A short conversation

I found this conversation thought-provoking.

1. Alison Kiddle ‏@ajk_44  Nov 30

   Random thought: how does the stuff done in maths lessons relate to what a professional mathematician thinks of as mathematics?
2. Sue de Pomerai ‏@suedepom  Nov 30

   @ajk_44 @ColinTheMathmo not very much!
3. Colin Wright ‏@ColinTheMathmo  Nov 30

   .@suedepom @ajk_44 Indeed. Does it matter? Should we change that?
4. Alison Kiddle ‏@ajk_44  Nov 30

   @ColinTheMathmo @suedepom I do think it's confusing that we use the word "maths" for Early Years number as well as calculus and beyond.
5. Mary Pardoe ‏@PardoeMary  Nov 30

   @ajk_44 @ColinTheMathmo @suedepom what's wrong with 'elementary', 'higher' and 'advanced'?
6. Colin Wright ‏@ColinTheMathmo  Nov 30

   .@PardoeMary What is done in university and beyond is not simply a more advanced version of what happens in school. CC: @ajk_44 @suedepom
7. Alison Kiddle ‏@ajk_44  Nov 30

   @ColinTheMathmo @PardoeMary yes, see the popular misconception that university maths is "doing big sums"
8. Mary Pardoe ‏@PardoeMary  Nov 30

   @ajk_44 @ColinTheMathmo where is the evidence for that misconception?
9. Colin Wright ‏@ColinTheMathmo  Nov 30

   .@PardoeMary My experience is that generally people think "advanced maths" means more complicated sums. CC: @ajk_44
10. Simon Gregg ‏@Simon_Gregg  Nov 30

    @ColinTheMathmo @PardoeMary @ajk_44 But generalise: do young children not write, read, produce art, because there is an adult version? 1/2
11. Simon Gregg ‏@Simon_Gregg  Nov 30

    @ColinTheMathmo @PardoeMary @ajk_44 2/2 and they are doing more than sums - reasoning, making connections, exploring, making generalisatins

Colin Wright‏@ColinTheMathmo

.@Simon_Gregg If what you say is true, why do all the adults I talk to think that maths is just about sums? CC: @PardoeMary @ajk_44

I'm not experienced in university maths (I did science), but from what I do know I want to say that there is a continuity, and not just out of respect for the efforts of young children.

Of course, Colin is correct: there are an awful lot of sums in schools, hopefully less than there were when we were at school, but still, many people do think that sums are the thing. And it must get boring getting thought of as a difficult sum doer!

But, but... there is another side to school maths, and one that I would like to see take over as people's picture of school maths.

Take this Kindergarten Interlude that Joe Schwartz posted on the other day.

Here are children in a comfortable situation, getting to know number, its constancy, its patternability, its many possibilities. I like how Joe says, he is there to "poke, push and experiment".

Now this is well-trodden ground, but children are building up their knowledge here, step by step, tentatively at times, in leaps at other times. Sometimes the knowledge will be certain: however you arrange three bears, they will always be three. Other times it will be a hunch: you need four bears before you can have a pattern.

Or take Kristin's post on Articulating Claims in Math, The elementary kids are doing "sums" here, but they're doing a lot more, they're making generalisations about the way sums work:

Now you might argue that proof involves more than this. That it involves formal generalised description. Or that it must be a shared and socially verified knowledge.

But I would say the exploration comes first, then the hunches, then more exploration, then the knowledge, then the sharing.

Consider Polya's treatment of Nicomachus's theorem. How would you first discover this? Polya writes:

Mathematics presented with rigor is a systematic deductive science, but mathematics in the making is an experimental inductive science.

And that is what is happening in many excellent maths classrooms, and could be happening in even more. I like Polya's example, not least because the nine year olds in my class had a go at exploring this last year.

A different kind of activity comes before proof. You get a sense of it in this video:

And proof is not about formal language either. There's the famous Bhaskara proof:

Bhaskara's only word: "See!"

As Keith Devlin says about symbols, "They no more are algebra than a page of musical notation is music."

So, I want to make the case, here as I do in my teaching, that there is a continuity, there is in the best classrooms a relationship with what kids are doing and what mathematicians do.

What do you think?

The list goes on

Another item for the list:

XI. Computing

When I was a kid at school I got into programming in Basic. It was mathematical in ways that maths lessons weren't. For instance, the only time I ever asked a teacher how to do something that hadn't been taught was when I needed a bit of maths for a program I was writing.

"How do I stop this weather data looking so spiky?"
"You need a moving average."

When I did my teacher training at the Roehampton Institute back in the early 80s, computing was as you know in its early days, not quite as early as when I was at school (there was a screen for instance!) but early days:

But there was a book I really enjoyed, and found captivating, Seymour Papert's Mindstorms. The idea of using Logo in the classroom to program a turtle was a really inspiring one, where you really needed to get to get to grips with maths to get a lot of things done. This short video from the time gives you some idea of what was starting:

Over the years, I've used Logo a lot. You know the kind of thing: forward 10 right 90...
I used the Microworlds  environment quite a bit. Now I use Scratch. It can have too many knobs on, too many attractive features, and I think the simple maths of Logo is the best; it continues to be a great way of really needing a lot of maths to achieve an end. I never seem to get quite far enough with it to get on to the wealth of exciting possibilities, but I think this might be changing with the new emphasis on coding in the computing curriculum. I'm using code.org's great resources and courses with my kids, and encouraging the whole school to develop this kind of coding, and although the finely-grained steps of the courses are mainly convergent, I think they provide a great preparation for wonderful divergent work.

It's this sort of blank slate tool that I like best of all. I use other packages that aren't blank slate (Education City, mymaths.co.uk) and there are lots of brilliant websites for developing skills, but the tools I like best are the powerful ones where it's down to the students to make something of them. (Geogebra is another brilliant example, one I used today for instance to get the students to generate lots of different kinds of hexagons.)

Here's a great tribute to Papert:

Even more...

As I said, the UK government wants "harder sums". It wants rigour. Picture phalanxes of Roman centurions - very comfortable with their Roman numbers - marching rigorously up very straight roads, their shields held close together. Nothing gets past them.

My strategy for conquest is different. I've made a list of some of its components. Like Caesar's Gaul, so far it's got three parts:

First part:

I. Pick subjects that give power.

II. Find the subjects where kids can be creative,

III. Go into history and biography

Second part:

IV. Enthusiasm

V. Discussion

VI. Presentation

Third part:

VII. Climb up and down the ladder of abstraction 

- § - § - § - § - § - § - § - § - 

But now I'm going to add another part:

VIII. Estimation

I asked my friend Charlie who works as an engineer what maths he thought really needed to be taught at school. Estimation, he said, you need that all the time. And luckily it's become more accessible and more engaging than ever with Andrew Stadel's estimation180.com . I've used this with my Y4 class last year, and we're going to start again next week. What's so great about it, is that the kids are interested in the estimation and they like the challenge. They especially like it when there's a video "reveal" at the end.

I have this idea that if we like it, we'll start creating estimation challenges in the Year 4 classrooms, maybe begin an estimation blog, perhaps begin to find estimations to do at home too, photo or video.After that we get other classes to have a go.  Nothing too ambitious. First we take Manhattan, then we take Berlin.

My trial challenge was not a complete success, but it's helped me to get the measure of what's involved:



Anyway, here's Mr Stadel talking about what he does:



IX. The real world

To be honest, this is something I know I don't do enough of. Using real things, real places, things you might find at home. We've just been looking at reading scales, and for the first time we've got the classes to look for dials and scales at home this week. The range is amazing: weighing scales, a barometer, pressure gauges on pumps, a metronome, the rpm and the speedometer in car, a clock... and some things from an aeroplane: how level you are and speed. There is just so much to talk about.

In fact I can't stick to the real world. We did a bit of not-so-real world with our creation of meters to measure things not normally measured. The idea was to create a bit more attachment to our dial by investing more in it than usual.

It gave us a good chance to talk about what kind of units you might invent, as well as looking what the un-numbered marks represented. It also meant we could spend a bit more time on dials and still be doing fresh things.

X. Modelling!

This as Turtle Gunn Toms says in a comment on Graham Fletcher's excellent post on modelling, means taking a situation and mathematising it.

It's another thing I really don't do enough of. Probably none of us do enough of it! The ideal is a situation where you have a question, you put numbers to it, out comes some kind of answer.

It's a lot harder to find good examples for the primary / elementary classroom. I'd like to have a collection of this kind of mathematical modelling question.

Here's one I'm thinking of trying soon: I was talking to the kids: "Here I am, standing in the middle of the room..." and it occurred to me, "Where  exactly is the centre of the room? How would you work that out?" I said my thoughts out loud of course.

Not a very natural question perhaps, but I'd be interested to see how the class go about answering that. Some estimation first of all of course...

The ladder of abstraction

I'm interrupting my list to write about this. It's sort of in reply to a tweet from Tracy Johnston Zager, though I suspect I haven't answered the question in exactly the way she intended:

@mpershan @MathMinds @Zakchamp Maybe @Simon_Gregg could chime in about how he handles/introduces manipulatives?
— Tracy Johnston Zager (@TracyZager) September 12, 2014

No, actually this chime can be part of the list.

7. Climb up and down the ladder of abstraction

I've been reading Roy Peter Clark's entertaining and instructive book Writing Tools: 50 Essential Strategies for Every Writer over the summer (link to free podcasts of this on iTunes). One of the 50 strategies is "climb up and down the ladder of abstraction". Here's a snippet:

The ladder of abstraction remains one of the most useful models of thinking and writing ever invented. Popularized by S. I. Hayakawa in his 1939 book Language in Action, the ladder has been adopted and adapted in hundreds of ways to help people ponder language and express meaning.
The easiest way to make sense of this tool is to begin with its name: the ladder of abstraction. That name contains two nouns. The first is ladder, a specific tool you can see, hold with your hands, and climb. It involves the senses. You can do things with it. Put it against a tree to rescue your cat Voodoo.
The bottom of the ladder rests on concrete language. Concrete is hard, which is why when you fall off the ladder from a high place, you might break your foot. Your right foot. The one with the spider tattoo.
The second noun is abstraction. You can’t eat it or smell it or measure it. It is not easy to use as a case study. It appeals not to the senses, but to the intellect. It is an idea that cries out for exemplification.

Here's Hayakawa's illustration of his ladder:

This fits very well with the way I like to teach. Say in maths, I want the kids to use stuff they can touch or be physically part of. To take an example that I think works really well, I'll get them using the Cuisenaire rods to make their own patterns, and then I want them to take the numbers inherent in those patterns, then beyond that, the relationship between the numbers, and if possible to abstract that relationship into algebraic form. I'm quite prescriptive about what I want them to do, but hopefully the limitations are creative, because I want them to be creative.

If you haven't read Richard Feynman on why there is no science education in Brazil, do. He was astonished at how little teachers went down the ladder again from abstract to concrete.

"I didn't see how they were going to learn anything from that. Here he was talking about moments of inertia, but there was no discussion about how hard it is to push a door open when you put heavy weights on the outside, compared to when you put them near the hinge – nothing!"

bench by Zaha Zahid

The architect Zaha Hadid is designing the new maths gallery for the London Science Museum, a building I spent a lot of time in as a kid. She has a maths degree, and she uses maths as a place to find new abstract forms for her buildings. She was also inspired by the abstract mathematical paintings of Kazimir Malevich.

Black square by Kazimir Malevich

So, she's using abstract mathematical forms and ideas, and, quite literally, making them concrete:

"When I came to do architecture people said you must know how to add. There is that aspect to maths, of course. But there is another that was of interest to me and that was abstract thinking, and that was when I realised how important that degree was."

Zaha Hadid's design for the Mathematics Gallery

To me, that's thought-provoking.

Even harder sums...

La Rentrée, as the French call it, is fast approaching. I'd better get on with my list of good ways to get to the challenging stuff. These are of course obvious to many of us teachers, but then again, they are not at all as universal as they could and should be, so they're worth reiterating.

Last time I gave my three ways of making maths harder - without the useless drudgery:

1. Pick subjects that give power. 
2. Find the subjects where kids can be creative
3. Go into history and biography.

So, three more:

4.  Enthusiasm

5.  Discussion 

6.  Presentation

alder trees in the New Forest

4. Enthusiasm - the teacher's, that is. This can be squeezed out by an over-structured curriculum, and pressure to get numerical results. But when it's there it can make school something more than just school. Take this case: Roger Deakin in his brilliant book Wildwood describing what his biology teacher set up:

…Barry infected us all with his wild enthusiasm. 

Although he would modestly deny it, Barry Goater was the instigator of an extraordinary educational experiment. In a quiet corner of the New Forest he established a camp for the detailed study and mapping of the natural history of a stretch of the wild forest woodland, bog and heath surrounding Beaulieu Road by his Biology sixth form. The camp became something of an institution at our school in the relatively treeless Cricklewood. It was traditional for each generation of us sixth form naturalists to return there again and again and taste the intoxicating pleasure of exploration and discovery in the wild for ourselves. Each of us had a particular project, literally a field of inquiry, and the work we were doing was genuinely original. We learnt the scientific disciplines of botany, zoology and ecology, and we kept our eyes open as all-round naturalists. What we discovered was particular to the place, and, best of all, it belonged to us. 

Beaulieu Road was our America, we were pioneers, and the map we jointly drew and refined through gradual accretions of personal observation represented not only the complex natural ecology of the place, but also an ambitious and entirely novel cooperation between several generations of the sixth form botanists and zoologists of our school. Through our cumulative endeavours we were charting the relationships between the plants and animals of the place. But the records we kept were also a testament to our own human relationships as naturalists, biologists and zoologists. We were learning at first hand how exploration and scholarship can evolve and progress in time through cooperation and the free exchange of ideas. Small wonder that the experience influenced so many of our lives so profoundly.

There's so much in this description. But isn't it interesting how a teacher's enthusiasm can lead to "the intoxicating pleasure of exploration and discovery in the wild"for themselves, to  a world that the students discover that belongs to them?!

4. Discussion: Roger Deakin talks about cooperation and the free exchange of ideas. Ideally, it comes naturally when there's some big project that the class or group is working on. Sometimes it needs to be structured. Lots of teachers naturally use a variant of the think-pair-share strategy: students think about a question on their own a little, then they talk about their ideas with someone else, then they might share what they've arrived at with the bigger group. It gets away from the teacher questions-pupil answers routine (which is useful some of the time) where only at most one student is getting to put their ideas into words at any one time. This is important, because to know something really well, it's best if you can explain it too, and hear other people's explanations of it. And even better if you can modify your understanding as you discuss, refining what you first thought.

5. Presentation - the students that is. As I say, it's important to be able to explain something, and you get to know it more deeply in doing so. When we made factor trees last year we explained our factor forest display to the other classes who would see it.  When four girls created a beautiful mathematical square, they explained it the other classes. 

To be continued.

Harder sums...

So the UK government wants "harder sums". (Part of a drive to raise standards - see Michael Tidd on The Level 4b myth for thoughts on this.) And they want to have kids learning their eleven and twelve times tables, instead of the tables from one to ten.

To me, this is not the way to go. Not because I don't want a challenge. I do.

Steep paths - even rocky cliffs - are fine, if they lead somewhere. If they are just a demanding rock face that leads to... more demanding rock face, without opening up onto a fertile and beautiful landscape, then maybe children develop grit or obedience or something, but they're not making the most of their maths learning.

Take the twelve times table. Not a big thing. But really, is that taking us somewhere?? Read Jon McLoone on Is There Any Point to the 12 Times Table? for his interesting thoughts on this.

Creating their own pattern

So how would I like there to be more challenge? I really want kids to go further, rather than that their work is harder. I'm trying to make it as easy as possible to learn as much as possible. Anyway I'm trying to get my ideas on this spelled out, so here's a beginning of a list:

1. Pick subjects that give power. The same sums with more digits, rarely-used algorithms like long division (on this, see Owen Elton's Why Gove is Wrong about Long Division) or dividing fractions don't seem to me to lead anywhere much. Beginning algebra (in a fun and appropriate way - see my Year 4 lessons this year for example) on the other hand gives a really powerful tool for making generalisations.
2. Find the subjects where kids can be creative, make something of their own. Get them up on the top of Bloom's taxonomy. An example is getting kids to generate their own patterns with manipulatives, and then describe and explain the pattern with numbers (example). As Keith Devlin said in his recent blog post, Most Math Problems Do Not Have a Unique Right Answer.  In the real world, creativity is going to be very useful.



Rolling like Galileo

3. Go into history and biography.The new maths curriculum for England has added Roman numbers . This could be just a dull dead-end, or it could be part of a sequence of lessons looking at how number systems developed that could really grab some children. Telling the story of a maths idea by talking about its discoverer will help the kids to go further with it. Take our work where we talked about Euler. The kids are prepared to go further because there's a narrative to engage them. (I'll probably do the Euler work again next year, but add something on graphing,  maybe using Joel David Hamkins' great booklet on graph coloring, chromatic numbers, and Eulerian paths and circuits) In Primary we have a bit more freedom - we teach the whole curriculum, so it's easier to make links - between maths and history, or,as in the case of our work on Galileo with science and English too.

That's a start. I'll  post more of my personal list later.

I'd really love to hear other people's ideas on all this, whether it be connected with the first three items in my list, or about any successful ways to extend children's learning.

What the Hare Heard

My friend Matthew gave me Oliver Byrne's Euclid for my birthday - a beautiful book!

(The bottom two are interesting. Notice how Euclid's definition of a rhombus, unlike ours, excludes squares.)

What struck me on this page is just how persistent these definitions have been (with just a little modification). They still look very like what is taught in primary school now. 

Why is that? 

Well, I can see that a lot of it is very basic and quite useful, and so it would persist on the basis of utility.

But I think there's more going on. It can't just be utility.

For one, there seems to be a persistence of things that are not really that useful. What adult - apart from a maths teacher - talks about a scalene triangle? A rhombus? {Note: re-reading this a few years later - 2017 - I now feel much more positively disposed to rhombus.}

And secondly there are lots of other things not mentioned by Euclid of equal importance that are not now taught.

Which makes me think that that this is a kind of meme (in the old sense). We're teaching it because we taught it. At one time Euclid was the backbone of maths teaching, possibly even the entirety of it. Parts of it linger on, like the redundant pelvis of a whale.

It's interesting to me to see a teaching meme persist so long.

Another meme that has lasted as long or longer than Euclid is the story of Henny Penny, which in fact is all about memes. Best to go back to the Buddha's version of the tale, The Sound the Hare Heard, which I recommend you read, not least as a landmark in our understanding of memes and what to do about them. As the Buddha says, "Those animals had placed themselves in great danger because they listened to rumours and unfounded fears rather than trying to find out the truth themselves." This I see as, ideally, part of the job of a teacher, not just to implement a curriculum, but to find out what should be taught for themselves.

What would I teach instead? Well, something which allows students to explore this kind of territory themselves rather than catching up with names and terms.

After all, Euclid relied on those who went before him, people who explored the whole territory themselves rather than learnt definitions. There may be a tight logic in The Elements, but the heuristic for arriving at it is not itself through logic, it's through play and exploration. The Greek mathematicians were people who, like my cat Tisha, wandered all over the territory, sat in every box that was going.

At this point you could watch Max Ray's "Why 2 is greater than 4: A proof by induction":

If we want to build up children's confidence and enthusiasm for maths, rather than simply tick off that they know something that the curriculum says they should know, then we should allow them to explore and to play, and hear what they have found, not just listen for what we want them to find.

We stayed clear of triangles and rhombuses this year, and inspired by Christopher Danielson's How I teach proof, focused on hexagons instead.



Our work on hexagons didn't follow Christopher Danielson's exactly, but we were able to explore shape without the long shadow of Euclid over us.

Equality for all

Twitter is great for getting thought-provoking discussions now and again. For instance Tracy Zager retweeted about work in Year 4 at my school using the number balances:

This is what I'm talking about! http://t.co/mcN4jh46gv h/t @TracyZager @Simon_Gregg @helenjwc
— Christopher (@Trianglemancsd) May 21, 2014

Actually, there was an entertaining conversation that followed (with more branches besides).

When Christopher says, "This is what I'm talking about", he's referring to this post on the equals sign.

He discusses the problem Tabitha has with this sum:

As she says:

8 plus 4 is something, then plus 5?

As he says:

We train children to think that the equal sign means and now write the answer. Arithmetic worksheets reinforce this idea. Calculators do too. (What button do you press to perform a computation on a typical calculator? The equal sign!)

But doing algebra requires that we understand the equal sign to mean is the same as or has the same value as.

So, teachers, get out your balances! As Tracy says:

@Trianglemancsd @helenjwc Just read #tmwyk. Made to order! Have this balance for my kids. @Simon_Gregg inspiring me to pull it out again!
— Tracy Johnston Zager (@TracyZager) May 21, 2014

(There's a lot more to this task than just seeing the equals sign in a different light. For me, it also involves getting used to a model of equality, which gives sense to calculating with unknowns or makes them concrete in a particular way. A lot of calculation is involved, but the route is not specified. I'm wanting the children to have a "feel for" this kind of equation, which might be reduced by having an algorithm for finding an answer. Not that one algorithm would really do the trick here. I'm also edging towards algebra with those unknowns...)

Stealing ideas

This week, in maths lessons with my Year 4 class I've been using "stolen" ideas. At least three things that I got from somewhere else.

This kind of theft has a lot going for it, not least:

• The stolen things doesn't get taken away; in fact they get multiplied;
• It is so very easy to do now - no need to attend training, or snoop round classrooms - we have the Internet;
• It means that ideas keep flowing, lessons stay fresh.

1.

The first of my thefts was Five Rectangles. This came from Gary Antonick's great Numberplay column in the New York Times. (A while back I got another great lesson from Gary's column, one that originally came from Steve Humble, Triangle Mysteries.)

Five Rectangles (aka "Sol Golomb’s Rectangle Puzzle") is basically very simple: create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units. I added Cuisenaire rods, which seemed the perfect vehicle for this - they mean you can handle this question, literally; they save time in trying out options; and they make the length x width = area nature of rectangles very obvious.

The arithmetic is just right - times tables up to 9 x 10. And the addition - five numbers adding up to a number between 100 and 200 is right too. And best of all, there are more intriguing questions - what are the maximum and minimum areas? - that take the children into unfamiliar territory, and call on their mathematical intuitions.

The original puzzle was for adults - but using a manipulative - the rods - means that it's well within the children's abilities to do some of it. It even adds new possibilities, which I hadn't foreseen, like splitting the rectangles up to make a square.

2.

The second lesson, followed on from our work on percentages perfectly.

We'd had had the computer generate a chart for us, using our data, but we needed more.

Children get to hear about a hundred percent, and know that it means "all of it". But they should experience other percentages without any confusing arithmetic coming in the way, and get to know the concept of a percentage first by examples (just as we understand "red" by examples of red things). And they should get to make pie charts without grappling with dividing by a total and multiplying by 360°. So I was really pleased when I saw this tweet:

Bar charts to pie charts #bcme8 with myself and mike Ollerton and lots of lovely peeps pic.twitter.com/aziZj7aBaf
— Helen J Williams (@helenjwc) April 16, 2014

Pie charts without the calculation! It was apparent to me that we could add a circle divided into a hundred divisions around the Smarties circle - and we would have percentages without calculation too! So that's what we did: Pie Charts and Percentages with Smarties.

pie charts made simple

Percentages made simple

Don't get me wrong: I think the calculation should come, that eventually children should learn how to do it. I just want them to get a feel for what it's all about first. And to not get bogged down or addled. A little struggling to get the Smarties into their circle is OK...

3.

Seeing that he obviously had stuff to nick, I put on my cat burglar suit and snuck into Mike Ollerton's website. There was no security at all, and there were all sorts of valuable goods that had been left there. More than I could fit into my sack in fact. The one I came away with was Being a Number.

I've printed up the exact same cards, and started using them. I know I'm going to get a lot of mileage out of them in terms of mathematical thinking.

+

So all in all, I've had a good cache this week. If you'd like to throw any of my stolen goods into your own sack, be my guest - I can recommend this life of crime!

Here is your target

The Guardian's "Secret Teacher" this week talks about "How I became trapped in the cheating game."

Some years ago I was called by my head of department to discuss the grades I'd predicted for a year 11 class. They were aspirational and realistic. I was told to change them. My forecast was not in line with school targets for A*-C so if I didn't change them I would be "targeting failure". I changed them.

I've got young kids, a mortgage and could do without the stress of a capability procedure. Morals don't pay the bills. The class achieved close to my original prediction. I was admonished over my underperformance and the inaccuracy of my predictions – the predictions which weren't actually mine at all. Following so far? Good. Because that's target-driven education; a farce.

Sounds familiar?

Who does the Secret Teacher say is to blame?

The fault for accepting the current system of smoke and mirrors lies not at school level but at societal level and speaks to bigger issues regarding our obsession with objectifying and quantifying every aspect of human endeavour.. I understood that corruption happens when an institution becomes solely target-driven.

Recently Finish educationalist Pasi Sahlberg commented on the implications of the PISA study. These are of course hotly debated. Sahlberg's writes:

"PISA shows how success is often associated with balanced professional autonomy with a collaborative culture in schools."

Top-down targets and testing and professional autonomy are opposed in the politics of education; and at the moment the targets are winning. 

Have a listen to John Seddon on the perils of the target-driven approach, "deliverology", "Why deliverology makes things worse in the UK":



Seddon refers in his talk to Deming. I've always liked Deming's approach. Deming's key principles are written for a business context, but they apply well to education.

Here's an excerpt:

1. Create constancy of purpose toward improvement of product and service.
2. 
   
3. Cease dependence on inspection to achieve quality. Eliminate the need for massive inspection by building quality into the product in the first place.
4. 
   
5. 
   
6. 
   
7. Institute leadership.
8. Drive out fear, so that everyone may work effectively...
9. 
   
10. Eliminate slogans, exhortations, and targets for the work force asking for zero defects and new levels of productivity. 
    1. 
       
    2. Eliminate management by objective. Eliminate management by numbers and numerical goals. Instead substitute with leadership.
11. Remove barriers that rob the hourly worker of his right to pride of workmanship. The responsibility of supervisors must be changed from sheer numbers to quality.
12. 
    
13. Institute a vigorous program of education and self-improvement.

Deming's red bead experiment is basic, instructive and funny. You can find Deming himself conducting it on YouTube. Here's a shorter version, with animals:




It all reminds me of the Nasrudin story where Nasrudin takes a leaking pot to the well and fills it up. All the water is pouring out of a gaping hole at the bottom, but he watches carefully and constantly at the top of the pot. "Look at the bottom," they say, but he ignores them: "I'm trying to fill the pot. When it's full the water will be at the top. I've got my eyes fixed at the top, that's how I'll know when it's full. What's the bottom got to do with it?"

I wouldn't remove targets and testing altogether. But, to me, there's a need to put the quality, even the nature, of teaching back into teachers' hands. Teachers are professionals, and should be treated as such. Professional development should include encouraging schools and teachers to participate in discussing what needs to be taught and how, rather than the drive to turn them into mindless operatives who follow some kind of foolproof operation which gets inspected and graded to oblivion. At the very least government should hand over the reins of curriculum to a professional body and stop meddling directly. If it was at all enlightened it would stop the political career-driven reform craze and allow those who know something about the job to have their say.