his training to “always give each child a clean slate every lesson”. Is that really something a child should expect after awful behaviour?

 Continued in:

Andrew Old’s top blogs of the week 11 January 2016

A Guide To My Favourite Bits of The Education Blogosphere

I’ve been relatively quiet recently on social media (honest), and I’ve tweeted far less (really) and barely blogged since before Christmas. Much of that time has been spent on my various side projects in education blogging, which often don’t tend to get the publicity they actually need and nothing like the readership of this blog. So I thought I’d give a quick guide to those parts of the education blogosphere that I am either involved in, or I’m most interested in and encourage you to get involved in them too.

I should probably start by mentioning this blog. It’s been going over nine years and there is a guide to all the posts here. I am hoping it will be more active this year than last year, and it will remain the first place to keep up with my opinions and issues that have interested me in education.

Most of my other projects are under the “Echo Chamber” banner. These have been built around publicising the best of the education blogosphere, or simply promoting all UK education blogs. The Echo Chamber blog can be found here and is my attempt to share the best of the education blogs. The growing nature of the blogosphere has made this a bit of an impractical task, and there is plenty of work still to be done to improve that service, but if you like what you find on this blog, then this should be a way of finding similar blogs. Non-UK blogs that I like can be found on the Echo Chamber International Blog.

As well as my selections, the Echo Chamber also tries to help you find your way through all the UK education blogs. My latest count found over 3000 education blogs written by people in or from the UK. Various lists can be found here and it includes a spreadsheet where you can add details of your own blog. To get some perspective on the whole of the blogosphere, there is Echo Chamber Uncut which attempts to link to every new post from every UK education blog with a working RSS feed. You may find it impossible to keep up with it, but you can browse it looking for things of interest. If you use the “search” facility it should help you find posts on topics that particularly interest you. There are also “mini-Echo Chambers” that share posts from bloggers from particular sectors or teaching particular subjects. If you teach the relevant subject then you should probably follow one of these blogs:

• The Art Echo Chamber
• The Business and Economics Echo Chamber
• The English Echo Chamber
• The History Echo Chamber
• The ICT and Computing Echo Chamber
• The Literacy Echo Chamber
• The Maths Echo Chamber
• The PE Echo Chamber
• The RE and Philosophy Echo Chamber
• The Science Echo Chamber

There are also mini-Echo Chambers for:

• Governors
• Headteachers
• FE lecturers

I’m always looking to expand the number of mini Echo Chambers, but these efforts have become somewhat bogged down in an attempt to create an Echo Chamber covering all the primary blogs. I hope to complete that soon, and then I will be looking for volunteers to create blogs for other subjects. So, if you are a teacher of MFL, geography or any other unrepresented subject, who also uses wordpress, please get in touch. Details of all these Echo Chambers (including Twitter accounts) can be found here.

The newest part of the Echo Chamber is a diary of events for teachers which can be found here. Please comment or use Twitter to contact @annaworth if you have any events to add. I am also thinking about what else should be added to the Echo Chamber in the future.

Another blog I run is Labour Teachers. If you are a Labour supporting teacher, please get in touch if you help write for it. However, in the interests of balance here are a list of the main party political education blogs.

Labour

• Labour Teachers
• Reform Time
• Fabian Society – Education
• Socialist Education Association
• Education For Everyone

Conservative

• Conservative Teachers
• Conservative Education Society
• Conservative Home (Not an education blog, but has more regular posts by teachers than all the other party politics blogs put together).

Liberal Democrat

• Liberal Democrat Education Association

The newest blog I have created is Starter For Five, a blog compiling advice for new teachers which can be found here. You should be able to follow it to get advice as it is posted. You can also add advice from this form here. Please make use of this.

That’s pretty much it for things I run, but other people have created some great resources for teachers. Let me point out a few places of interest.

• Staffrm is a blogging site for teachers. It specialises in short posts and a generally positive vibe. It’s a particularly good place to start if you want to begin blogging.
• researchED is an organisation for helping teachers find out about (and challenge) education research. It holds regular conferences.
• Teachmeets are events for teachers (often free) in which teachers share ideas.
• Knowledge organisers (for collating subject knowledge).

Obviously this is all my own personal guide to what’s out there for teacher bloggers, and I have concentrated on my own work and my favourite sites. Feel free to suggest what else is important in the comments.

Top Rated Posts in 2015

The following posts got the most views in 2015. A lot of them weren’t actually written in 2015.

1. The Darkest Term: Teacher Stress and Depression
2. How to Destroy NQTs
3. What OFSTED Actually Want
4. A Myth for Teachers: Jobs That Don’t Exist Yet
5. Good Year Heads
6. It Seems I Won’t Be Joining The College Of Teaching
7. Nobody Believes in Learning Styles Any More, Do They?
8. A Guide To Scenes From The Battleground
9. The arguments against the phonics screening check have been discredited
10. The College Of Not-Actually-Teaching
11. Is this the most clueless OFSTED report ever written?
12. What OFSTED Say They Want
13. Is Phonics Being Implemented Correctly?
14. More OFSTED Good Practice that isn’t
15. The Return Of The Most Annoying Question In Education
16. A Very Short Summary of the Phonics Debate
17. There’s One Thing Worse Than Green Pens
18. Enough With The Green Pens!
19. Never Forget: Learning Styles are Complete Arse
20. Does teaching philosophy to children improve their reading, writing and mathematics achievement?