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