The area of the square on the hypotenuse of any right-angle triangleis equal to the sum of the areas of the squares on the other sides.Pythagoras' TheoremI 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 rightThe 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.Higher thinkingWhile 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.

CRDF Global is an "independent nonprofit organization that promotes international scientific and technical collaboration." CRDF Global was authorized by the U.S. Congress in 1992 under the FREEDOM Support Act and established in 1995 by the National Science Foundation. This unique public-private partnership promotes international scientific and technical … Continue reading →

Mathieu d’Aquin (The Open University, UK) is one of the world’s most able experts in artificial intelligence, he had created a report "Linked Data for Open and Distance Learning" for the Commonwealth of Learning. The purpose is to utilize Semantic Web mechanism to help educators find the needle they want in the haystack of options.... Read More ›

As many of us will agree, one of the greatest things about the Web is its openness. And this rings true for many of the social networking sites in use - notably through the use of APIs that enable other web services to interact with them. However I feel this could start to become their downfall.....I'm starting to think that the abundance of services connecting to the likes of Facebook and Twitter could be a problem. For example, my nephew recently set up his new games console over Christmas, and I noticed the options to link to Facebook and Twitter. The device can then share information about your gaming activities with followers on the sites - 'Charlie played Fifa2014', etc. Other similar examples include the auto-sharing of: blog posts (Blogger & Wordpress); photographs (Blip & Instagram); progress in certain games (Candy Crush); and people's physical workouts (Nike+). In fact this list could be endless! Of course many of these services can disable the auto-sharing but many people don't. In fact, people actively link such services to social media sites so that they can share the information. I do. And in these early days, this model is working well - after all, I only looked at and engaged with Blip through seeing updates from the likes of +Sheila MacNeill. Success?Moving on, there is a well know (and contested) saying for digital business models, that says 'If you're not paying for the product, you are the product'. What I fear may be What is happening to the social web, is that those people who engage with the likes of Instagram, Blogger, Nike+ and Candy Crush, are the greatest marketing people the companies could ever employ! And they get it for free, whilst building multi-million dollar empires! And the users of Facebook and Twitter are the target demographic - bombarded with advertisements whether they like it or not. Facebook are taking things to a completely next level though, by deciding which of your friends can see your updates - I came across the video clip at the bottom via +Alan Cann 's post 'When Social Media Stopped Being Social', and found it fascinating. You should definitely watch it!So what will happen to our activity on sites like Fb & Twitter? Either, we won't pay much attention to our activity streams because it's bombarded with advert type updates, or we'll just stop using those sites altogether. As such, I fear the worst for the very same services that have revolutionised the Interweb! The Reed Diaries by Peter Reed is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License

The use of e-learning in NGOs is increasing dramatically, like in any other type of organization. It is mostly thought as a mean to train the employees, volunteers and partners. However, creating and sharing online courses can also help out … Continue reading →

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-artistis that the artist is the one who does it.- Helen GarnerIf 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 nurturedCreativity 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 OsbornThe 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 usThe 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;expel companions;set your habits to a life of solitude;then will the faculties risefair and full within.- Ralph Waldo EmersonWhen 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

[republished from my 'work' blog at http://hlstel.wordpress.com/ ]Ensuring quality when introducing technology to support and enhance learning and teaching is something that often slips our mind. We tend to just get on with our plans without going out of our way to specifically consider quality assurance, so this post hopes to raise a couple of things to help make sure students are at the forefront of our plans.ILT QA for online CPD documentQAA Code of PracticeThe Quality Assurance Agency published their Code of Practice back in 2007, with a particular section on 'Flexible and Distributed Learning' (FDL). Whilst in technology terms this was a long time ago, it's still very relevant and a great thing to consider when introducing elements of technology. My only criticism is that it's very wordy and 'fluffy', so I've put together a 1 page version (particularly with our online CPD work in mind, but more broadly relevant) which I think makes it more accessible. Taken as a kind of 'Good Practice Guide', I think this could be useful for colleagues.Access the guide here, or the original via the QAA Website. Blackboard Exemplary Course Programme The Bb ECP is a really interesting initiative run by Blackboard. I was first made aware of it by an Mark, an old colleague at Edge Hill University, who done particularly well in last year's awards.Blackboard provide their ECP Rubrics which enable course designers to work towards. This not only helps ensure high quality provision, but can also win some awards and get an invite to the Blackboard World Conference in Las Vegas!So what now? Well if you have any questions about any of this, or just want a discussion about these issues, feel free to give me a shout. I'd love to work with people aiming for those awards! QuestionsAre these the most effective resources for assuring quality in TEL?What other resources do you use?These might be good for maintaining a baseline, but what about more adventurous uses of technology?As (online) education evolves, are these still suitable?Are these resources applicable to things like MOOCs?Peter@reedyreedlesThe Reed Diaries by Peter Reed is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License

Continued from Linked Data for Open and Distance Learning - Part 0… What is Linked Data The foundation of the Web is that it is a network of documents connected by hyperlinks (see Figure 1a). Each document is identified by a Web address, a URI (Berners-Lee et al, 1998), and might represent a document which content... Read More ›

Kristiina Pääkkönen, the Country Manager of FundedByMe in Finland, just launched a new course about crowdfunding on Eliademy. We are glad to republish the article she wrote on LinkedIn: New online course: How to start crowdfunding When I met Daniel Daboczy … Continue reading →

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.ModerationDuring 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.Biased opinion?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 commentsOver 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.