Achieving outstanding numeracy outcomes

Searching for effective teaching practices to improve numeracy outcomes is a key factor in our current work in Victoria as Teaching and Learning Coaches. The report What’s ‘making the difference’?: achieving outstanding numeracy outcomes in NSW primary schools aimed to establish what educational practices make the difference in enabling primary school students to achieve outstanding numeracy learning outcomes and to explore to what extent and how such educational practices could be successfully transferred to other schools.

Abstract
This project, undertaken between January 2001 and February 2004, set out to investigate which numeracy practices in NSW schools were achieving outstanding numeracy results. Effective numeracy practices were identified at 45 case study schools. Those practices were then trialled in other schools that wished to improve their numeracy outcomes. The trialling was supported by extensive professional development for teachers. Successful numeracy practices included:

The use of hand-on materials to support the understanding and development of numeracy concepts

Small group work to encourage discussion and exploration of ideas

Use of open-ended questions by both teachers and learners to establish, consolidate, extend, reinforce and reflect on concepts, skills and applications

Discussion during lessons to enable students to engage with and understand new and established mathematical concepts

Catering for individual needs of students through consistent and varied assessment, differentiated teaching and learning, and opportunities for interaction with the teacher or peers

Collaboration in planning between teachers which provided opportunities for innovative teaching and

Whole-school commitment to numeracy with all teachers implementing policies and programs consistently in all classrooms.

Schools trialling the successful numeracy practices found that a Key Group, usually supported by the school principal, was crucial in driving the project and in supporting continuing change at the school level. Continuity of teaching styles appeared to sustain and improve numeracy achievement. Schools which demonstrated greater than expected growth in numeracy achievement over the life of the project focused on either the language of mathematics or the use of practical resources to support concept development in numeracy. An important outcome of the project was the finding that quality professional development of teachers that improves their specific knowledge of numeracy teaching and their ability to direct and embrace change leads to measurable improvements in the numeracy outcomes of students.

The Best Slow Dancer

One of the great sites that you can subscribe to is Garrison Keillor's The Writer's Almanac. The title of this cought my attention as writer of Slow Learning Blog

The Best Slow Dancer
by David Wagoner

Under the sagging clotheslines of crepe paper
By the second string of teachers and wallflowers
In the school gym across the key through the glitter
Of mirrored light three-second rule forever
Suspended you danced with her the best slow dancer
Who stood on tiptoe who almost wasn't there
In your arms like music she knew just how to answer
The question mark of your spine your hand in hers
The other touching that place between her shoulders
Trembling your countless feet lightfooted sure
To move as they wished wherever you might stagger
Without her she turned in time she knew where you were
In time she turned her body into yours
As you moved from thigh to secrets to breast yet never
Where you could be for all time never closer
Than your cheek against her temple her ear just under
Your lips that tried all evening long to tell her
You weren't the worst one not the boy whose mother
Had taught him to count to murmur over and over
One slide two slide three slide now no longer
The one in the hallway after class the scuffler
The double clubfoot gawker the mouth breather
With the wrong haircut who would never kiss her
But see her dancing off with someone or other
Older more clever smoother dreamier
Not waving a sister somebody else's partner
Lover while you went floating home through the air
To lie down lighter than air in a moonlit shimmer
Alone to whisper yourself to sleep remember.

"The Best Slow Dancer" by David Wagoner from Traveling Light.© University of Illinois Press.

Is multitasking a myth?

I recently read an article in The Australian by Ruth Ostrow about the need to slow down, that we are leading busier lives and need to "flick the off button."

She quotes research by Hewlett-Packard that shows that IQ falls by 10 points when people multitask or get distracted by electronic communications, which is the "equivalent to smoking a joint or not sleeping for 35 hours."

Harvard lecturer Tal Ben-Sharar, who was in Australia for a Happiness and its Causes conference in Sydney believes most people suffer from what he calls TBD (Too Busy Disorder). Rostrow's article goes on to say that Ben-Sharar described a controlled experiment that showed the majority of participants felt "overwhelmed" by the things they needed to do, half of them to the point of feeling depressed.

"People today are chronically busy and then they front up to therapists, asking: 'why am I not happy? I have a wonderful family, great work, friends? they are suffering TBD."

In another reference Ostrow refers to Jim Loehr and Tony Schwartz's book The Power of Full Engagement, which discusses being completely present as the way towards productivity. They suggest 'working in focused spurts ... as opposed to doing marathons that exhaust us. ... we take pride in our ability to multitask and wear our ability to put in long hours as a badge of honour. As a result, we never have full attention or peak energy.'

Is multitasking is a myth

As often happens when you begin thinking about a topic such as multitasking a serendipitous connection occurs. In my case it was coming across a blog about multitasking by John Medina.

Here's what he says in his opening paragraph:

Multitasking, when it comes to paying attention, is a myth. The brain naturally focuses on concepts sequentially, one at a time. At first that might sound confusing; at one level the brain does multitask. You can walk and talk at the same time. Your brain controls your heartbeat while you read a book. Pianists can play a piece with left hand and right hand simultaneously. Surely this is multitasking. But I am talking about the brain’s ability to pay attention. It is the resource you forcibly deploy while trying to listen to a boring lecture at school. It is the activity that collapses as your brain wanders during a tedious presentation at work. This attentional ability is not capable of multitasking.

Students often claim that they can do more than one thing at a time but the evidence that the brain focuses sequentially one concept at a time should give us reason to think about the overstimulation that kids experience.

But more of this later, after I've had time to let the ideas wash around my brain and then, to paraphrase E.M Forster, write another blog post to find out what I think.

Thinking of the big idea

Photo by Millicent Bystander

There is a fascinating article in the New Yorker by Malcolm Gladwell about big ideas and the importance of someone looking at a familiar fact with a fresh perspective. It's about thinking. The following extract from the article is about Nathan Myhrvold's Intellectual Ventures, LLC--the idea that cancer can be detected long before a tumor is formed. Myhrvold, one of Microsoft's pioneers, brings intellectuals from different disciplines together to brainstorm new ideas--in this case physicist Lowell Wood meets with a group of doctors:

Last March, Myhrvold decided to do an invention session with Eric Leuthardt and several other physicians in St. Louis. Rod Hyde came, along with a scientist from M.I.T. named Ed Boyden. Wood was there as well.

“Lowell came in looking like the Cheshire Cat,” Myhrvold recalled. “He said, ‘I have a question for everyone. You have a tumor, and the tumor becomes metastatic, and it sheds metastatic cancer cells. How long do those circulate in the bloodstream before they land?’ And we all said, ‘We don’t know. Ten times?’ ‘No,’ he said. ‘As many as a million times.’ Isn’t that amazing? If you had no time, you’d be screwed. But it turns out that these cells are in your blood for as long as a year before they land somewhere. What that says is that you’ve got a chance to intercept them.”

How did Wood come to this conclusion? He had run across a stray fact in a recent issue of The New England Journal of Medicine. “It was an article that talked about, at one point, the number of cancer cells per millilitre of blood,” he said. “And I looked at that figure and said, ‘Something’s wrong here. That can’t possibly be true.’ The number was incredibly high. Too high. It has to be one cell in a hundred litres, not what they were saying—one cell in a millilitre. Yet they spoke of it so confidently. I clicked through to the references. It was a commonplace. There really were that many cancer cells.”

Wood did some arithmetic. He knew that human beings have only about five litres of blood. He knew that the heart pumps close to a hundred millilitres of blood per beat, which means that all of our blood circulates through our bloodstream in a matter of minutes. The New England Journal article was about metastatic breast cancer, and it seemed to Wood that when women die of metastatic breast cancer they don’t die with thousands of tumors. The vast majority of circulating cancer cells don’t do anything. “It turns out that some small per cent of tumor cells are actually the deadly ones,” he went on. “Tumor stem cells are what really initiate metastases. And isn’t it astonishing that they have to turn over at least ten thousand times before they can find a happy home? You naïvely think it’s once or twice or three times. Maybe five times at most. It isn’t. In other words, metastatic cancer—the brand of cancer that kills us—is an amazingly hard thing to initiate. Which strongly suggests that if you tip things just a little bit you essentially turn off the process.”

That was the idea that Wood presented to the room in St. Louis. From there, the discussion raced ahead. Myhrvold and his inventors had already done a lot of thinking about using tiny optical filters capable of identifying and zapping microscopic particles. They also knew that finding cancer cells in blood is not hard. They’re often the wrong size or the wrong shape. So what if you slid a tiny filter into a blood vessel of a cancer patient? “You don’t have to intercept very much of the blood for it to work,” Wood went on. “Maybe one ten-thousandth of it. The filter could be put in a little tiny vein in the back of the hand, because that’s all you need. Or maybe I intercept all of the blood, but then it doesn’t have to be a particularly efficient filter.”

Wood was a physicist, not a doctor, but that wasn’t necessarily a liability, at this stage. “People in biology and medicine don’t do arithmetic,” he said. He wasn’t being
critical of biologists and physicians: this was, after all, a man who read medical journals for fun. He meant that the traditions of medicine encouraged qualitative observation and interpretation. But what physicists do—out of sheer force of habit and training—is measure things and compare measurements, and do the math to put measurements in context. At that moment, while reading The New England Journal, Wood had the advantages of someone looking at a familiar fact with a fresh perspective.

And not a Thinkers Key or Green Hat in sight.


Malcolm Gladwell, "In the Air," The New Yorker, May 12, 2008, pp. 58-59.

Training in real life systems

All right, allright, I get the message, I need to write some blog entries. so here's the first one for 2008. What a slackarse I've been!

I've begun a new job called a Teaching and Learning Coach - raa, raa go get 'em. The job is to work with teachers in schools to develop their teaching skills in order to improve students learning, which is why we teach, although some of us seem to forget this. The system has at last recognised that the most effective professional learning takes place in the workplace, the classroom. Here's a couple os snippets from McKinsey research 2006/7 'How the world's best-performing school systems comeout on top':

...despite substantial increases in spending and many well-intentioned reform efforts, performance in a large number of school systems has barely improved in decades... you could define the entire task of (a school) system in this way: its role is to ensure that when a teacher enters the classroom he or she has the materials available, along with the knowledge, the capability and the ambition to take one more child up to the standard today than she did yesterday. And again tomorrow.

...despite the evidence, and the fact that almost every other profession conducts most of its training in real-life settings (doctors and nurses in , clergy in churches, lawyers in courtrooms, consultants with clients) very little teacher training takes place in the teacher's own classrooms, the place in which it would be precise and relevant enough to be the most effective.

There you go. Makes sense doesn't it.

The Importance of Learning Slowly

Earlier this year I came across a review by Gary Woodwill of a book about learning, thinking and acting. It was the title that grabbed my attention "The Importance of Learning Slowly". The book is by Manfred Spitzer, The Mind within the Net: models of learning, thinking, and acting.One of the comments Woodwill makes about the book is that:

While a single event can have an impact, it usually takes many events to have a relatively permanent change in the brain (aka “learning”) and to extract general features and generate rules from experience ... and according to Spitzer "It must learn quickly for obvious reasons, but it must learn slowly in order to generalize in a way that will produce the optimal solution without oscillating around it or forgetting it because of some other stimulus.” (p. 53)

We often find our models of understanding the world in the latest technologies available to us. Piaget developed his multi-stage theories of learning from observing his own children, and then applying the dominant mechanical metaphors of his day. In the 19th century, Adolphe Quetelet, a Belgian astronomer, coined the term “the average man” based on the pendulum (Piaget’s “equilibrium”), while Herbert Spencer wrote a psychology of adaptation using the newly created thermostat as his model (Piaget’s “adaptation and assimilation” within set limits).

As Foucault taught us in Discipline and Punish, much of the psychology of the twentieth century is based on disciplinary practices derived from factories and prisons, giving us such learning technologies as classrooms, regular rows of seats, raising of hands, incremental rewards, recess, time periods, and the power of the teacher’s gaze.

In the second half of the twentieth century, two models of computing competed for dominance. One model was artificial intelligence, based on a model of inputs, storage, processing, and outputs - in other words, a factory metaphor. The other model was that of neural networks, modeled on what was then known about the functioning of brains in humans and other animals. In the 1950s, AI became the darling of computer science, leaving neural network development far behind in terms of funding and attention.

After more than 50 years of development, the hopes of those developing traditional artificial intelligence have hit a brick wall. While powerful computers using brute force in the number of computations they can carry out have beaten grand masters at chess, the same computers cannot recognize anything for which they have not been specifically programmed. In other words, they can memorize a seemingly endless set of facts, but have no flexibility to be creative with what they “know”. On the other hand, new developments in brain research has stimulated renewed efforts in using neural networks to produce flexible learning processes in computers, and to help researchers understand learning in living organisms.

Manfred Spitzer’s The Mind within the Net is one of the best non-technical narratives on how minds work using the neural network model. Some of these explanations are startling, while others reinforce positions of strong advocates of individual freedom and the power of informal learning, such as Stephen Downes, George Siemens, and Jay Cross.

Like neural networks, the brain is based on vector algebra, rather than numerical computations. Vectors have strength and direction, and many vectors, representing multiple inputs, unite to form a result. The result in the brain is strengthening or weakening of a set of neural connections, a relatively slow process. While a single event can have an impact, it usually takes many events to have a relatively permanent change in the brain (aka “learning”) and to extract general features and generate rules from experience. Spitzer says that “… there exists a tension, a problem, for every learning organism. It must learn quickly for obvious reasons, but it must learn slowly in order to generalize in a way that will produce the optimal solution without oscillating around it or forgetting it because of some other stimulus.” (p. 53) This conclusion challenges those who advocate extreme learning and other forms of speeding up the learning process. In fact, according to Spitzer, trying to learn to quickly can actually be detrimental:

“… the interactions of an organism with its environment can be generally conceived of as a sampling of data in order to predict the true (i.e., adaptively valid) values of parameters. As stated above, this task can only be accomplished if every single experience (every single input pattern) has only a very small impact on the changes in the network. If the changes are too large, estimates may oscillate around the true values rather than approximating them. Again: the system only works with learning happens slowly.” (p. 54)

Spitzer also believes that children can and need to learn more quickly than adults. Children need a rough and ready view of the world while adults want to increase their depth of understanding. Spitzer relates this to the pace of change in today’s society. “The old master violin building makes better violins than the young student of the trade. If, however, all of a sudden the customers want music synthesizers, student will adapt to change more readily.”

The importance of feedback is apparent in both brains and neural networks. Neural networks have a technique called backpropagation of errors that simulates feedback loops in the brain that slowly change the hidden layers between input and output. This means that learning is much more to do with practice and observation than being told what to do. “Children learn from examples,” says Spitzer. The brain stores its learning in “self organizing feature maps.”

Spitzer is a psychiatrist in Germany, so it is not surprising that he has a chapter entitled “The Disordered Mind” in which he discusses autism and oppression. Most of his conclusions are on the best way to raise children, making this book less applicable to the adult learning. However, there are so many insights going through it that I highly recommend it to everyone in education and training. Spitzer’s newest book is on learning and will be translated into English by the end of the year. I’m looking forward to reading it.

Chess Tournament in Castlemaine's Old Gaol

Yesterday one hundred and sixty kids from Castlemaine area primary schools walked and travelled by bus to Castlemaine's Old Gaol for the 2nd Chess Tournament. This is the culmination of two terms of chess learning and playing in primary schools as one of the numeracy lessons.

What struck visitors was the enthusiasm of the students. We had kids from grade 2 to grade 6 competing.

Each student played 7 games beginning at 9:30am and finishing at 2:pm.

Watching the kids play a game and then run outside, jump around and talk excitedly, Randall, the manager of the gaol said, I don't know how you teachers can do it."

The enthusiasm of the kids was tiring.

The winning team was grade 4 boys from Castlemaine Primary School.

Wind Turbine at Cults Primary School

The reason I visited Cults Primary School in Aberdeen was to check out their wind turbine, which I heard about in Australia. Susan Clark who I mentined in the previous post took me on a guided tour of the school and gave me some details about the turbine.

Cults Primary School in Aberdeen is the first school in Scotland to harness the wind to generate its own power. The wind turbine at Cults school will provide energy for the school and awareness of renewable energy among pupils, other schools and the wider community.

The 5-kilowatt Iskra turbine is powerful enough to provide enough energy to run most of the school’s catering operation. The cost has been covered by the Scottish Energy Saving Trust (£13,326), Aberdeen City Council (£9,500), the school’s Parent-Teacher Association (£1,000) and Cults Community Council (£1,000).

The turbine should deliver an approximate saving of £650 per annum at current electricity prices and will contribute to reducing the school’s reliance on fossil fuels. The school expects to cut its CO2 emissions by 5,633kg per year--and by 112,660kg over the lifetime of the turbine.

A 32-inch LCD screen has been installed indoors, allowing pupils and staff to monitor wind speed and direction, power output, and the tonnage of carbon dioxide which would otherwise have been pumped into the environment if the school were using conventional power sources. The school has installed the equipment to let the pupils make a real contribution to renewable energy generation and learn about enterprise, citizenship and working with others. While I talked with Susan in the school's corridor, students stopped in front of the monitor to read the information.

The principal Ian Smithers (the one with hair), said the monitor keeps the students interested in what energy the turbine is creating and saving. It has to work at a certain speed to be generate enough energy to save electricity and money.

I wonder what schools in Mount Alexander Cluster can do? Challenge 2 Change is moving in this direction.

Cults Primary School is an Eco-School

Today I visited Cults Primary School to find out more about their wind turbine and eco-school status. TheHead of School, Ian Smithers introduced me to Susan Clark ,the key person behind the project, who is team leader for the Pupil Support Assistants and the school's Information Technology among other things. I was impressed by the involvement of students in the decision process in the designated areas a school needs to cover to be awarded a green flag.

The school has been awarded two green flags which doesn't mean much to an Australian but is very significant in Scotland.

Susan showed me the documentation that has to be kept to demonstrate the involvement of children and she added that when the committee came to evaluate the school, they spoke at length to students. Obviously if the pupils weren't really involved it would be very obvious.

We walked around the school past the sensory garden which was designed by pupils in collaboration with parents, including a garden designer. The garden is for special needs kids and involves touch, smell, visual and other senses.

You can see the raised beds for kids in wheelchairs, the water fountain is powered by solar power. It does switch off in Scotland. I said our problem in Australia is not the solar power but the water as we are experiencing drought conditions.

There were numerous other areas of great interest which I'll report in another blog.

But it's wonderful to see the results of commitment by a school in giving the kids real responsibility.

Is there a chess connection with Glenfiddich?

Well it's a shame that after the Chess Conference we had to do a bit of touring. As you can see here Steve Tobias, Steve Carroll and myself took a break from our demanding cognitive work, to relfect on our experience. The sign had nothing to do with visiting Glenfiddich and nothing to do with having a wee dram. Steve Carroll was thinking hard, as you can see by his frown, about the chess and mathematics connections with visiting a whisky distillery.

Today we dropped Chess-squared initiator Steve Carroll at the airport with his 5 suitcases of presents for his wife Megan, kids Darcy, Jack and Gracie and numerous others he felt needed something from Scotland. By the time we loaded the suitcases into the boot of the car and Steve into the back seat the front wheels were airborne. We had to move Steve to the front seat so I could get the wheels on the road to enhance our steering capabilities.

However while we sat in a lounge with a cappuccino - don't get me started on the appalling coffee here - we began working out the future directions of our chess initiative in schools. One area to follow up is more focused interviews with students about what is going on in their heads when playing chess. What makes chess interesting for them and what makes mathematics interesting and boring?

Lots of ideas to follow up.

Steve Tobias has contact with one of the professors from Turin University who is keen to cooperate with the research the team is doing and to publish a joint paper in italian and English.

This afternoon we are visiting two researchers in Education at Aberdeen University to explore possible networking with schools in Mount Alexander Cluster and Aberdeen on energy conservation.

And I'm going to write to Tourism Scotland advising they need to train barristas. Maybe Edmund from Coffee Basics in Castlemaine, could be flown over.

Susan Polgar supports Chess-Squared

Susan Polgar, the world's first woman chess grandmaster is shown here supporting our cluster schools by writing a message on an autographed photo, for all schools in our cluster. Steve Carroll organised the photos and signing. This is an entry from her blog.

These are our friends from Castlemaine program in Australia. They are here at the International Chess Conference in Aberdeen, Scotland. Talk about commitment to chess and education to fly half way around the globe to attend! A numeracy initiative of the Mt. Alexander cluster of schools funded by Innovations and Excellence. A partnership supported by Castlemaine Chess Club, Castlemaine Community House, School Focused Youth Service, and James Cook University- School of Education- Queensland

Here is their blog: http://mtalexandercluster.blogspot.com/

Mount Alexander Cluster of Schools Chess paper

Yesterday the team - Steve Carroll, Steve Tobias and myself delivered our paper to the conference and we ran out of time. But we got our message across about the good things happening in our schools with our Chess-Squared initiative.

Steve Carroll outlined the background to the project and explained how the idea hatched from his fertile brain and that the key person for us in getting the tutoring going so successfully is Harry Poulton who as I said, "Is the only one of our group who can really play chess."

I spoke about the key partnerships with principals and teachers and that their commitment is real.

Steve Tobias talked about the research background and the notion of performance versus mastery learning. Our work is based in mastery learning that intelligence is not fixed at birth.

Feedback to our presentation was really positive. People liked the team presentation which demonstrated that we worked as a team and there is interest from Aberdeen and Turin Universities in doing some follow-up work with us.