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Lies, Damned Lies and #WomenED Statistics Part 2

February 3, 2016

Last time I discussed how, despite 66% of headteachers being women, it was claimed that there were too few female heads. In this post I will deal with a couple of cherry picked statistics used to justify this claim. Both of these statistics tend to be accurate, but misleading.

The first statistic is the difference between the proportion of women teachers and the proportion of women headteachers. 75% of classroom teachers are women, so why 66%, not 75%, of heads? My immediate response has always been to ask “why would they be?” Heads are not a random sample of teachers; headship is not a universal aspiration for all teachers. Many factors could explain the difference without any women losing out just because they are women, not least an acceptance that wanting a career in management is not necessarily a good thing, and that those without this ambition are not “failures” or being deprived by not having this ambition.

However, before I go too far down this route of explaining the alleged “discrepancy” in terms of human behaviour, I should point out there is no need for this sort of explanation. Statisticians are familiar with the rule of “regression to the mean”. I should be careful here, “regression to the mean” is defined in different ways, some of which may not apply here. However, the basic principle is that when you measure something and get an extreme value, then further measurements (even if related to the first measurement) are likely to be less extreme. This is why, if you look at the students who did best in one test, they are likely to do less well in the next test, and those who did worst in the first test are likely to do better in the next test. This is why the children of very tall parents are, on average, less tall than their parents and the children of very short parents are likely to be taller than their parents. (This also came up here.) Extreme measurements are not easily repeated, even when the first measurement is likely to be correlated to the second. Whether or not what I have been describing here can be labelled as “regression to the mean”, there is definitely a similar problem here. Because the population of classroom teachers is so skewed towards being women, it is highly unlikely that the population of heads would be skewed to the same degree.

Without any need for discrimination against women, or a prejudice against women leaders, or a reason for some women not becoming heads, we would expect the population of headteachers to be skewed towards being women, but not to the same degree as classroom teachers. And that’s what we’ve got, a large majority of heads are women, but not in the same proportions as classroom teachers. This is not unfairness or inequality; this is just how statistics work. We should be very careful to watch out for attempts to obscure this. A number of people have referred to the ratio of female heads to female teachers as a measure of the “likelihood of promotion” or “the prospects of promotion” as if it measured opportunities for advancement. To assume that an individual’s opportunities are measured by the statistics for their gender is to assume that appointments are made on the basis of gender, the very claim that is at issue here. What we have here are two connected, but distinct populations, and while the number of women classroom teachers is likely to affect the number of women heads, it was never likely to determine it and, given the extreme gender imbalance among classroom teachers, it would have been highly unlikely that there would have been the same imbalance among heads.

The second figure used to suggest a shortage of women is that for secondary heads. According to the workforce survey, only 37% of secondary heads are female (it might be 36%, as my figures are rounded and I have heard that figure quoted a lot). This is probably the best evidence of an actual discrepancy between men and women in educational leadership, although why the dominance of men in secondary is more of a problem than the even greater dominance of women in primary is not usually explained. But, again, we should hesitate, and remind ourselves how statistics work. Secondary heads account for only a sixth of heads, and we can expect at least some subsets of any population to depart from the rest of the population just by chance. This is why statisticians warn about “subgroup analysis”. There are bound to be anomalous subsets, and if it hadn’t been found by subdividing by sector, could we have found one by subdividing by region? Age? Race? Type of school? Without knowing what else would have been considered a cause for concern it’s hard to judge whether this should be. All we do know is, it is unreasonable to assume that all possible subsets of headteachers would have as many (or more) women as men. That’s not to say there is nothing to be explained here. The “regression to the mean” argument I used earlier does not apply in the secondary sector and the problems of subgroup analysis may not be enough to explain why the proportions in secondary are so different to the proportions in primary, but the mere fact that there is a subset of schools with more men than women as heads should not, in itself, be of concern.

Even after all this, I cannot rule out that there are no issues relating to gender that affect women’s opportunities to become school leaders. All I can say is that we are yet to have reliable evidence for this. I’m happy to endorse any (rigorous) effort to acquire that evidence, and research into application rates and differences in ambition would be a good place to start. But until that evidence is found, then #WomenEd remains a campaign against a problem that may not even exist and the question of why people want to convince others that the problem exists should be asked.

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Lies, Damned Lies and #WomenED Statistics Part 1

February 2, 2016

People seem aware that I don’t like fallacious arguments. Bad logic winds me up. But that’s not what really gets my goat. If you want to annoy me, get statistics wrong. It’s like the sound of nails scratching a blackboard. And in recent months one movement on education social media has gone all out to get the stats wrong: #WomenED. The organisation is mainly concerned with helping women into leadership positions in education. However, the problem with this aim is that women are already in leadership positions in education. A few months back I took the mickey out of this in a post called What have women ever been allowed to do in the education system? pointing out all the roles in education in which women outnumber men, from headteachers, to secretary of state. Although I haven’t got hold of the data, I have been told by reliable people since then that I could have added school governors and school business managers to the list. So having been set up to deal with a problem that may not exist, those involved in #WomenED have set about the task of either denying or reinterpreting the stats.

Let me start with denial. The following are all from blogs reacting to #WomenED. Please remember that according to the 2014 workforce survey. in state schools 66% of heads and 68% of deputy and assistant heads are women.

We should be shaping the educational agenda and bringing people along with us so that they see that a more representative educational leadership brings about better outcomes for all.

From https://jenjaynewilson.wordpress.com/2015/11/15/what-womened-means-to-me/

But… educational leadership would be more representative of society if there were fewer women.

Some of our collective goals:… * To achieve equal representation in all areas of education and advance equality for all.

From http://staffrm.io/@misswilsey/AN4r60WyFA

But… equal representation would mean fewer women.

The group’s vision is that headteacher and senior leadership positions should reflect their school’s student and staff bodies.

http://www.innovatemyschool.com/blog/item/1672-.html#womened-starts-2016-with-60-new-regional-leaders&Itemid=191

But… leadership teams would, on average, need fewer women to represent the gender balance of their student body.

But so too does male heavy decision makers in the Department of Education and other influential educational bodies.

From http://staffrm.io/@jules/JAxo3a66PG

But… the secretary of state is a woman. The senior civil servants in the DfE are 48% women, (although that’s 44% for top management posts) which is hardly overwhelmingly male. The main teaching unions and Ofqual are lead by women.

But now I need to take the next step to headship.  And to do that I need to find the feminist Governing Body that is prepared to defy the statistics.

From https://inspiringtchers.wordpress.com/2015/10/04/maternity-works-womened/

But… the statistics show that 66% of appointments are women.

At WomenEd, we’re committed to being the change we want to see so that educational leadership can be more equal and representative of the profession’s diversity.

From https://jenjaynewilson.wordpress.com/2016/01/17/leadership-developement-it-starts-earlier-than-you-think/

But… leadership is already more diverse than the profession in terms of gender, and increasing the number of women would make it even less diverse.

Just to be clear, I’m not advocating a reduction in the number of women in educational leadership. I don’t think women are being forced into educational work at gunpoint, or even due to financial insecurity (young women now earn more than young men), so I’m not offended at the profession being female dominated. I’m merely pointing out that educational leadership is already overwhelmingly female and the inevitable result of any attempt to make school leadership more diverse, more representative of society or more equal would be a reduction, not an increase, in the number of women in school leadership.

What usually happens when you point this out to #WomenED partisans (after they thank you profusely for correcting their error) is that some statistics are cherry picked to prove that there is, nevertheless, a shortage of women in school leadership. I will discuss these next time.

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Why You Should Welcome Times Tables Tests: Part 2

January 30, 2016

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.

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Why You Should Welcome Times Tables Tests: Part 1

January 30, 2016

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.

 

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What education bloggers have said about times tables tests

January 23, 2016

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”.

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

January 22, 2016

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.

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The #OFSTEDMyths Videos

January 21, 2016

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:

Screenshot 2016-01-21 at 18.32.44

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