Tuesday, December 27, 2011

Relax - and improve

One of my most favourite quotations is this one;
“Every now and then go away, have a little relaxation, for when you come back to your work your judgement will be surer. Go some distance away because then the work appears smaller and more of it can be taken in at a glance and a  lack of harmony and proportion is more readily seen.” 

It is great advice.  As educators we tend to stick at a job until it is completed, a solution is found or at least a workable solution is developed (even if this solution may not be perfect).  In the short term this may be necessary and possibly even unavoidable.  However, over time, this approach can reduce educational leadership to mere management.

As the holiday season arrives and we are able to “take a break” perhaps we should do just that. Leave the blog alone.  Forget your RSS feeds, the PLN and the #education hash tag. Forget the phone.

Then, and only then, reflect - and, if necessary, reform.  
But do so with a clear mind and relaxed soul and a sense of perspective.  When at work are you doing that which is important - or merely necessary?
Take some personal time to improve your professional time.

Your school will be better for it - don’t take my word for it, trust the author of the words quoted above - Leonard da Vinci.

Image = http://boingboing.net/wp-content/uploads/2011/09/Leonardo_Da_Vinci.jpg

Monday, December 19, 2011

Christmas comedy

Christmas - it comes in two forms, a religious festival (the discussion of which I will avoid) and a secular form which requires the abandonment of logic and the adoption of gluttony.  And we love it.

Countless artistic minds have created their own responses to the phenomenon of Christmas.

I’d like to share two of my favourites.  

The first is an audio play first broadcast by the BBC several years ago dealing with the response to the “true love” who sends the famous partridge in a pear tree.  The script by Brian Sibley is brilliantly read by Penelope Keith.  Enjoy “Yet another partridge in a pear tree”.  

The second deals with the mathematics and science of the Santa character - regrettably,  I am unable to name the original author (but this version came from here).

The mathematics of Christmas
So the story goes….a portly gentlemen dressed in an elaborate red dressing gown affair has tamed a bunch of elves and reindeer and controlled their will. The Elves must be at the forefront of just-in-time production in order to create a production line capable of producing just about any toy. Heaven knows what volume of patent, copyright and trade mark infringement this presents. For the Reindeer it means a level of training that would make Dolph Lundgren’s Rocky 3 workout look like a walk in the park. Below we tackle some of the issues presented by the story of Santa…

1. No known species of reindeer can fly. BUT there are 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, this does not COMPLETELY rule out flying reindeer which only Santa has ever seen.
2. There are 2 billion children (persons under 18) in the world. BUT since Santa doesn’t (appear to) handle the Muslim, Hindu, Jewish and Buddhist children, that reduces the workload to 15% of the total – 378 million according to Population Reference Bureau. At an average (census)rate of 3.5 children per household, that’s 91.8 million homes. One presumes there’s at least one good child in each.
3. Santa has 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west(which seems logical). This works out to 822.6 visits per second. This is to say that for each Christian household with good children, Santa has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house.
4. Assuming that each of these 91.8 million stops are evenly distributed around the earth (which, of course, we know to be false but for the purposes of our calculations we will accept), we are now talking about .78 miles per household, a total trip of 75-1/2 million miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding etc.
5. This means that Santa’s sleigh is moving at 650 miles per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man- made vehicle on earth, the Ulysses space probe, moves at a poky 27.4 miles per second – a conventional reindeer can run, tops, 15 miles per hour.
6. The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium-sized lego set (2 pounds), the sleigh is carrying 321,300 tons, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 300 pounds. Even granting that “flying reindeer” (see point #1) could pull TEN TIMES the normal anoint, we cannot do the job with eight, or even nine. We need 214,200 reindeer. This increases the payload – not even counting the weight of the sleigh – to 353,430 tons. Again, for comparison – this is four times the weight of the Queen Elizabeth.
7. 353,000 tons traveling at 650 miles per second creates enormous air resistance – this will heat the reindeer up in the same fashion as spacecrafts re-entering the earth’s atmosphere. The lead pair of reindeer will absorb 14.3 QUINTILLION joules of energy.
Per second.
8. In short, they will burst into flame almost instantaneously, exposing the reindeer behind them, and create deafening sonic booms in their wake.The entire reindeer team will be vaporized within 4.26 thousandths of a second. Santa, meanwhile, will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250-pound Santa (which seems ludicrously slim)would be pinned to the back of his sleigh by 4,315,015 pounds of force.
So, we are struggling to understand how Santa does it.
Must be magic.

Merry Christmas.

Xmas maths via http://www.gallery.je/santa

Audio for Penelope Keith reading “Yet another partridge in a pear tree” http://kazza.id.au/files/AndyetAnotherPartridgeinaPearTree.mp3

Text of “Yet another partridge in a pear tree” is available at  http://briansibleytheworks.blogspot.com/2008/01/blog-post.html

Santa image: http://www.vectorarts.net/wp-content/uploads/2011/05/christmas-santa-claus.jpg

Audio image:

Monday, December 12, 2011

What I learnt teaching teachers

My time in this role is coming to an end - soon I leave the university environment and return to that alternate reality known as the school.  

There are some things I will miss and some things I will not.

I will not miss the endless stream of marking.
I will not miss the countless hours of sitting in front of a computer dealing with online students.
I will not miss the politics, nor the relentless desire for growth.

But I will miss working with adult learners.
I will miss the conversations with like minded individuals - and the chance to learn from their expertise.

The thing  I will miss the most I find strangely disturbing to acknowledge as this is the only workplace in which I can honestly say I have felt this.  I will miss the respect for learning and knowledge which fills this place.  After three decades in education I find it truly disturbing that I have never had this sense in any school in which I have taught.  Do we as teachers really value learning...or do we merely value mastery of skill sets?  Do we value exploring ideas or merely understanding test items? I’ll miss the conversations about why we do certain things rather than how we do them.
I’ve learnt a lot in my time here – much of it shared on the pages of this blog.  But perhaps my biggest learning is something so obvious as to be often over looked.  We don’t really create teachers here.
We introduce students to learning theories, we examine classroom practices, we analyse curriculum content and practise delivery methods.  We discuss objectives and assessment and what takes place in-between.  We discuss behaviour management and student motivation. We talk about issues to do with student differentiation and human development. We teach how to plan and deliver effective units of work. We show student-teachers how to write grammatically correct essays and follow academic conventions and referencing techniques.  But, despite our best efforts, we simply cannot create teachers.
To be a teacher you need to have at least one student.   It is the student that transforms an educator into a teacher.  The crucial part about being a teacher is that you must care about your students – not in a mushy, overly emotional sort of way, but with a genuine regard for their well being, learning and personal development.   We can’t really “teach” relationships here.  We can discuss concepts such as respect, fairness, confidentiality, compassion, consistency, equality and differentiation.  But that is like confusing a list of ingredients with the act of cooking – it is how those ingredients are blended together in reality that is important.  
Although we can introduce students to a raft of important concepts during their training it is in the school where they learn to apply these concepts and skills.

Dr. James Comer  said that “No significant learning occurs without a significant relationship”. 
He was right.

Image credits:  http://i.telegraph.co.uk/multimedia/archive/01485/students_1485569c.jpg

Tuesday, December 6, 2011

Mathematics education - as seen on the screen

The stats for this blog indicate that my previous collections of web-based videos have been popular.  Hence this post...

Why use web based video in mathematics education?  Don Tapscott, author of “Grown Up Digital”, uses the expression “screenagers” to describe the youth of today.  Like it or loathe it, the fact remains that our students are conditioned to interact with screens. By using their medium of choice we are more likely to engage them - assuming that the content is worthy. Video - moving pictures and sound - is the language of our students. There is considerable research evidence that interest leads to engagement - which leads, on average, to better performance.   

This classic clip of Abbott and Costello demonstrates how easily errors can flow from faulty understanding of procedures - procedural knowledge without conceptual understanding.
Abbot and Costello maths 7x13=28

Apart from the appeal of seeing adults make mistakes this clip can easily move from viewing to  activity by investigating where is Abbot going wrong. How could students convince him that he is wrong - and help him from making the same mistake in the future?
This clip is one of many on Youtube featuring what has been called “Mayan multiplication”. (The name may be something of a misnomer as there is some evidence that it may have evolved in India as a part of the vedic tradition.)
Mayan multiplication

This clip  is clear and “lo tech” which  generates the impression that anyone could use this technique. Can they? Students could explore the technique  - but then contrast it with the traditional method of multiplication  to compare ease of use - especially with larger numbers.

So how does it work?  The wondrous Vi Hart both demonstrates and explains here.
Younger students can also benefit from drawing lines - to investigate patterns in numbers.
Number Patterns

Once this video has been viewed it is a small step to recreating it in real life - and then investigating the patterns created by other numbers.  

Lines - of symmetry - also feature in this clip.  In an earlier collection I included an amazing clip of paper placed in water which unfolded to create a complicated flower-like shape.  This is similar - but much simpler and could also be used to prompt an examination of symmetry - and being simpler might be suitable for younger students.

This site features a reasonable number of educational videos with a special section on mathematics.  Included is an “inspiration” section which links to photographs with an accompanying maths challenge.

It needs to be said that I see these clips as a means of promoting interest in mathematics rather than as an end in themselves - I see these as useful ways of introducing topics which can then be explored in a more traditional manner.   Using visual images in mathematics classes can help bring the subject alive while still allowing teachers to address the requirements of the curriculum.

If you enjoyed this collection you may like to visit others here and here - or my page of “maths” posts here.

Credits: all information available by following the relevant links.

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

Monday, December 5, 2011

Educational reform? Start with the right questions....

Educational reform is a complex area - not only are individual aspects complicated in themselves but the various aspects often interact and entwine and become jumbled in our thought processes.
So where do we start?  How do we know where to direct our energies?  One answer is to ask the right questions before we dilute our energies on activities that may not result in improved student outcomes - irrespective of how they are measured.   A recent post at the The International Review of Research in Open and Distance Learning may have recently done just that by identifying what the authors call “...the Seven Definitive Questions” of learning.

So what are these questions?
  1. How does learning occur?
  2. Which factors influence learning?
  3. What is the role of memory?
  4. How does transfer of knowledge occur?
  5. What types of learning are best explained? (If we can understand it better we can provide for it more.)
  6. What is the relevance of instructional design? Five assumptions are made about learning here:
      1. Learning is multidimensional
      2. Learning occurs in various planes simultaneously
      3. Learning consists of potentialities which exist infinitely
      4. Learning is holistic
      5. Learning environments are living systems.
     7.  How should instruction be structured to facilitate learning?

So what does it all mean?
The authors identify several implications, including;
  • Online learners have the capacity for a breadth and depth of knowledge that in the past was reserved for the minority with geographical access to educational institutions.
  • Courses can be designed that have less reliance on set texts and readings. “Instead learners can be provided with topics and themes and encouraged to seek out information sources and resources to inform themselves.”
  • The “isolation” of online learners may actually be a blessing in disguise as it allows “undistracted thinking and reflection”.  “Further, online learners have the freedom to learn at a time and place that is right for them. That is, they have more control over their learning environments. Learning can be engaged in comfortable, personally motivating spaces and places that become their individualized classroom.”
A question that occurs to me after reading this piece is why is it that our classrooms are perceived to be uncomfortable and disengaging places? Certainly they can be - but surely not all should be classified this way? There is a sense though in which the answers provided by the authors may not be as important as the responses their questions might prompt at the school level.  If teachers can confidently explain their understanding of these “definitive” questions they are likely to have a sound understanding of the educational process.  If not...perhaps some professional discussions around these questions would be of benefit. Or perhaps this list is not as “definitive” as the authors suggest?  Schools could do worse than trying to identify what they think are the really important core questions to do with education. Some of my own questions would include;
  • “What do we think we know about how students learn?”
  • “What are some of the ways in which we teach?”
  • “Does our method of teaching align with the way our students learn?”   
  • If not, what will we do about it? *
Of course, coming up with “the answers” is the easy part. The real reform begins when our teaching practice reflects our beliefs, not just convention.

Post Script:
I have to admit that I found some aspects of the original article cited here rather dense and wordy. Whilst it  appears to be talking about learning theory in general it then leans towards adult learning, particularly in the online environment (which I suppose is hardly surprising given the focus of the e-journal).
There is also some significant content that I have not presented here but which would reward examination. The source article is certainly worthy of both reading and reflection. Read the source article by Janzen, Perry and Edwards here.

* I have asked myself these and similar questions many times and have come up with the TARGETS mnemonic to guide my educational practice. It is the result of my own reflection and research into effective education and may be of interest.

Credits; graphic http://www.radiowroclove.pl/wp-content/uploads/2010/01/question-mark.jpg

Monday, November 28, 2011

Marcus' mental mathematics mistake

In 2009 Marcus du Sautoy, Professor of Mathematics at Oxford University and Simonyi Professor for the Public Understanding of Science, teamed up with an unlikely co-presenter,  comedian / actor Alan Davies, to present an episode of Horizon dealing with the joys or otherwise of mathematics - “Alan and Marcus go forth and multiply”. In one part of the documentary the two participate in an experiment to see if the brain of a member of the public who dislikes maths (Davies) and the brain of one of the most recognisable mathematicians on the planet (du Sautoy) process mathematics differently.  However, the interesting thing for me was this clip extracted from the session.

Play this embedded clip and pay particular attention to du Sautoy’s answer to the third question.
I need to make a clear statement here - it is not my intention to take a cheap shot at Marcus du Sautoy - just the opposite in fact.  Later du Sautoy easily answers more complex questions before I, in the comfort of my lounge chair,  have even processed the information required. He admits  that he was nervous about getting simple calculations wrong as it would be embarrassing for a man in his position to do so.  We can also assume that du Sautoy could have insisted that the error be edited out of the program - but clearly he didn’t and this reflects positively on him.

The interesting thing to me was that when nervous or under stress even one of the most prominent minds in the field of mathematics can make a simple errors.  If this holds true for an expert practitioner such as du Sautoy how much more significant might it be for students in school?

This may prompt some to review their teaching practice in mathematics classrooms. Reducing  stressful situations (and for some students stress may result from  something as simple as being required  to provide an answer publicly in class) would surely make the process more enjoyable for all - and it may just remove a barrier to learning.

Monday, November 21, 2011

What can QWERTY teach us about education?

 History has virtually forgotten Frank E. McGurrin – which is perhaps a pity given his  unintended but very real impact upon virtually every  person living in the developed world.   It could be argued that it was McGurrin, as winner of the first ever typing contest, that cemented the place of the QWERTY keyboard as the dominant key board layout for typewriters – which evolved (or perhaps mutated) into the computer keyboard.
The survival of the QWERTY keyboard is worth contemplating as it is truly a bizarre story.  The layout of keys with which we are so familiar was actually designed to make typists less efficient – or at least slower.  Early typewriters were mechanically cumbersome and the mechanisms jammed if typists struck the keys too quickly. So,  keys were arranged in such a way as them harder to press quickly – letters that are used more often were moved so that weaker fingers were used to type them or to places where fingers would need to be moved more in order to press them – in other words to slow down the user.  There was considerable experimentation to find the right balance and produce a keyboard that was efficient enough to be better than writing by hand but not so easy as to result in jammed machines.    It is possible to write 70% of all English words using the letters   D H I A T E N S O R  - yet few of them are in favoured positions on the keyboard.   Amazingly, salesmen also apparently had input into the QWERTY design – they wanted to be able to create the word TYPEWRITER  using letters on one line of the keyboard to demonstrate the ease of use of the new machine – and they got their wish.
McGurrin, was employed by a Ms. Longley, also largely forgotten by history despite being the founder of the Shorthand and Typewriter Institute in Cincinnati.  A rival company, using a different configuration of letters on their machine, challenged Longley to a contest to see which company was producing the best typists – McGurrin was nominated to represent his employer and duly won the contest.  This was seen as endorsement of the superiority of QWERTY over other layouts and helped propel the configuration to undisputed domination of the market. (An interesting footnote to this anecdote is that McGurrin was apparently the first typist to memorise the keyboard – and it may well have been the simple fact that he may have been the first touch typist in history rather than any design feature of the keyboard that enabled him to win the competition.)
Over the years typewriters improved, non-jamming machines were created and more efficient keyboard layouts were devised. However, they were not widely adopted – despite being demonstrably more efficient. Even in the electronic age of computers QWERTY continues to rule supreme – despite there being absolutely no phsycial reason for it to do so. I’m writing this on a QWERTY keyboard, every computer in this building have one, all the  keyboards in my house are of that configuration, even my smart phone uses the layout. The  DVORAK keyboard, generally considered to be much more efficient than QWERTY, lies overlooked  in obscurity simply because we have become accustomed to QWERTY . In short, QWERTY is a survivor , it continues on and on and on – despite there being no compelling reason for it anymore. 

There are aspects of the education system that have a striking similarity to QWERTY  in that they continue long after their  usefulness has past. Examples include:
·         Starting and managing student progress through the layers of school according to the calendar rather than on progress, demonstrated learning or readiness.
·         “Streaming” students despite both social-constructivist theory and formal testing programs suggesting this does not enhance students.
·         Confusing factual recall with understanding.
·         Teaching “subjects” in silo-like isolation.
·         Clinging  to paper based practices when the world outside of the school ground  is essentially  digital.
·         Pretending that the school is still the primary source of information available to students.
·         Teaching all students more or less the same thing at more or less the same time in more or less the same way – regardless of interest, ability or appropriateness.
·         Spouting social-constructivist learning theories but practicing behaviourist techniques (seen a “star chart” lately?).
·         Providing A-E type feedback to students and parents.
·         Using formal testing data to evaluate school performance – regardless of the various social and economic factors known to impact on education.
·         The standard school day itself  is fixed and based upon the needs of a bygone era. (Why do some schools offer “before school”  and “after school” care? Why not just change the hours of operation of schools to reflect social needs?)
This list is of course far from complete...and is obviously open to addition, agreement or disagreement. In a sense agreement is not necessary here, it is discussion that is important. We as educators should question the fundamentals of our practice.  We need to examine our basic assumptions about what makes a good school, how we can best serve our students, what are we trying to achieve and how we are trying to achieve it. Then we need the courage and energy to act upon our reflections.
 If we don’t we are essentially engraving QWERTY on our educational practice.


Historical information about the surprisingly interesting history of the typewriter is sourced from Stephen Jay Gould’s book “Bully for Brontosaurus”, published by Penguin.  

Wednesday, November 16, 2011

When is a school a school?

I was privileged to be given a tour of a new school recently.  It was, without exception, the most exciting school building I have ever been into.

The design of the buildings was thoughtful and, dare I say it, “modern”.  ICT was present everywhere (but not always obvious), major walls were sound “proof” but flexible in that they could be opened (in effect removed) to increase teaching space and allow for co-operative learning, or inter-class interactions.  The school had avoided the trap of creating computer labs - instead each area had access to a half dozen or so desk top machines which were supplemented by a generous supply of lap tops via a booking system.  Wireless technology with fast connection speeds was ubiquitous and covered every area in the facility (or so we were told). Teachers had pleasant individual office space.  Each section of the school, or “pods” as they were called on site, contained significant art installations.  Large windows dominated the wall spaces filling the  facility with light and enhancing the impression of spaciousness. Classrooms seemed to have adequate resources. One of my fellow visitors commented that the staff room had the feel of an upmarket hotel rather than a school staff room.

Outside it was just as impressive - attractive from all angles, functional yet not overly institutional.  Play areas were clearly well used and functional.  It was, quite simply,  a wonderful building - but it wasn’t a school.

Then the siren went.

The empty rooms quickly filled with chatter, children moved to desks, teachers started explaining tasks, students started asking questions, books were opened, computer screens burst into life, the sounds of productive work became the back-ground audio-track for the visit.  Parent helpers slid quietly into a classroom to be greeted with smiles and accepting nods of “hello” from the students. A class of children walked past in an orderly but not overly regimented group. Seeing their teacher smiles burst onto the faces of the first few students as they entered the room.

Then it was a school.

Image: http://www.wes3rdgrade.com/uploads/7/8/3/3/7833021/8576233.jpg?252

Wednesday, November 9, 2011

Using formal algorithms too early - it doesn’t compute?

Picture an early childhood or middle  primary mathematics classroom.  What are the students doing? How are they recording their work?  Chances are, if you have a traditional view of effective mathematical teaching,  the students are using some form of formal algorithm.  This has been the case for many many years.  Yet, this entrenched  practice  may be actually reducing student understanding of mathematics.

According to Professor Doug Clarke of the Australian Catholic University, “The teaching of conventional written algorithms in primary schools dominates the (mathematical) curriculum with concerning effects on both student understanding and self-confidence.”  In his paper “Written algorithms in the primary years:Undoing the “good work”  Clarke challenges the effectiveness of teaching formal algorithms to students in the first five years of primary school.  His claim is based upon his research conducted with 572 students over two years.  It found that students who were “taught” mathematics by methods which required them to invent and use their own “informal” methods achieved more highly than those who were taught more formal algorithms. (Follow above link for details.)

Among reasons given for this is the notion that formal written algorithms do not match the way people naturally deal with numbers.  Formal calculations in primary school tend to operate from units, tens and into hundreds and so on - in other words, from right to left. However, people who are efficient users of mental calculations tend to operate from left to right - the opposite direction.  Thus the methods actually used by efficient mental calculators seem significantly different to those taught formally.  The introduction of formal algorithms also tends to encourage students to abandon their own intuitive methods of dealing with numbers - which in some cases has been shown to reduce the mathematical reasoning abilities of students.  (A useful overview of mental calculation and estimation techniques and its relationship to the teaching of formal algorithms can be found here.)

Clarke is not alone in his calls. One researcher has gone so far as to call formal algorithms in grade one and two “harmful” to understanding. Others, such as Kamii and Dominick, conclude that the teaching of algorithms too soon may “unteach” the child’s pre-existing understanding of place value and thus hinder development. *

So when should students be introduced to formal algorithms?  Clarke suggests this is appropriate when students are capable of mentally adding or subtracting two digit numbers.  Approximately 60% of students reach this stage by the end of grade four - but the obvious corollary of this is that nearly 40% of students do not.  The implication of this, if Clarke and the other researchers are correct,  is that large numbers of students are introduced to formal mathematical procedures before they are intellectually ready to benefit from them.

This calls for a wider discussion on the use of formal algorithms in education.  Clarke cites research by Northcote and McIntosh  who found that in one survey of mathematics use by adults only approximately 11% of calculations involved written calculations.  The same survey found that in around 60% of cases of adult mathematics use only a reasonable estimate was required. The conclusion drawn was that “It has become increasingly unusual for standard written algorithms to be used anywhere except in the mathematics classroom.”

The call to delay the teaching of formal algorithms should not be confused with a call to cease teaching methods of calculating or manipulating numbers. The opposite is the case.  This resource by Alistair McIntosh presents several significant methods for developing mental computation skills - and does so in a way that develops an understanding of the number system.

Clarke acknowledges that formal algorithms are have merit. He shares the views of others in observing that they are powerful procedures, particularly when dealing with large numbers, that they can allow for rapid computation, that they provide a written record of computation that enables error tracking (and correction), and that they are easy for teachers to manage. It’s just that they should not be introduced until children have internalised an understanding of numbers, place value and the specific concepts being addressed.  Repeating the information above - for many students, this readiness does not come before the end of grade four.

There is little doubt that these findings might come as a surprise to many parents - and possibly even a number of teachers. After all, according to John Van De Walle, lead author of “Elementary and Middle School Mathematics”, almost every commercial curriculum available teach using formal algorithms. He cites more than a century of tradition plus parental expectations as sources of pressure exerted on teachers to teach formal algorithms earlier than research would advise is appropriate. Van De Walle is a realist.  In view of the fact that students do not live in a vacuum it it probable that they will be exposed to formal algorithms outside of the school environment. His advice is to delay the teaching of formal algorithms in early grades if possible, but acknowledges that community and school expectations may make this difficult.

The issue then becomes, do we ignore the research (and there is much more than mentioned in this post)  and continue to teach “the traditional way”, or do we act upon it - in which case significant change is required in many classrooms?

A change of context might be useful here  - would we consult a doctor using established techniques practiced for over a century, or would we choose a doctor using newer treatments that have been found to be more effective?  When presented in medical terms  I suspect most would support research based practice. It is not so clear how people will respond to essentially the same issue when based in the educational realm.

Credits & references


Most sources cited in this post have an active link to the source. The exceptions are:

* Kamii & Dominick, 1997, “To teach or not to teach algorithms”, Journal of Mathematical Behaviour, vol 16, issue 1, 1977. (I have been unable to source a free electronic copy of this source - hence no direct link).

Van De Walle et al, 2010, “Elementary & Middle School Mathematics”, Pearson, Boston

Thursday, October 6, 2011

Schools - Formula 1s or 4X4s?

I’ve been thinking / reading about educational reform lately. What struck me was how little things have really changed over the course of my career.   With the exception of a few islands of excellence, many of the classrooms that I encounter on school visits are predictably generic – and demonstrate pedagogy enshrined in practice now for generations.  In fact, many of the people who helped train me would be able to dust themselves off (literally in some cases) and step into the role of a current teacher easily – despite being out of the classroom for decades.
How can this be? How is it possible that the technological advances in recent years have not transformed education?  Surely, when one considers the explosion of digital technology, the growth of the Internet and the transformation of society in general, schools surely must have changed?  Yet it is still possible to visit schools that almost seem to pride themselves on resisting genuine educational innovation.  Some schools use a shield of “educational rigor” to disguise the rigor mortis that defines their programs.

It occurs to me that schools are more like Formula 1 teams than Four Wheel Drivers. By this I mean that school teachers and administrators are hard working and dedicated people working towards a common goal – they pour their energy into their jobs and do so with great skill and commitment.  The same could be said for the Formula 1 teams.  Their goal is set – and it has been for years; to make their car go faster, to go from start to finish in the shortest amount of time possible.  They do this by making minute adjustments to their car – retuning the engine, changing tyre composition, modifying the aerodynamics  and generally tweaking the car to maximise performance.  The teams have been going to essentially the same tracks for years and years; season after season, lap after lap,  with one aim – to help get the driver from point A to point B faster than anyone else.

Contrast this approach with that of the four wheel drive enthusiast. The 4x4 car is well maintained and in good order.  Great care and concern is taken to ensure mechanical reliability. The difference is not in attention to detail – the difference is the destination.  The 4x4 driver is likely to try to go to new places by new routes – even if there is only a track rather than a road – and sometimes not even a track.  The fact that the journey may be over new or rarely explored territory adds to the allure of the trip. Being “better” simply has no relevance in this context.

In short, the 4x4 driver thinks about the destination while the Formula 1 team thinks about the process.
Our schools are now the equivalent of Formula 1 pit-crews  – hard working,  skilled, focused and putting large amounts of effort into making minor revisions that produce very small advances – if in fact they prove to be effective at all. The other parallel that strikes me is that Formula 1 cars are irrelevant in any other situation. You cannot take them on “the open road”, you couldn’t use them to get the shopping, or transport the family or do any of the other required functions of cars in the “real world”.  How many of our educational practices are limited in relevance to only the school environment?  If we are to break from the unproductive “reform” practices maybe we need to be more like the 4x4 drivers – work out where we really want to go and then do what it takes to make that happen.  

We need to have a serious look at the curriculum – not just in the sense that we re-badge or reorganise it. What do our students really need?  What is the best way we can provide it for them? What activities and projects will enable them to acquire the skills necessary for modern life and keep them engaged in the process?  How can we change education from something we do to students to something we do with them? What needs to change at the class, school and system level to enable this to happen?
There are many educational issues  that would benefit from genuine consideration and action including;
  • ·         What do our students want from their schools?
  • ·         What are we trying to achieve – in specific terms – with our students?
  • ·         What content should we have in the school curriculum?
  • ·         How do engage students in the educational process?
  • ·         How do we use ICT effectively in the classroom?
  • ·         How relevant is what we teach to our students?
  • ·         Is the curriculum ever-expanding like the universe –  or can we acknowledge that students can learn some things elsewhere and hence omit some aspects. If so, what can we cease to teach?
  • ·         What is the purpose and impact of formalised testing?
  • ·         How can we embed a growth mindset into students,  staff...and “the system?”

Of course, governments and education departments all over the globe have been “reforming” education for decades.  But, to return to my earlier metaphor, the mind set in use has been that of the Formula 1 team – “We already know the objective, let’s improve the process”.    However, there are other groups that have taken the 4x4 approach – and their alternatives to vanilla flavoured education are freely available on the labyrinth of the Internet.

To continue the motoring metaphor, before commencing any journey it helps to have a map so you can choose the terrain over which you want to travel.   The equivalent to that might be this site -   the Apple Classrooms of Tomorrow Today  and the associated PDFs.  The document isn’t exactly a road map – but it might help you work out where you might like to go – and provide some of the insights that might help you get there.

Photo credits:
4x4 on beach