Now We Are Eight

Today marks 8 years since my blogging career began. A year ago I attempted to sum up the first seven years of blogging, but it feels a lot like there is more to report back on from the last year alone than from those 7 years. For a start, the total number of hits on this blog went over a million recently. As the blog used to appear in a couple of other places which wouldn’t be included in the total, the actual millionth hit could have been much earlier but was probably still this year.

There were two remarkably popular posts this year. The first, A Christmas Miracle – OFSTED Get It Right For Once, was simply an update on changes in the OFSTED handbook during the Christmas holidays and seemed to be popular mainly because it was the first place people heard the news. But it was also widely suggested that the changes reflected some of the constant campaigning over OFSTED that had been part of this blog for the previous 10 months. The other blogpost, one that still seems to get around 100 hits a day even now, was The Darkest Term: Teacher Stress and Depression which was a series of anonymous accounts of teachers’ experiences of stress and depression. Sobering reading, although I know some of those who contributed are much happier now. Its popularity says a lot about the profession.

This is the year that Michael Gove ceased to be education secretary. My comments at the time can be found here. He was a regular reader of this blog, and mentioned it in a number of speeches. Although constantly attacked for not understanding what schools or teaching were like, he had been in charge of his party’s education policy for 7 years and had built up a knowledge of the system, and the debates in education, that no other politician can come close to. He’d also made education one of the most important cabinet posts. It’s a shame to see it sink back into obscurity and for the debate to be once more dominated by those who don’t actually seem to realise what’s at issue. I mean, teacher’s oaths? Really?

This is also the year that I went public. As a result of others trying to expose me in an apparent effort to shut me up (how’d that work out for you?) and the fact that I had left my permanent job to go part-time, I decided to end my seven year run of being anonymous and made a number of public appearances. I’ve gone from being absolutely terrified of public speaking in a room of about 30, to really rather enjoying it and daring to appear before one audience that was in the hundreds. I’m particularly fond of discussions as I can get stuck into the debate and don’t have to spend hours preparing. I also like events where there are biscuits.

I’ve appeared in print (as opposed to only online) for the first time this year. Firstly, I wrote the foreword to Robert Peal’s Progressively worse: The Burden of Bad Ideas in British Schools. Then, I contributed a chapter to Rachel Jones’s Don’t change the light bulbs: A compendium of expertise from the UK s most switched-on educators (it’s for charity, buy it!).  More recently I’ve written for Academies Week, firstly about my hobby of going to education events and secondly, contributing a round up of the best education blogs of the week.

I’ve met a number of people who are big in either education or policy for the first time this year, like: Doug Lemov, James O’Shaughnessy and Maurice Glasman (none of whom actually knew who I was at the time), Liz Truss (when still education minister), David Goodhart, Jonathan Simons, Mike Cladingbowl and Sean Harford. I also met television’s Vic Goddard and Oliver from Tough Young Teachers, and came within in a heartbeat of talking to Johnny Ball. I’ve also met and socialised with various education bloggers and tweeters, particularly by organising curries, and I have been doing my bit to try to help good new bloggers find an audience, particularly through The Echo Chamber.

And probably the most exciting experiences were my two contributions to Radio 4 programmes. Firstly, I shared my opinions in an episode of The Report about OFSTED and, more surreally, I was interviewed in my front room by Reeta Chakrabarti for One to One. Fortunately the programme makers edited me into some form of coherence.

No doubt, once I’ve posted this, I’ll think of some even more exciting blog-related activities from this year and add them in the comments. But it’s been an exciting year to be a blogger and a real change from the early years of blogging which mainly consisted of people telling me I should shut up because only bad teachers think there is anything wrong with the education system or progressive teaching. Here’s to the next 8 years.

My Interview with the OFSTED Big Cheeses

I realise this has been available in another format for a while, but I have only just found it in a form I can embed on my blog. This is the interview I did with OFSTED’s Mike Cladingbowl and Sean Harford at ResearchED last month. It has been cut so that it misses out the bit where I say I’m going to take questions via Twitter, so it may look like I lost interest and started playing with my phone part way through. Honestly, I’m not playing Candy Crush, I’m just looking for questions.

Update: 22/10/2014 Actually, if I’m pointing out something about OFSTED I should probably also publicise:

1) My post about meeting Sean Harford in July, as I think a lot of people missed it because it was in the summer holidays.

2) The latest OFSTED clarification about what they want. Some particularly helpful comments in there about marking and observation that everyone should know.

Has The Debate Moved On?

It’s very easy to think that the education world has been transformed. People who used to tell me to shut up because nobody agreed with me, now claim that I should shut up because nobody disagrees. OFSTED are no longer blatantly pushing the progressive bandwagon (although when you look up the consultancies some of their inspectors work for, it is still terrifying). Opinions, that at one point nobody dared to express openly for fear of pariah status, are now mainstream.

But there have been a couple of blogs recently that made me wonder. It was not that I disagreed with their contents (you can look here for some  things I’ve disagreed with recently) but that the writers didn’t seem to realise that what they were saying was going to be controversial. Perhaps they are unused to the internet, and the idea that if you say publicly something people disagree with you will, at the very least, be asked questions. Or perhaps they didn’t realise that many, many people would strongly disagree. But they were all views that made me think: “Did the writer realise that people would disagree strongly with this?”.

One was “Using Lego StoryStarter to Engage A-Level students with the Hitler Myth” in which a teacher described the great success of getting sixth formers to analyse Hitler’s public persona with the German people by use of Lego. I don’t know if the writer missed the controversy over teaching about the Nazis through the medium of Mr Men, but if they did, they clearly didn’t let it affect their choices. The two biggest objections raised then still apply. Firstly, it is infantalising, even more so in this case as it is sixth formers doing A-level, which is meant to be a step to university level study. Secondly, it is poor taste. These are events that led to genocide, not a children’s story. It’s also noticeable that the work produced is not obviously of A-level standard (unless A-level history has changed drastically since I took it). While this might be understandable so early in the year, and I’m not attempting to criticise the students for their work, it seems to provide very little justification for the effectiveness of the method used. Yet the writer seems to have missed all this. He did write a response and as far as people who had criticised thc blogpost had seized on typos or were rude, it’s fair enough to object. However, the key objections, that this is not what sixthformers should be doing, was only dealt with by the defence of saying other people agreed it was okay, including colleagues and students. Perhaps it is acceptable in this teacher’s school; perhaps in behaving this way he was only following orders. However, it was his choice to publicise it and declare it a great success and one wonders how many parts of the education still give the impression that work that resembles play, even for sixthformers, is the best sort of learning.

The other blogpost,  “When swearing in class was a reason to rejoice #restorativepractice” was one that had me fuming rather than bemused. Written by a senior teacher it described how a disciplinary incident was dealt with. A boy has sworn at some girls in a class and upset them. Instead of being punished (some Twitterers tried to deny the absence of punishment, but in a subsequent post the writer makes it clear they object philosophically to punishing chilren), he was made to apologise. The girls did not accept the apology. The boy then became furiously angry, swearing at the blogwriter as well. Still no sanction was issued, but there was a promise to speak to the girls, and as far as I can tell there was an attempt to persuade them to change their attitude. The teacher appears to be entirely motivated by the fact that the boy has been labelled as having “Aspergers” (they don’t say who by) and that other students should make allowances for this. The girls are described as having “closed minds” for wanting the boy to be punished. Standing their ground at first, one eventually caves and accepts the apology. This girl admits she was angry because she had endured similar abuse in the past, and she is put in touch with a colleague who will helps students “manage their emptions”.

It still shocks me that any teacher could excuse such behaviour from any student. SEN is not an excuse for allowing children to be treated in ways that would generally be considered abusive. The denial of natural justice is infuriating. Treating the victims as if they were in the wrong, for objecting makes it worse. The gender politics makes it all even more disturbing; should girls really be told that when boys treat them badly, then an apology makes it okay? The follow-up post uses the false dichotomy I mentioned last time, of claiming that the alternative to letting kids get away with bad behaviour is “behaviourism” as if B.F. Skinner invented the idea of punishing naughty children. It combines this with a narrative of presenting badly behaved children as victims, an approach that’s dehumanising at the best of times, but particularly inappropriate in a case where the actual victims were treated so badly. But the author’s position is clear, she will not punish children:

If Tom had been punished, according to a set of inflexible ‘do this and you’ll get that’ rules, he would not have had the opportunity to practice the skill of apologising and he would already be questioning his ability to succeed within the mainstream.

It’s still one of the most shocking posts I have ever read. If I was a parent at that school I would be looking for somewhere safer for my children. It’s probably the first time I’ve read a blogpost and thought, despite everything, “OFSTED should do something about that”. That a senior teacher in a secondary school could behave like this worries me. That they thought they should share it with the world on a blogpost is just stunning, and does leave me, again, wondering how many schools proudly still have a culture that the right to “inclusion” trumps the right to be treated decently by one’s peers?

I’m sure that there will be no shortage of people who accuse me of misrepresenting the posts, even though I’ve linked to them and would encourage everyone to read them to see if I’m being honest. I’m sure there are those who will advocate the principle of never criticising what somebody else does or writes about, for fear of being negative*, even though debate would be impossible under such a constraint. However, I did think it was important to get these posts out there. They celebrate dumbing down and lenient discipline of a sort that teachers too often claim is only an invention of the Daily Mail and Tory politicians. Most of all they show that there are fundamental differences of value within teaching, that should make us question the idea that any institution, or any oath, or any curriculum, could ever represent the views of all teachers.

 

*Whenever I disagree with her, Sue Cowley usually claims not to be saying what she appeared to be saying no matter how unlikely this actually is. If she claims that in this case, then please just take this as a general point, rather than one specific to her.

Avoiding the Difficult Choices in Education

I wrote this post about a week ago, and it largely follows on from my attempt to attend a large number of education events in a short period of time, described here.  A number of comments I heard about education over that time gave me pause for thought and for similar reasons.

The first was during the Battle of Ideas panel discussion that I was involved in. Emma Knights claimed that there wasn’t a debate over the role of knowledge in education, at least not in schools. (With hindsight, the two of us on the panel who did object were also the only two who are currently employed as teachers).

The second was in reading this article from Academies Week about Nicky Morgan, in which she adds “the fifth priority” of creating well-rounded youngsters “emphasising character, resilience, grit” to the other priorities of her department.

The third was during a “Policymeet” on the fringes of Conservative Party Conference, when Ty Goddard from The Education Foundation, claimed that some of the debates in education should be re-evaluated as “false dichotomies”, and seemed to give many examples, such as knowledge versus skills, academic education versus vocational education. I was not the only person present who was sceptical about this:

Can I make a plea for some 'false dichotomies' re-evaluating to actually be re-re-evaluated as actual dichotomies? #policymeet

— Jonathan Simons (@PXEducation) September 29, 2014

I’m not claiming any of this is exceptional. With regard to the “fifth priority”, in education you can set lists of priorities so long that it would be easier to say what isn’t a priority. You can design a curriculum with dozens of aims.  You can give out so many prizes that nobody actually feels rewarded. You can promote almost every teacher in a school without giving them any actual power. When people don’t want to make difficult choices they often find that choosing everything is almost the same as choosing nothing. Like giving a child a 17th final warning, you can create the illusion of making a decision without actually committing yourself to anything.

Similarly, when there are apparently stark choices, (including those relating to knowledge) it is easy to claim that they are “false dichotomies”. Don’t know whether small children are in school to play or to learn? Just claim that they learn best through play. Don’t know whether schools are for education or for socialisation? Just claim children are educated best through socialising. Don’t know whether children should be learning academic subjects or concentrating on hobbies? Just claim that everything is academic. Or nothing. It amounts to the same thing.

There are some genuine false dichotomies in education. There are options that are too vague to be meaningful (like educating the whole child, or encouraging creativity in maths). There are times when certain choices are hidden in order to make an unpalatable position seem the best option. For instance, anyone who wants to let kids get away with bad behaviour is likely to claim the only alternative is a philosophy of “behaviourism”. Or those who want it to be okay for kids to learn nothing, will claim that the alternative is a system driven only by exams. But in cases where we have a choice of what to teach, or what to spend resources on, the choices are unlikely to be false dichotomies. People will have to choose what money is spent on and what is taught in lessons.

All of the examples that I started with, seem to come down to an evasion of difficult choices. And perhaps this is why bureaucracy thrives in English education. For a system to function effectively people do have to decide what they are aiming for. They have to decide what gets priority. They have to commit themselves to their decisions. I am always been sceptical when people claim the NHS faces infinite demand that means resources have to be rationed. But in education, there is always more we can do. We cannot do everything. We cannot prioritise every child and teach every desirable personal quality. Sugar paper, post-it notes and brain-storming might generate lists but they don’t generate decisions. In the system we have, people become unpopular not by making the wrong choices, but by making any choices at all. In systems where nobody chooses what it is that must be done first, nothing gets done, and afterwards people try to find somebody to blame for not doing it.

It is important not to pretend there is no debate to be had. There is debate over everything and there needs to be. There are people we should argue with.

• There are writers on education who would bring back the culture of endless resits;
• There are senior leaders in schools who are against the teaching of knowledge;
• There are teacher training companies who think the internet has replaced teachers as the source of students’ knowledge;
• There are teacher trainers whose advice about managing behaviour includes sharing learning objectives and catering to learning styles;
• There are educational consultancies where scepticism about educational ideas gets you fired.

These are real debates, and while I don’t doubt there are those will try to dodge them, telling me that nobody meant what they appeared to be arguing, or that none of the apparent conflicts are actually real. But I cannot accept this. The differences in opinion are real and important. So please: make a decision; choose a side; express an opinion. It’s the only way anything gets done.

A Teacher’s Oath

A couple of years ago I wrote an oath. It was a declaration of my own values as a teacher. Some agreed with it, some hated it. Nobody would ever suggest that others should be made to swear it. We are a divided profession. For some of us, education is an academic pursuit. Our job is to make children smarter, and in order to do this we must have authority to tell children what to do in order to become smarter. For others, schools are (in R.S.Peters’s words) “an orphanage for children with parents”. They are social institutions designed to develop in children particular values that their parents cannot be trusted to impart, and to provide the companionship and affection their families and communities cannot be trusted to provide. From this point of view, academic learning cannot be a high priority, and expecting children to be compliant is simply ensuring that the society the schools are trying to engineer is authoritarian.

For this reason, the teaching profession does not have a shared set of values. Just a series of disputes. This is why some of the arguments have been so intense, and why the attempts to enforce the latter position, about ten years ago, created a culture of fear for those of us holding the former position. Tristram Hunt’s latest failure to understand how education works (it can be found here) is to suggest that an oath can be written to commit teachers to “the values of their profession”. To pick one set of values and make teachers swear loyalty to them, is not to improve teacher professionalism, but to brainwash the profession into thinking that we must be on one side of the debate. What he hasn’t asked is “whose values?” But then we know, ever since he made it to the front bench, he has gradually adopted the values of the progressive camp. He has moved to opposing attempts to increase rigour, and, instead, has been proposing to replace academic learning with the teaching of “character”. The last thing we want is an attempt to force us all to commit to those values. If progressive types wouldn’t commit to my oath below, why should I have to commit to their values?

The one argument that I’ve seen used to defend the idea is that it would be a step towards reversing the undermining of the profession. This is to confuse political rhetoric with reality. People who hated Gove, used to selectively quote things he said (not what he did) and declare “that’s attacking the profession”. But it was always just hot air. It is such an easy attack that Nicky Morgan said pretty much the same thing about Tristram Hunt in her Tory party conference speech. It doesn’t mean anything other than “I don’t want anything to change in teaching, if you do then I am offended”.

If we want to raise the status of teaching, it doesn’t take gestures; it takes tough choices. It takes more cash. It takes better training. It takes making it tougher to become a teacher. It takes reforming management. It takes making the job less unpleasant to do.

Scenes From The Battleground

This is my contribution to the second Purpos/ed 500 words campaign.

I swear to teach to the best of my ability. I swear to do everything I can to develop my students’ intellects;  to teach them some of the best of that which has been thought and known. I want my students to partake in the full fruits of their civilisation and will not willingly leave anybody ignorant or convinced of a falsehood.

I promise never to waste my students’ time with activities that serve no educational purpose. I promise never to seek to entertain rather than to educate. I will choose my teaching methods on the basis of how they will aid learning. I will be blind to educational fashions, uninfluenced by incoherent ideologies and sceptical of unproven theories. I will strive to improve my knowledge and my teaching. I will make decisions in the interests of my students…

View original post 356 more words

Top Blogs of the Week : Academies Week (October 2014)

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

Character, Resilience and Grit by @thegoldencalfre

An RE blogger turns his attention to the recent fashion, endorsed by Nicky Morgan and Tristram Hunt, of directly attempting to teach character in schools. He argues that: “Whilst character development within schools is unquestionably important, Morgan’s belief that the government can encourage it to happen meaningfully is not only optimistic, but also requires her to navigate dangerous obstacles.”

Continued in Top Blogs of the Week : Week commencing 6 October, 2014

Fluency in Mathematics: Part 3

I gave a talk in March at Pedagoo London (my first public appearance) and again the weekend before last at the La Salle Education maths conference on fluency in mathematics. This post is based on those talks and so, inevitably it has taken several posts and revisits some old ground. Parts 1 and 2 are here and here.

Finally we come to my advice for teaching for fluency. Firstly, something I started doing this year, is starting all learning objectives with “know” or “practise”. I find this covers everything that’s worth teaching and establishes what you are trying to achieve. But the big challenge is over resources. Here are my recommendations.

1)  math-drills.com This is an American website (note the lack of an “s” in “math”). However, it has a wide range of free worksheets that emphasise practice. It’s particularly good for number bonds and times tables.

2) Ten Ticks. Probably already known to every maths teacher reading and very common in schools. But there is often a sniffy attitude that Ten Ticks sheets have too many questions on. I beg to differ. If you are using them sensibly (don’t just read off the levels) then they provide the right amount of practice, and usually the right level of increasing difficulty.

3) Mymaths. Again I’m recommending something that is already widespread. However, what I want to point out, to those who already have access, are the many “Beat the Clock” activities. These are absolutely ideal for developing fluency.

Beat the Clock game on Mymaths

4) Make your own worksheets on Excel. If you need students to repeat very similar work then you can create worksheets in Excel which can then be significantly altered by changing only a few cells. So, for instance, by making the answers random numbers it is possible to generate similar but different equation questions repeatedly.

 

An Excel Spreadsheet. The answers are randomly generated and can be easily changed to generate different versions of the same worksheet (below).

5) Old Textbooks. The fashion for letting students look things up themselves and the hostility to practice has seen textbooks expand their explanatory material and decrease the number of questions. Most of the high achieving maths departments I’ve worked in, or visited, have had textbooks from ten or more years earlier.

A page from a textbook published in 1919

A page from a textbook published in 2008. Those 2 questions are the only ones covering those topics.

The most important principle is not having to hide that you are doing any of these things. Teachers should be allowed to get kids to practise.

If you have any other resources that are good for developing fluency, please suggest them in the comments. Two things that came up in the questions after the talks are Times Table Rock Stars and mental mathematics practice. The latter is one I use a lot, particularly where it is possible for students to hold up answers.

Okay, this isn’t me giving my talk at the maths conference, but if you look closely, it is me sat behind Johnny Ball. Really.

Fluency in Mathematics: Part 2

I gave a talk on fluency in mathematics in March at Pedagoo London (my first public appearance) and again the weekend before last at the La Salle Education maths conference. This is based on those talks and so, inevitably, it is one in a series of posts. Part one can be found here.

“And this was the greatest number of words I could fit on a single Powerpoint slide”.

At both talks I asked the audience to discuss reasons they may have been wary about giving explanations, using prolonged practice or focusing on fluency in maths. I also asked about reasons others had used to tell them not to teach that way. I then asked whether they came up with the same answers I did. Most of the following featured to some degree:

1) Understanding

The issue of whether students ability to answer questions should take second stage to understanding of some sort is not a new one in mathematics. Tom Lehrer satirised it in the 70s.

The real problem is that understanding is not well-defined. I found four definitions for it and wrote about them here, and for these talks I added another possible definition that it could mean “knowing the connections between topics”. It is only with these multiple definitions of “understanding” to confuse matters that explanation and practice can be sidelined. When “understanding” is tied down to a specific meaning we invariably find that a clear explanation and the building up of fluent knowledge, is the best way to promote understanding.

2)  Problem-Solving

While problems might well have a part to play later on in practising the application of knowledge, it is unclear why anyone would imagine problem-solving is useful for the acquisition of new knowledge. It causes a distraction from what we should be thinking about (the thing we need to know) and is likely to tax working memory unnecessary making retention more difficult. While problem-solving approaches to maths have been continually fashionable, their effectiveness is far from proven. Hattie (2009), who summarised research using effect sizes, where 0.4 showed average effectiveness, found problem-solving learning to have a very poor effect size of 0.15:

3) Discovery/Inquiry

This is a very similar point, in that in practice it also involves engaging students in activities where new knowledge is meant to result. Again it is very fashionable. And again, the same objections apply: it is likely to distract from what is to be learnt and to limit retention. Again, Hattie found an unimpressive effect size:

4) Engagement/Enjoyment

It is not always clear what “engagement” means as I discussed here. If it is used to mean enjoyment, then there are serious questions to be asked about the assumption that students learn best when enjoying themselves. There is too much research on that question to reference here, although hopefully I will get round to blogging about it soon, but while anxiety or hysteria won’t be great for learning, there’s strong evidence against the general principle that we learn more effectively the happier we are.

5) Groupwork/Discussion

If I’ve described anything else as “fashionable” then this tops that tree. There’s no clear evidence that groupwork is as ineffective as problem-solving or discovery, but Hattie’s effect size of 0.41 for cooperative learning would indicate it is unexceptional as a method. I would not seek to prevent groupwork, but find its aggressive promotion unwarranted.

There is a lot of psychology literature on how people work in groups. Different conditions make it more or less effective. Its potential negative effect on motivation, known as “the Ringelmann Effect” is long-established and there are certain types of thinking that are thought to be less effective in groups. The widespread belief that groupwork is an essential part of good teaching seems implausible, and provides little reason to crowd out other methods of teaching.

Update 7/9/2014: It was pointed out to me on Twitter that Hattie also quotes one meta-analysis that takes subject into account and found an effect size of 0.01 for cooperative learning in maths.

6) OFSTED

The first time I gave this talk I could only confirm that OFSTED did seem opposed to developing fluency and this was the one point on which I could not deny the objection. The details are described here and I showed some of this video to underline the point:

When I gave the talk last week, I could be more optimistic. Inspectors should not be requiring a particular way to teach and shouldn’t be grading you individually anyway. The old subject survey guidance that laid out a depressingly trendy vision of how to grade maths lessons is now gone. Hopefully, this demon has been slain.

7) Technology

The idea here is that technological change has changed the nature of schooling or society. I’ve used these before, but in a week where the TES published this, it is worth remember just how long the claims that traditional teaching is doomed have been going on. Here is some of the usual rhetoric:

The idea that our schools should remain content with equipping children with a body of knowledge is absurd and frightening. Tomorrow’s adults will be faced with problems about the nature of which we can today have no conception. They will have to cope with the jobs not yet invented.

 

…we find ourselves in a rapidly changing and unpredictable culture. It seems almost impossible to foresee the particular ways in which it will change in the near future or the particular problems which will be paramount in five or ten years.

 

Books will soon be obsolete in the public schools…Our school system will be completely changed inside of ten years.

 

These quotations are actually from 1966, 1956, and 1913, respectively. (Sources for the latter 2 can be found by searching my blog, and for the first from this book).

This does not disprove the argument about technology, but it does seem to shift the burden of proof. A more developed case can be found here,  here and here.

8) Independence

The philosophical arguments about independence and autonomy can be found here. And I would add to it now, that if independence from the teacher was so important, then it is hard to explain the effectiveness of Direct Instruction, a method of teaching very much focused on the role of the teacher:

9) Research and Training

Probably the biggest reason for the poor view of fluency many maths teachers have is that we’ve often been trained by those who would deny its importance. We’ve also often been told that this is justified by the research. A proper take down of the shambles that is maths education research here and in the US would take a whole blogpost, but you can get a flavour of it by looking at the work of Jo Boaler, the criticisms of it, and the methods she uses to silence critics. This does not resemble scientific research or academic debate in anyway. The field is mainly propaganda for groupwork, mixed ability teaching and the methods of “fuzzy maths”. There does now seem to be the first signs of debate, and I was able to mention a few papers that challenge improve on the research methods and challenge the orthodoxy, but it seems early days and too much of what I have found is by economists and not published in maths education journals despite seeming to be of much higher quality than the studies that do get published:

• Duflo, Dupas & Kremler (2008) – RCT on setting;
• Berlinski and Busso (2013) – Unpublished RCT on pedagogy;
• Haeck, Lefebvre and Merrigan (2014) – Analysis of Canadian maths reform;
• Schwerdt, Guido & Wuppermann, Amelie C. (2011) – Compared lecturing with problem-solving.

Continued in part 3

Teachers need the time to get out more: Academies Week

Education is enough of a national concern that there is no shortage of organisations arranging meetings and conferences about different aspects of the subject. Being addicted to Twitter has allowed me to keep up with much of this. Being a blogger has also meant I receive invitations to speak at events, or am placed on the guest list for ones not open to everybody. However, such events are not evenly distributed across the year, and the last 11 days have seen my diary overloaded.

Despite living in West Midlands, the Saturday before last I was in the centre of London attending the launch of a book,
Don’t Change the Light Bulbs (edited by Rachel Jones). The following Tuesday, I heard Teach Like a Champion author Doug Lemov in Walworth, giving a lecture on leadership…

Continued in Teachers need the time to get out more : Academies Week

Fluency in Mathematics: Part 1

I gave a talk on fluency in mathematics in March at Pedagoo London (my first public appearance) and again last weekend at the La Salle Education maths conference. This post is based on those talks and so, inevitably it is long enough to take several posts and revisits some old ground.

My talk at Pedagoo London

I started by asking the audience the following questions (yes I know, exciting start), and giving them a couple of minutes to work them out:

1. 7×8
2. Simplify 49/84
3. Find √729
4. Solve 3x+40=19
5. Write √7/√175 as a decimal

At both talks there was somebody who took not much more than a minute and others who struggled. It is possible to answer every one of those questions in a few seconds if you have memorised the correct basic facts, such as times tables, and how negative numbers and surds work, and can recall them fluently. Both times though, I appeared to be the only person in the room to have memorised the first 27 square numbers.

As well as being useful for solving problems, fluency is now one of the major aims of the new maths National Curriculum, quoted below:

Aims

The national curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
• can solve problems by applying their mathematics to a variety of routine and non routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

To have fluency as the first of three aims is a big change compared with the old national curriculum, the aims of which seemed to include everything else but fluency:

Curriculum aims

Learning and undertaking activities in mathematics contribute to achievement of the curriculum aims for all young people to become:

• successful learners who enjoy learning, make progress and achieve
• confident individuals who are able to live safe, healthy and fulfilling lives
• responsible citizens who make a positive contribution to society.

The importance of mathematics

Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy. Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of pleasure and wonder for all pupils when they solve a problem for the first time, discover a more elegant solution, or notice hidden connections. Pupils who are functional in mathematics and financially capable are able to think independently in applied and abstract ways, and can reason, solve problems and assess risk. Mathematics is a creative discipline. The language of mathematics is international. The subject transcends cultural boundaries and its importance is universally recognised. Mathematics has developed over time as a means of solving problems and also for its own sake.

Which to me, now, really sums up an era where you could have every variation of progressive education together in one document, while missing any mention of what is worthwhile knowledge.

One of the main reasons I think this has now changed, is a change in the understanding of how we think. One of the more popular diagrams in education today is this one from Dan Willingham’s book:

It’s a very simplified, but uncontroversial, model of how we think. We have a limited working memory, where conscious thought takes place, and a potentially unlimited long-term memory.  To use working memory effectively, we draw on information that is already in long-term memory. To get things into long term memory we have to overcome the limitations of working memory. Having useful information in long-term memory, and being able to recall it without difficulty, makes thinking easier. In maths it is useful to be able to fluently recall a lot of knowledge, particularly basic number facts, rather than work everything out from first principles. The question at the start about simplifying 49/84 was an example of this, as fluency with the 7 times table makes the question trivial.

In order to build fluency we need to acquire knowledge and to learn to remember it without effort (automaticity).

See? I did say this

And if that is our aim then, in maths, the best method is to tell kids what they need to know and set them lots of questions where they practise recalling it.

Continued in Part 2