Teachers - do what you love and do it often.

Burnout is a major problem in schools.  It shouldn’t surprise anyone - teaching is a demanding occupation.  As well as being educators teachers are part social worker, part nurse, part de-facto parent, part careers advisor, policeman, counsellor and even relationship advisors. Balancing the dictates of the curriculum and  the requirements of site administrators with the capabilities of the students is in itself no easy task. Add to that the emotional impact of dealing with students who often come to school with emotional baggage and stressful domestic issues well beyond their control - and often their comprehension.  While addressing these issues teachers also have to keep in mind the special needs of individual children - some of which can be literally life threatening if things go wrong. Into this recipe for stress throw in some seasonal variations such as the lack of hours in the day at peak times like report writing or parent teacher sessions and it is easy to see why burn out is all too common.   Teachers, after all, are only human.

Teachers are people, not robots.  Through observation of effective teachers over three decades I have noticed one important characteristic that effective long-term educators have in common. They all have interests outside of school.  Their careers are important to them, very important in fact, but they have other aspects to their lives.  They are not defined but their job - it is an important part of their lives but only one aspect.They have balance - and they cling to their interests despite the unrealistic pressures put on them by the job.  I think it is aptly summed up by the opening lines of the Holstee Manifesto;

“This is your life. Do what you love and do it often.”

Teachers need to follow their passion for life outside of school in exactly the same way that we encourage our students to do.  Sometimes we have to discover what it is that stops us from doing what we love - and make some changes.   This is probably the only antidote I know for burnout. Outside interests re-energise and re-invigorate people at the personal level. Doing what we love doing makes us healthier people - which in turn helps us to devote real energy to education when we focus on it - and there is plenty of scope and need for that. In the end, our students are the ones who really benefit.  

What greater advice can we give our students than to quote the opening of the Holstee Manifesto to them over and over again? “This is your life. Do what you love and do it often.” If that attitude is the only thing our students pick up from us we may well have taught them one of life's most important lessons.

Enjoy this great interpretation of the Holstee Manifesto. 

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Credits:
Holstee manifesto image: Google images.
Video - via youtube.

The emotion of learning

I’m breaking a self imposed rule with this post. I’m writing it while on holiday. The reason is simple,  I’ve achieved a boyhood ambition - decades after the seed was planted.

Today I created fire.

Not with a match.

Not with a lighter.

With a magnifying glass. 

For as long as I can remember I have wanted to do it.  Memories of summer delights as a boy have resurfaced – as a boy / teenager I used to use a magnifying glass to burn my initials into my summer thongs with a magnifying glass.  My public explanation was that it made it easier to find my thongs when “the gang” came over and all our thongs were piled up by the back door.  True enough – but the other truth was that I enjoyed doing it. I enjoyed seeing the snail trail of my initials “magically” appear as a result of nothing more complicated than the sun and some curved glass.  However, given the long, tinder-dry grass in the paddocks that surrounded my boyhood home,  I never attempted to  light a true fire – despite a burning desire to do so (pardon the pun).

Today, decades after my teenage years faded into the fog of time, I finally tried to light a fire using nothing  more than the material I wanted to burn and a magnifying glass.  In theory there was no doubt that it would work and I knew that it would take marginally more effort than using a match. But I wanted to do it – simply because I wanted more than intellectual knowledge that it would work. I wanted to actually do it.   So I did.

It occurred to me while I was holding the magnifying glass that there were broader lessons in the action.  I needed to maintain focus – my own and that of the magnifying glass. The pin point of concentrated solar energy had to be held over the same spot and I had to concentrate to ensure that this happened. It is probably dignifying the action a little to say that I needed to employ a technique but in a sense it was true.  If I didn’t hold the glass in the correct way nothing would happen.    I also needed to clarify my own definition of success.  Was singeing the paper the same as creating fire?  I decided “no” - but it was probably acceptable as an encouraging sign.  Was creating smoke (after mere seconds) creating fire?  Again I decided “no” – but it was probably proof of concept.  What did I mean by fire? I decided that it was flame that consumed the material that I wanted burned and that only that could be considered success.  After passing through the first stages towards success I needed to adjust my approach by  getting some smaller twigs from the garden – which, in academic terms could be considered refining my practice in the face of observable results.

So I was learning.  But the feeling of success and achievement when the flame burst into life was out of all proportion to the lack of effort required to achieve it.  It turns out the lighting a fire with a magnifying glass is as easy as it is reported to be.  But the key aspect for me is that now I know it, I’ve done it myself.  Second hand knowledge has been replaced by experience. 

The other aspect is that this was a fiercely personal objective. I doubt any of my family or friends share this desire to “achieve” this goal.  In world terms it is insignificant. But in personal terms it brought a glow to my face that was not simply a reflection of the fire. 

It occurs to me that this is true of all personal learning.  Is this why musicians try to reproduce the sound of their favourite guitarist when the mp3 player can do it effortlessly for them?  Is this why painters use pigment to capture the landscape when a camera can do a more accurate job in an instant?  Is this the feeling of truly significant personal learning?  If it is, then surely we as teachers owe it to our students to let them experience this success in Iearning or achieving something of personal significance?   I wonder how many discipline problems would fade away and how the motivation levels of our students would increase if this feeling was a regular part of our classrooms? 

 

Easily the most popular post on this site is one I wrote dealing with PBL.  If I may say so my-self it provides a good summary of the concept and links to a host of  very useful resources.    My experiences today re-affirm my reasons for writing that post; we need to meet the personal interests of our students in our programs.  Adding the emotion of learning to our classrooms may be a key ingredient in a truly motivated learning environment.

Truly personal learning is significant; it produces emotion in the part of the learner – not just intellectual advancement.  If it doesn’t then maybe it isn’t as significant to the learner as it is to the teacher.

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Credits:

Image via google images:  http://www.clker.com/clipart-2285.html

The second most important word in education?

It has been said that the most important word in the language is a person’s name.  And it is probably true - we all respond well to the use of our name, we feel that the speaker knows us, which makes us feel valued.

But, at  professional development session recently with Dylan Wiliam, author of “Embedded formative assessment”,  he mentioned a word he ranks as the most important word in education.  “Yet.”
It is a simple word that carries a powerful message.
Consider the child who says “I can’t do this.”  The educator’s response is “Yet."


The message is clear - this simple word sends powerful messages;

• You may not be able to do this task now, but with effort and practice you will be able to.  

• You have the capacity to do this.
• You can improve.
• You can get better.
• You can and will learn.
• Making an excuse is not an escape -you can and will learn this thing.

What a simple way to deliver a powerful message - possibly the most effective way of sending this message I’ve come across - yet.

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Readers might like to read a longer and more detailed post on a similar theme - “The more I practice the luckier I get - mindset”  here.

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If schools are gardens of children - I want to plant seeds

Schools have been likened to gardens. It’s well known that the German educator Friedrich Frobel coined the term “kindergarten” - which means “children’s garden”.  If that’s the case, then teachers can be likened to gardeners.  The metaphor has much to recommend it - but recently I’ve been asking myself do I do anything but weed the garden? Do I actually plant any seeds?

For classroom teachers the answer to this is easy - of course teachers plant seeds. They do it every day, in every lesson.  But the answer is not so obvious for educational administrators. Sure, we work hard to ensure that the garden has everything it needs, and we support our “gardeners” to the best of our ability.  But it is the “gardeners” who actually plant the seeds.

So today I left the paperwork for 15 minutes  and sat on the floor while a grade one child read me a story.   I did a lot of other work today - including some significant weeding and supporting of the “gardeners”. I dealt with a lot of students - but mostly “weeding” or perhaps “pruning” might be more apt. I did a lot of good things.  But as I walk towards the car park thinking of the highlight of my day it was the 15 minutes I spent on the floor hearing a child read.

I had planted a seed.

The curse of Max Headroom in the classroom...and everywhere?

Many years ago there was a short lived T.V. program called “Max Headroom”. It was a spoof on egotistical T.V presenters and supposedly hosted by the worlds first “computer generated host”. It wasn’t -  it was a heavily “made up” actor.  Part of the scenario was that the world had evolved into a place where there was a TV everywhere - in every private room, in every public place - everywhere. Everywhere you went in this future world Max was there with you, babbling away in the annoying smarmy language that is the domain of television hosts. There was no way to escape this for the TVs came with no “off” switch. The television could never be turned off, never be silenced - it was a constant aspect of people’s lives.

What was once a parody is now almost reality. Screens are with us now far more than even in the Max Headroom scenario - screens are not only everywhere but they are mobile; computers, tablets and smart phones mean that we now have screens with us everywhere all the time.  Children in cars now don’t have to ask “Are we there yet?” They may have DVDs to watch or PSPs (or equivalents) to keep them occupied.The social impact of this is debated frequently in social media and serious literature.   

I’m far from a luddite. In fact, I am a huge fan of technology. I enjoy being online and consider the web as much a part of my recreation as of my employment.  

But it occurs to me that, in an age of “screenagers”, we are actually missing something. Our students are conditioned to rapidly respond and react to stimuli via the screens. They can find out what other people think in an instant.  But what do they think? When do we teach them how to reflect?

I’m not simply speaking here of using the powerful  “wait time” approach when asking questions in the classroom. When do we teach students that there are some things that Google can’t answer, that merely “liking” something on Facebook is not really making a social contribution or a sign of involvement?

I’m talking about giving students time in which to think about matters of substance to them.  But what are these significant questions? What is important to our students?

Perhaps we should ask them.  
In person.
Face to face. 

As Miles Kington said, "Knowledge is knowing the tomato is a fruit, wisdom is not putting it in your fruit salad."  

Since knowledge is now effectively available at the press of a button we need to develop wisdom and understanding - and that means giving students time to think for themselves.

Unless of course there’s an app for that.

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Credits:
Active links go to original sources.
Image via Google images:

The WISE model - A quick and nasty guide to evaluating classroom ICT use.

I’m fortunate to be able to visit every classroom in our school. Like most schools, we have invested heavily in ICT. Are we getting value for money? Is the investment really improving educational outcomes? In some classrooms I could answer “Yes” - but in some the answer would have to be a disappointing “No”.

It is not necessary to have an in-depth formal instrument or formal testing to get a sense of how well ICT is being used in classrooms.     

The first “rule of thumb” indicator I have is a simple one - are the students CREATING product ...or CONSUMING product... or both?  If the students are simply consuming product, i.e. using “drill and practice” programs or merely absorbing content from the ‘net, then ICT use in the classroom is likely to be making only a limited contribution to student learning. However, if students are CREATING product then there is a good chance that ICT is being put to good use.

If students are creating learning artefacts then a simple acronym provides another lens through which I can quickly evaluate the significance of the classroom program. That acronym is  WISE.

WISE stands for...

W hy? (or WHAT). Why is ICT being used? Could similar artifacts be produced via traditional means? A hand drawn poster is as valid as a Publisher document for example.   What are the teacher’s  SPECIFIC objectives, what are the SPECIFIC curriculum links? What can students achieve  using computers in this context that could not be achieved otherwise?   

I mportant (or interesting) Is the project / experience both IMPORTANT and INTERESTING to the student? (Tasks need to be important or interesting to the student - not just ”fun”.)  If not, then the chances are that the task is electronic “busy work”.

S haring.   How are the students sharing both their end product and the process of creation?  How are they sharing their artifact with the educational community beyond the classroom? If they are not sharing the artifact...why are they producing it in the first place?  If it only has worth inside the context of the classroom then why would students value it? If it has wider significance why is it not being shared?

E valuation.  How do the students demonstrate their learning? Is the artifact itself significant outside of the classroom environment?  What skills need students display / include? Do they know this? How can a development of skills be demonstrated?

This acronym is hardly cutting edge. (I could dignify it beyond it’s worth and call it “The WISE model”.) However, it does provide me with a lens through which to quickly get a sense of how well ICT is being used in a classroom.   As with all technology, classroom ICT is neutral - it is how well it is being used that is important. And to assist with that we all need to be a little WISE when it comes to classroom use of ICT.

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Credits:
Image = Google images
http://blog.lib.umn.edu/tel/blog/Computers-TwoKdgStudents.jpg

A modern problem meets ancient wisdom?

I’ve been puzzling on reconciling what the research says about motivation and how to enact it at my workplace.  For this I am indebted to the work of Dan Pink and his book “Drive”.  For those not familiar with the book I’d suggest you can get a more than adequate overview from this RSA animation of his TED talk.




Pink identifies three prime motivators - autonomy, mastery and purpose.  
Purpose.
Teachers should have little trouble with a sense of purpose; surely the profession is one of the most noble and worthy of all?  If a teacher doesn’t feel a sense of purpose then perhaps he or she is in the wrong job.
Mastery
The desire to master a task is also easily embedded within teaching.  Who can honestly say that they can not improve their practice? Who can not improve their ICT skills, or their questioning ability, or the inclusiveness of their lessons? Teachers have almost limitless opportunities to improve their practice - and the day when they believe otherwise is the day they are in the wrong job.
Autonomy?
Autonomy, however, creates some issues for schools. How do we grant teachers genuine autonomy in an environment of regulation, mandated assessment, school wide procedures and protocols that dictate the shape of lessons and learning experiences?   A common response is to say that staff are consulted and included in new school initiatives but then adherence and a common response is required. This is often seen as acceptable since the staff had the input into the decision making process.  But is this “input” enough - or even real?

The economic realities of life are such that most teachers need a job - and disagreeing with the administration of a school can require real strength of character - and perhaps tenure. I recall being at meetings where principals have discussed using “guided democracy” to get the staff to make the decision that they wanted. I recall countless planning meetings designed to shift teacher understanding to where school management believed teachers needed to be.  In short, staff meetings can be subtly directed to arrive at the destination that the leadership wants. However, such processes only produce superficial compliance; genuine commitment to the concepts being discussed is often lacking.

All of this leads us to a situation where the scope for teachers having significant autonomy is limited.  Increasingly teachers have little control over the content of what they teach - and the process by which they teach can also be either “guided” or mandated.  Which means that teachers end up with minimal genuine autonomy.

Yet how can it be otherwise? Effective schools are more than a series of classrooms sharing the same building. A common framework allows  schools to operate in a coordinated manner, to structure activities in a way that allows efficient teaching.  A common approach in many areas is not only sensible but essential. So, schools with clear direction regarding curriculum content and a commitment to “best practice” methods are understandable - in fact, desirable.  Where does this leave teacher autonomy?

Good schools need structure...but passionate teachers need a degree of autonomy.

This is where shared vision becomes essential - not a veneer, not an engineered process with a pre-determined outcome, not merely a collection of protocols..  Teachers who share the vision of the school will feel more control over their efforts. In schools with a shared vision and mindset teachers will have a sense of autonomy - they will feel as if they are working towards goals and objectives that they themselves value.  The fact that the teacher in the next classroom is making the same decisions will be insignificant, for each will be working towards achieving their goals.

When schools do not really listen we end up with a mismatch in vision between the school and at least some of the teachers who teach there. If Daniel Pink is right, this will lead to teachers not feeling in control of their actions, to teachers who lack a sense of autonomy.  And a lack of autonomy leads to a decrease in “drive”.  In the school context this manifests as mediocrity, of minimum standards rather than striving for excellence.Surely this leads school management with a paradox? To create group consensus  we need to genuinely listen to the voices of the individuals within that group. We need to establish our shared values, we need to be clear about our shared vision - for these things guide the fundamental direction and actions of the school.  It is the values and aspirations of the teachers who drive classrooms.  If we want teachers with drive we need teachers with vision - a vision they truly share with other teachers in the school.

Creating a situation where teachers can drive their own classroom in the direction that the system dictates is a challenging task for educational administrators. It reminds me of the adage taken from ancient spiritual leader Lao Tzu; “A leader is best when people barely know he exists, when his work is done, his aim fulfilled, they will say: we did it ourselves.”

Then we will have teachers with "drive".

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Credits:
RSA Animate version of Pink's TED talk:
http://www.youtube.com/watch?v=u6XAPnuFjJc&feature=player_embedded
Lao Tzu image: Google Graphics

Teaching - building a cathedral?

There is a an ancient parable that goes something like this...

Centuries ago three stone masons were working together chipping away at large blocks of stone.  A stranger approached them and asked them what they were doing.
“I’m chipping away at a block of stone,” replied the first mason.
“I’m working to feed my family,” replied the second.
“I’m helping build a cathedral,” said the third.

Same job - but very different attitudes.

Teachers can be like that.  The task of teaching is a hard one that is slow to produce results - not unlike chipping away at stone. We all know teachers who have views about their workplace or their job that is similar to the first or even the second mason. We also know that this is reflected in their approach to teaching.   However, the good ones know that their “job” is more significant, that the rewards and the outcomes go beyond the here and now, that they are doing something of real significance.
Do our teachers think they are teaching phonics … or helping a child learn to read? Do our teachers think they are teaching computation techniques... or introducing students to the wondrous world of mathematics?


It is our attitudes that direct our actions...and our actions that direct student achievement. The challenge for us all is to see our actions, not as chipping away at a stone, but as building a cathedral.

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Credits:
Parable source =  anon
Image = “The Stone Mason”   http://www.diego-rivera-foundation.org/The-Stone-Mason.jpg

Educational reform; like building a plane - in flight!

I love this clip. To me it is a wonderful metaphor for educational reform.

One of the major issues with educational reform is that schools have to be operational while education is transformed. We can’t simply shut down the schools and learn new and more effective educational techniques. We need to test and trial our learning when and where it matters - in the classroom with our students. We need to learn new skills while we teach via established methods. There are those who suggest that teachers can learn new approaches when students are on vacation - and to some extent this is true. However, the important aspects of classroom teaching can only be learnt through implementation in the real world - and that means while the students are present. There is a time when a trainee pilot needs to land a plane in real life and not in a simulator.

There are obvious issues with this. Our students are not guinea pigs or lab rats. We should not experiment with them. On the other hand, we need to continually improve our practice - and that means we need to be constantly trialling new approaches or trying to refine and enhance established ones. This balance can be difficult to achieve - perhaps this explains the almost glacial pace of school reform.

Clearly there are risks involved in any educational reform - if any innovation is ineffective then students suffer in comparison to what they may have achieved with another approach. However, there are more risks involved in educational stagnation and ignoring new possibilities and potentials.

So how do we build an educational plane in flight? We start by being clear about what we want to do and why. We acknowledge that established techniques may not be appropriate in this operational environment. We try to anticipate any likely issues and develop responses in advance - or at least be observant and flexible to respond to issues as they arise. We clarify our roles - who does what, when and to what standard? Who checks and assists? How do we know when we have succeeded? We accept that the task may be difficult - but, if we are clear about our objectives, it should be worthwhile.


And then we take a deep breath and build our plane.

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Credits: EDS commercial via youtube @ http://www.youtube.com/watch?v=L2zqTYgcpfg

Original idea to link to education: Thanks to a long forgotten presenter at a SPERA conference in Darwin who used this clip in his session.

The most important sticky note you'll ever read?

I came across this video the other day -  a “feel good” effort with a twist at the end that I won’t spoil - all is revealed in the clip.

Video from KarmaTube


It occurs to me that this clip has implications beyond the relatively narrow focus of the target audience. So what relevance has this video to broader aspects of education?  There are several messages really - one is that  education requires open and genuine communication.  As teachers we need to listen to our students as much as we talk to them - if not more.

Another is that this relationship needed time to develop - the relationship could not blossom until there was a degree of trust.  Again, there is a message there for teachers.

But watching this reminded me of one of my favourite quotations which is attributed to Dr. James Comer;  “There is no significant learning without a significant relationship”.  Put simply, if we want our students to learn from us we need to spend the time to develop genuine relationships with them. How we do this is up to each teacher as an individual - for we too have our own personalities, interests and foibles. However,  unless we take the time to value our students they will not value us - or what we are trying to share with them.

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Dr. James Comer is more than a source of an inspirational quotation.  He has developed the Comer School Development program as a vehicle for school reform.  An interview with Dr. Comer can be accessed here.

The kindness boomerang

We live in an era when success at school is defined by many as achieving high marks in exams, or possibly on the sporting field.  We live in a society that boasts “life coaches” to help individuals achieve their personal goals. We live in a time where an unstated belief in “social Darwinism” is rampant - the cream rises to the top, the rest...well, they don’t deserve to be successful.  In short, we live in a society that emphasises individual achievement and success; perhaps this would be more palatable if the meaning of “success” was broadened beyond the limits of economic worth.

However, we rarely hear of the value of simply being a decent person - of helping someone else without  thought for personal gain.  For an antidote to this mode of thinking watch this wonderful video - the Kindness Boomerang.

From an educational view point this video is clearly worth sharing with students - even students from a relatively young age could appreciate this.  Those interested in helping to make the world a nicer place one person at a time (starting with themselves) might be interested in visiting the “Random Acts of Kindness” site for some ideas. This site also has some ideas suitable for using in schools.

This site also has some ideas suitable for using in schools.  Or you might enjoy reading this as an adult - especially if you appreciate the joys of a good coffee.

Teaching students that they can be people of worth regardless of their age (and income or “status” in later life) may just be one of the most important lessons we can teach them. As Martin Luther King is purported to have said “Life’s most persistent and urgent question is, ‘What are you doing for others?’”


Those who enjoyed the video above might also like to view my post “Validate - it’s great”, which features another inspiring video well worth viewing. I challenge you to watch it without smiling...

Herding cats in the classroom?

Teaching is a challenging activity.  Keeping track of a class of students who are operating at a range of different ability levels, often from vastly different socio-economic backgrounds, catering for a range of learning needs, dealing with any individual health issues class members may have, managing the administrative requirements of your school or system, attempting to match curriculum requirements to the needs of students in the class, dealing with “helicopter parents” or, even worse, parents who are as insubstantial as the abominable snowman, acting as a part of a team when your specific class requires focused and immediate attention, trying to make your lessons as interesting and engaging as possible...it takes a special type of person to do it well.
It is not unlike herding cats.



One thing we know about cats is that is easier to get them to come to you than to make them go somewhere that they don’t want to go.  With cats this is easy - entice them with food.  Although we do not bribe students via their taste buds we can learn from this approach - efforts put into developing student motivation is an important aspect of effective teaching. Structuring the educational environment to get students interested and wanting to learn through engaging and challenging activities where they value the outcomes of their efforts and feel secure as they explore their boundaries changes the educational process from that of herding cats to managing learning.
If teachers feel as if they are herding cats in the classroom it might be worth looking at what is on offer. Motivated people, even young ones, don’t need to be herded; they drive themselves.  The challenge for teachers is to guide student interest in ways that reflect the outcome requirements of the curriculum. And that is far from easy.  There are many sites and blogs offering advice or guidance in this area - a brief but worthy offering can be found here.
One important aspect of effective education is often overlooked however. Teacher reflection is an important part of becoming an expert practitioner.  Teachers need to find the time to think about what is going on in their classrooms and their educational practice - this is as important as thinking about the response of students to lessons. How else can areas for improvement be identified? Reflection is not a luxury, it is an essential part of personal professional development and adaptation.
For some personal reflection needs to be done alone - perhaps over a coffee whilst appearing to stare out the window. Others need guidance and stimulation.  Technology may come to the rescue for those in this category. Apple’s Itunes “university” section has FREE lectures on a variety of educational issues and subject areas while Harvard also offers free podcasts on educational issues.  Podcasts can be thought provoking ways to stimulate reflection - and can be absorbed during the daily commute.

To paraphrase Margaret J. Wheatley, reflection “...is not just a nice thing to do if you have the time. It is the only way you can survive.”

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Credits:
video = commercial from http://www.youtube.com/watch?v=Pk7yqlTMvp8
Embedded link via Larry Ferlazzo at Education Week.
Harvard and Itunes links go to original sources.
Margaret Wheatley link goes to source.

The hoax of Hanoi

The Tower of Hanoi is one of the more popular puzzles amongst recreational mathematicians and in education.  Almost everyone is familiar with it and the story that usually accompanies it - often couched in terms something like this...

“There is a legend of a temple near Hanoi in Vietnam.  The temple has three golden poles. One one pole sits 64 golden discs of different sizes. The rings are arranged with the largest at the base progressing in order to the smallest disc which sits on top of the pole.  The monks who tend the temple have been charged with moving the rings from their current pole to the end pole - one disc at a time - but there is a special rule that they must follow. They must never place a larger disc on top of a smaller one. When they complete this task the world will end. How many moves will it take the monks to do this?”

We probably don’t need to work ourselves up into a sweat worrying about the monks finishing their task which will signify the end of the world.  It has been calculated that if the monks were able to move the one disk per second it would take them around 585 billion years to complete the task - 18,446,744,073,551,615 turns.    In classrooms the number of disks is usually drastically reduced to around five in the early stages - which is enough to prompt some interesting explorations.   In this age of the Internet there are several interactive versions - which have the advantage of being readily customised and also of making suggestions for optimal moves. Examples can be accessed here and here.

It is a great puzzle - a surefire hit in the classroom.  But what makes me love this puzzle so much is the simple fact that it is a hoax.  Traditionally there was no such legend in Vietnam - or in India either, which is another popular location for the site of the temple.  The whole thing is the invention of mathematician Edouard Lucas. When the puzzle was first published in 1883 it appeared complete with legend and was credited to  N. Claus de Siam (an anagram of Lucas d’Amiens - Amiens being the town of his birth).  

Lucas was a significant mathematician in his own right - so significant that he has his own number series named after him - the Lucas sequence (similar to the Fibonacci sequence but instead of starting 1,1,2,3,5,7...  Lucas’ starts at with 2,1,3,4,7,11,18...) and he developed a test for large prime numbers still  in use today.

Lucas’ death is also worthy of interest - he is possibly the only mathematician in history to die as a result of a piece of crockery. A clumsy waiter dropped a plate which broke and shard from the plate cut Lucas on the cheek. The cut became infected and he later died of erysipelas - a serious streptococcus infection.

The myth and the puzzle are well known … but the puzzle has a rather curious property that  is less so.  The movements of the pieces can be represented in a graph as depicted here.
This bears an uncanny resemblance to  to the famous  Sierpinski triangle- which is a fractal.   The fact that the movements of a game can be linked to fractals is, to say the least, intriguing. (More on this at the source.)
 


The Tower of Hanoi has recently become a movie star. A disguised version of it appears in the move “Rise of the Planet of the Apes” - disguised, fittingly given the manner in which it as first published, as the Lucas Tower which was used to test the intelligence of the apes.

What can we learn from this wondrous hoax? When it comes to education sometimes a touch of showmanship and playfulness can improve a strictly mathematical experience. It is important that the mathematics remains central - but the “power of story” is a significant tool to generate engagement and interest  - which may contribute to the “holy grail” of teaching;  a self-directed learner.  We can help foster this when we show our students that there is more to mathematics than just the numbers.

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Credits: http://www.wooden-toy-store.com/images/Tower%20of%20Hanoi.jpg

Undirected graph of movements: http://en.wikipedia.org/wiki/File:Tower_of_Hanoi-3.svg
Sierpinski triangle: http://upload.wikimedia.org/wikipedia/en/thumb/8/88/Sierpinski_Triangle.svg/220px-Sierpinski_Triangle.svg.png

If you enjoyed this post you may enjoy my other maths related posts available via the maths page or by clicking here.

Classroom teachers - the real educational experts

Our staff had a professional development day recently.  The group was asked some “simple” questions such as “How do children learn” and “What do you do to facilitate learning”.  The thoughts of the group were then collected and presented as a word cloud.  Obviously this is a relatively crude way of summarising the ideas of the group - but it does capture the essence of what was discussed.

It seems to me that this is a solid representation of the “wisdom of the group” approach. There were no “outside” educational leaders or gurus present at this workshop, no-one was flown in from interstate to facilitate, no-one earned a cent in presenters fees.  Yet the result is a more than fair representation of the things that effective teachers do. In fact, if each item was to be expanded and clarified we would have the basis of a fairly satisfactory professional text.

Obviously knowing what to do and being able to do it are two different things. If our staff can enact these practices in the classroom our students will be the beneficiaries.  However, it strikes me that the knowledge base in our staffroom is a fairly significant one. There is an expression that an expert is someone who lives more than 100 miles away. Upon reflection it is obvious that we all must live 100 miles away from someone - and thus can all be classified as experts.

Whilst it must be acknowledged that effective teachers need to be effective learners themselves and always strive to develop their skills and knowledge base, perhaps it is time to place more value on the “home grown” wisdom within our schools.

Effective classroom teachers may well be the real educational experts.

A track less travelled

Like most people I am a creature of habit.  I am also a keen bush walker - partly for exercise, partly for photography, partly for personal therapy.  My most favourite site just happens to be a World Heritage area less than two hours from my home - Cradle Mountain.

I tend to stick to well  trodden paths when I visit. With scenery like this waiting why not?

When you know you will be seeing this why would you go elsewhere?

Yet that is just what I did recently - due, in part, to weather conditions.  Seeing as though my favourite tracks were shrouded in morning mist I went on some of the less well known tracks... and “discovered” this...

and this...

I even met some of the locals...

Not only did I add some gems to my walking catalogue but I also discovered tracks to two other destinations that I had been wanting to visit.  In short, by breaking my habits I discovered some “unknown” locations - but also found some exciting places to explore in the future.

So how does this relate to education?  It struck me that my habits prevented me from exploring other options and opportunities.  This happens in classrooms too.  How many teachers cover the same material every year?  How many people use the same task design year after year? No doubt these are successful teachers - if it didn’t work they wouldn’t do the same things repeatedly.  Yet this approach reduces innovation and exploration of alternate methods - especially in the nature of what the students do.  The curriculum may dictate what students are to be taught - but usually teachers have freedom to select how they  present and get students to explore material.  This is easy to say but possibly a little harder to do - but there are some simple ways for teachers to expand their instructional horizons.  

One might be to use this resource - the Kelly Tenkely's blooming peacock.  This resource identifies areas of Blooms taxonomy and then identifies software that addresses that mode of thinking.  Another llist, by Kathy Schrock ,does the same thing but limits the software to that produced by Google - meaning free and web based. Andrew Churches' Blooms Digital Taxonomy  worksheets also provide advice on how to address Bloom via technology. One way for teachers wishing to expand their skills and move beyond their current habits into 21st Century skills might be to choose one new piece of software per unit and become an accomplished user of that site or program. Once done, select another site that suits your purpose from the next level up in Bloom’s taxonomy. Over a relatively short period of time teachers will have learnt not only a range of useful skills and programs  but shifted their teaching towards the higher end of Bloom’s spectrum.

Taking a fresh look at how we teach and trying something different is likely to be very rewarding - for the teacher as well as the students.

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If you like the images displayed in this post you may like to view this video I made of walks completed last year.