Tuesday, January 26, 2010
In 1972 I took my first permanent teaching job in an elite Edinburgh secondary school. Just the year before, it had been a private school. James Gillespie’s High School (JGHS) always prided itself on its high standard of education.
A maximum class size was among many standards that JGHS maintained. It strove to have no more than 25 learners per class. The belief was that a finer relationship between teacher and learner could be attained. Through this practice, significantly better educational successes were achieved.
The number of scholars who left JGHS to take up business careers, or went on to higher education, was proof enough of this accomplishment.
It was a fantastic start for me as a teacher to be with classes of this size. But it was certainly no preparation for the learning environments that confronted me in teaching positions I took up after that time.
In 1974, I had a form class of 36 learners in a school that maintained an average class size of 35.
An elearning counterpart
Almost 30 years later, research into educational achievement through elearning methods suggested that there was an optimum size for elearning groups led by a teacher.
In any group of elearners, there will always be those who can be considered ‘active’ – others who learn despite their apparent inactivity in engagement with a teacher or facilitator – and those who are neither active nor engaged significantly in learning. Time has to be distributed fairly in attending to the needs and wants of each these groups.
An e-teacher who has more than 15 to 20 ‘active’ learners in a group is always extremely busy. When the number of active learners increases much above 20, strategies have to be developed and practiced to cope with the constant learner-teacher activity that inevitably occurs in those environments.
Symptoms of stress and exhaustion are inevitable in any teacher who succeeds in engaging enough learners so that the active group comprises much above 25. My own experiences of this have been confirmed by those of my colleagues teaching in e-environments similar to my own.
A recent experience
Recently, I’ve been actively engaging in discourse with groups of people in Second Life (SL). In the months that I’ve assiduously studied in this networking environment, the number of ‘friends’ in my Friends List has slowly increased. The size of my list is now well over 60.
Within that group is a sub-group of 15 to 20 friends who actively use instant messaging (IM) to contact me whenever I am online. It is a great experience to network with people in this way. Not all of this is done locally – that is to say, my avatar is not necessarily appearing on the same screen as the avatars of those who are IMing me.
Of late, I have found it difficult to be online while following any intended single pursuit. Two weeks ago, I became an ISTE docent, as avatar Kallan. In adhering to the expected commitment that comes with this office, I discovered that my group of ‘active’ friends caused me significant concern when attending to docent duties on campus.
At first, I was torn between being seen to be ignoring my friends, while attending to a duty which I enjoyed. Even sending messages of apology to IMing friends was an activity that I found distracting while attending to docent duties.
I’ve since learnt from other colleagues in similar SL situations that they often simply ignore the incoming IMs during the time that they are occupied with more immediate activities. Obviously they too have difficulty reading and responding to incoming IMs when engaged in other cerebral activity.
In translating this to the elearning environment, I can see clearly how a teacher can become stressed and overworked. There is the part that is played by commitment. There is also the aspect of prioritisation.
Who gets priority from the teacher in a learning environment?
When a teacher is actively assisting several learners together, how does she cope when a learner puts forward, out of the blue, a desperate plea for help?
What strategies can she employ to ensure that this learner, who may well be one who has never before communicated directly with her, gets the necessary immediate support?
What provisions must administration provide in a school to ensure that the number of active learners in a teacher’s group is kept to a manageable level?
How can administration ensure that teachers are not forced to adopt strategies to disengage themselves from needy learners in order to protect their own stress levels?
Friday, January 22, 2010
WARNING - The content of this post may disturb some readers.
The vagaries of censorship are mentioned throughout Hillary Clinton’s recent speech advocating Internet Freedom. Censorship is an action that often takes place behind the scenes. It is sometimes difficult to detect. You can be sure that someone somewhere will be confused, disturbed, annoyed, or even enraged when its occurrence is noticed.
Lately, printed news has come under threat. There is a belief that blogging might replace newspapers with a more up-to-date, less censored conduit. As well, the Web2.0 channel is purportedly a space for open debate and discussion.
Well, I wonder about all this. I believe that there is a place for censorship. Furthermore, my experience tells me that censorship is alive and well and is existing quite comfortably – in the blogosphere.
By the way, this post is not meant as a rant.
During my first month of blogging I was introduced to some of the technologies that permit a blogger to choose whether or not a comment is published. Comment moderation is such a facility.
Some blog applications can even permit the content of a comment to be edited, before or after it is published. Comment moderation also gives bloggers relief from the increasing nuisance of spammed comments.
Hand in hand with all this is the idea that, through the provision of comment guidelines, commenters can sometimes be given the opportunity to learn what is likely to be accepted by a blogger on his or her blog. (Here’s a link to mine.)
Comment guidelines give the valid reasons for the culling of comments that may be in contravention of the blogger’s guidelines.
But comment guidelines are not the only criteria that may be used by a blogger who culls a comment. Am I not entitled to delete any comment that appears in my list of comments to be moderated, whether or not it meets all criteria in my comment guidelines?
How could I be accused of any discrimination even if I do cull comments containing valid opinions other than those that are aligned with my own? Who’s going to know?
You might say, “But isn’t this still a form of raw censorship?” Well of course it is. It also stymies healthy debate and discussion.
Okay, I’m being a tad hypothetical.
Or am I?
My quality comments
Over the years that I have been actively commenting on blogs, I‘ve witnessed this form of censorship. Of all the hundreds (perhaps thousands) of comments that I’ve entered against posts on other blogs, there have been a significant number, through the bloggers’ discretion in comment moderation, that have never appeared on the Internet.
You could say that this is a reflection on the quality and calibre of my comments. Well, there are enough of them still left out there. Take a look and judge the quality and calibre of my comments for yourself.
But I have always been careful to note, when my comment was removed or excluded, if the blog had any associated comment guidelines that I may have contravened. Most bloggers do not provide comment guidelines. I put it down to raw censorship.
So you may think that the blogosphere is entirely a place for freedom of expression. Just check when you leave comments on posts that have comment moderation. You could be surprised at the proportion of your comments that never appear on the blogs you post against.
Tuesday, January 19, 2010
I took my daughters out for a coffee the other day. Just before we left, Hannah who is age 19 and the older of the two, stepped out of her bedroom looking like a Vogue model. I was charmed that she took time and effort to change before going out for coffee with her old dad.
“I like your outfit, especially the belt”, I said as we got into the car.
“Two dollars in a second-hand shop”, she quipped with a cheeky smile.
That’s one way a second year Art student at AUT demonstrates her creativity to the world – by choosing appropriate clothes to dress smartly on a minimal budget.
Did she have to study Art to express her imagination this way? Certainly not. Anyone can do it if they have a mind to.
But Hannah worked very hard to secure her place in her course at AUT. When she studied Art at High School, she created many different things. Not everything she did was as successful as she’d like it to have been. But she did it all the same. It all contributed to her portfolio – time after time.
- To me, the difference between the artist and the non-artist
is that the artist is the one who does it.
– Helen Garner
If a thing’s worth doing . . .
When my son, Jack, was to be married a few years back, I wrote a waltz in honour of his lovely Irish bride, Ailish. She had told me that she loved dancing to waltzes. As it happened, she liked the tune I wrote for her. I commissioned a local Irish dance band to play at the wedding.
A musician friend of mine who was a member of the band obviously didn’t like my waltz. When the band was rehearsing it under my supervision, he asked me why I composed stuff like this.
I explained that the alternative was that I did nothing at all. Then the bride would not have her own waltz for her wedding day. He quietly picked up his violin and played the music – beautifully.
Creativity has to be nurtured
- Creativity is so delicate a flower that praise tends to make it bloom, while discouragement often nips it in the bud. Any of us will put out more and better ideas if our efforts are appreciated.
– Alex F Osborn
The connection between Art and creativity is so intimate, it is almost impossible to define a difference between the two. One thing is clear, and that is that creativity has first to exist before Art comes into being. Creativity tends to be the easier to recognise, while identifying Art can often be an elusive and subjective assignment.
Schools have a big part to play in encouraging creativity in learners.
But they are not the only important influences, and this has been demonstrated by the work of some of the world’s greatest artists, many of whom were influenced by factors well beyond the precincts of the school grounds.
The importance of what is within us
The mind inhabits a complex organ. The self has to be nourished from within. Two undoubtedly brilliant artists in two discrete disciplines, who lived their lives in different countries and in separate centuries, had very similar views on what nurtures and brings out creativity from within. Check them out.
- Go cherish your soul;
set your habits to a life of solitude;
then will the faculties rise
fair and full within.
– Ralph Waldo Emerson
- When I am . . . completely myself, entirely alone . . . or during the night when I cannot sleep, it is on such occasions that my ideas flow best and most abundantly.
– Wolfgang Amadeus Mozart
Friday, January 15, 2010
- The area of the square on the hypotenuse of any right-angle triangle
is equal to the sum of the areas of the squares on the other sides.
I was hopeless at Mathematics when I began High School. Teachers despaired at my ineptitude. But I had a natural interest in Science.
It was mainly due to good Scottish teaching, and a genuine willingness on my part to engage in learning, that I studied Mathematics to a level that let me reach the highest academic levels in Science.
It was also due in part to the curriculum I followed. I believe that it taught me how to think. It wasn’t that it taught me to think. I could do that. It taught me how to think, and to be able to think in specific ways.
In the 1970s, I taught High School Mathematics to senior level.
Recently, I have become familiar with fundamental changes in the way mathematical thinking is taught in High School in New Zealand.
I suspect that these are similar to changes in the Mathematics curricula in other western countries.
Get it right
The Euclidean proof of the useful Theorem of Pythagoras was one of the things I had to learn for my early qualifying examinations at High School. My mother learnt the same proof when she attended High School.
Euclid’s proof was taught in New Zealand schools until changes were made in the curriculum towards the end of last century (20th). It is now supplanted by what I’d call a non-proof. What young minds are required to study about the Pythagorean Theorem in New Zealand today is certainly not a proof of it.
Euclid’s proof is based on the properties of rectangles and of triangles that are each of the same shape and size – as well as associated geometry ideas involving these shapes drawn between parallel lines. There are several hundred proofs of this fundamental theorem. Some are outlined in Wikipedia. A few I learnt at High School.
All of the proofs I learnt permitted me to understand, not only how the Pythagorean Theorem can be proved, but also what it is to know the significance of a universal proof. It is a way of thinking that permits a learner to appreciate that a proof needs to be watertight.
What does it prove?
Euclid’s proof can be applied to ANY right-angle triangle, not just a few special triangles. Therein is the difference between what used to be taught and what is now taught.
In High School today, a learner in Mathematics is instructed on how to show that a given right-angle triangle has the Pythagorean property. The instruction is not about any right-angle triangle, but applies only to a particular right-angle triangle that the learner draws.
Essentially, learners follow a recipe that shows that the Theorem may work for their triangle. It provides no real understanding of proof.
Here’s what they are instructed to do:
Learners in Mathematics are shown how to draw a right-angle triangle on a grid, using simple mathematical drawing equipment. They are also shown how to draw squares on each of the three sides of the triangle. By counting the number of grid squares that make up each of the squares, they can show that the Theorem is followed approximately.
While this recipe permits the learner to practice skills in using drawing equipment, it provides no understanding of a mathematical proof.
It does not even show conclusively that the Theorem works. However carefully it is done, not every attempt at adding the squares will show that the Theorem is precise. Check out the squares shown above.
One can argue over the need for the knowledge of how to prove the Pythagorean Theorem. But the significant learning is nothing to do with that knowledge. The thinking skills learnt that permit the learner to understand what a watertight proof is all about are really what are far more useful and relevant to higher thinking skills.
This is the whole point of teaching the proof. It has the potential to permit the learner to realise the significance of a theorem that can be applied universally, and why it has this property. It is a way of thinking analytically that is not being taught today.
Wednesday, January 6, 2010
At the beginning of last decade, I attended a session for teachers. The topic was pedagogy. There were about a dozen participants – teachers from early childhood through to senior secondary.
The facilitator asked that we consider what was meant by ‘pedagogy’. We each wrote a few sentences about it on a sheet of paper, to be read and discussed later in the session.
I was amazed at the diversity of ideas that were revealed. It seemed that from a significant group of teachers, no two had the same idea of what was meant by pedagogy. Some said it was to do with the lesson plan. Some indicated that it was about how things were taught.
A few spoke of proven teaching methods and theory. Others mentioned how the learner could be involved. Of course, it could encompass all of those and more.
But the miscellany of ideas brought forward was so varied that it was difficult for me to see any commonality among it at first. I wondered about this. I wondered that in a group of a dozen or so teachers, opinion about the meaning of pedagogy could be so disparate.
Pedagogy a practice
Fortunately, as the session evolved, things became more distinct. We agreed that pedagogy was to do with what was practiced and what was found to work best in particular learning situations. It was not some idea or strategy for teaching that was dreamed up on the spur of the moment. It does not work like that.
Pedagogy is the product of a cycle practiced by a teacher, and this has components that can be considered as part of an action research cycle: theory and recognised practice – planning – application – evaluation – reflection.
Wikipedia explains pedagogy as “strategies of instruction” and “the correct use of teaching strategies”. It gives the literal meaning from the Greek as, “to lead the child.” This description suggests a definite focus on how to go about teaching a young mind.
I usually have adults in my cohort of learners. Some of them are at least as old as I am. Is using pedagogy appropriate when teaching adults too?
Elearning resources and pedagogy
Certainly, pedagogy has to be involved when digitally created resources are being chosen for a learner – scaffolding – level – cultural appropriateness – timeliness of use. It could be argued that this is when the ultimate pedagogical decision is made – whether to use a resource or not, and if chosen, how it is to be used.
What relevance does pedagogy have in the creation of digital learning resources – of the type that may be designed and built by an instructional designer? Is pedagogy any use to the instructional designer? Should its application be restricted to the realm of the teacher?
The construction of a resource and its pedagogical usefulness does not happen by chance. If it is sound enough for a teacher to contemplate its use when applying correct pedagogy to a learning situation, then it follows that a fair amount of pedagogy also has to be considered when the resource is built.
What components of pedagogy also contribute to the considerations that are part of the creation of a resource? What pedagogy is appropriate? How much should involve both teacher and designer when pedagogical considerations are being made? What, if any, should be left to the teacher?
Sunday, January 3, 2010
I thought I’d start the year off with a colourful post. I’ve been doing some building in Second Life (SL) recently. I got stuck when I came to interpreting how the colour codes work when scripting some effects.
Perhaps I should explain for those who are not so familiar with SL.
All of SL, including the avatars that frequent it, is constructed from what are known as prims, or ‘primitives’ – polygonal three-dimensional shaped objects, like the ones Kallan demonstrates here.
Of course, not all that can be seen in SL is made entirely from these primitive shapes alone. They can be distorted by an effect, called sculpting, to reshape, or ‘tortured’ by changing their shape and size by other means.
Painting things in SL
Colouring, or painting prims can be done in at least two ways. Choosing a single colour by using the colour picker, is a way of painting. The S-shaped sculpted sphere, above, was coloured this way.
Another is selecting a texture, which is really an uploaded image, and using this to give a defined pattern or intricate detail to the prim.
The picture here shows my friend Lara Nguya wearing a pendant that is decorated and coloured using this texturing method.
The standard RGB colour code is used. Each colour is defined digitally (8-bit) by its Red, Green and Blue components – shown as numbers between 255 and 0, in so-called vector arrays.
The code for white is (255, 255, 255) and for black is (0, 0, 0). All other available colour combinations in the colour picker occur as permutations between these two vectors.
One way of imparting effects to objects in SL is by using scripts. In Lara’s candle, for instance, she uses a script that gives the wick the effect of a flickering flame.
When it came to scripting, I was completely baffled at first by colour codes and how they worked. Lara, showed me that an arithmetical code is used in scripting – different from the 8-bit coding used for colours in non-scripted prims.
The arithmetical code embraces a similar RGB range of colours, with some minor limitation in the range of hues available.
The RGB components are represented by numbers between 1 and 0, instead of 8-bit digital numbers between 255 and 0.
An easy conversion
Lara explained it to me this way:
Whereas 255 is the maximum number allowable in the 8-bit digital code, the corresponding maximum number is 1.0 for scripts and for some other uses in SL.
This means that any RGB code has to be converted to the equivalent code before it can be used in a script. The numbers in the 8-bit digital codes must be divided by 255 to be corrected for use in scripting.
The code for white used in script becomes < 1, 1, 1 > and the script code for black becomes < 0, 0, 0 >.
(48, 128, 20)
The arithmetic in the code conversion for sapgreen is as follows:
- 48 converts to 48/255 = .19
128 converts to 128/255 = .50
20 converts to 20/255 = .08
So sapgreen 8-bit digital code (48, 128, 20) becomes < .19, .50, .08 > .
Another example is blueviolet. Its 8-bit digital code is (138, 43, 226). The code for the colour used in script is < .51, .17, .89 >.
The same process can be used for any other colour expressed in 8-bit digital code.
I am grateful for assistance and advice given to me by Lara Nguya.