## Thursday, 12 August 2010

### Math, Moodle and Costing Choice

The blame for this post comes from my Synergy Learning colleague @jonbolton, who asked if I was going to next month's eAssessment Scotland conference (on September 3rd in Dundee, if you're interested. And it's free!)

As is usually the case when an great event like this is brought to my attention I've sadly already agreed to be somewhere else. The seminar I would very much have liked to have joined is being presented by the University of Birmingham's Chris Sangwin: Automatic e-Assessment of Mathematical Word Problems (STACK). Chris has been doing some great work with computer aided assessment (CAA) systems for mathematics. The result of this work is STACK - System for Teaching and Assessment using a Computer Algebra Kernel.

And what's great about STACK is that it fully integrates into Moodle. Click here for details.

How to make marking algebra homework a nightmare for teacher

Imagine you've completed the first question of your math homework and the answer is 3x+4. Part of the reason your math teacher wants you to write down your answer as 3x+4 (i.e. in that order) is that if all the class has written their answer with the term in x first then you don't have to confirm the math, you can just visually check that the answers are laid out correctly. But say a student has given their answer as 4+3x? It's still mathematically correct (albeit against the usual convention of writing linear expressions in the form something times x plus a constant) but, because we aren't really attempting to check the math - just the way the answer is laid out (lazy, I know) - then it's all to easy to accidentally mark an answer as incorrect when it is, in fact, right.

My example of 3x+4 is a fairly trivial linear expression. What about a quadratic? If the answer is x2+4x+4 then my student could have written that... or (x+2)(x+2), or (x+2)2... you get the idea. All are mathematically/algebraically equivalent but having to check the math for every question you're marking can become a bit of a chore.

Which is why, in exams, questions are usually very specific about how you should answer a question. For example "factor/factorize completely" or "write your answer in its simplest terms" or words along those lines.

I always get asked what the right way is of answering such-and-such a question and, to be honest, outside of an exam, I'm not that precious about it. If I'm giving one-to-one tuition in their home my usual answer to a student will be "Well, I could have come to your house by car, jet pack, helicopter. I could have come straight here, gone via Scotland (I live a long way from Scotland)." In fact I could have gone round and round the world three times. As long as I get there, and as far as the student is concerned, it really doesn't matter.

So what decides which route I take? What decides which mathematical method we should use? The answer is cost. Cost (in the accounting/economics/project management sense of the word, i.e. in the "cost benefit analysis" sense) is all about taking the most effective choice within known constraints. I tell my students to chose a method (i.e. make a choice) that they feel most comfortable with. A choice that, when they are actually doing the math, they feel they are less likely to make a mistake. That, for them, will be the most cost effective route through the problem. It's a very common project management approach (effectively the one we're using for the international Moodle rollout I'm currently working on) and it can work wonders in math teaching.

A worked example

In the best traditions of math textbooks, let's explore what I mean about choices having a cost with a worked example. Chris included this poser in his abstract:

In a railway journey of 90km an increase of 5 kilometers per hour in the velocity decreases the time taken by 15 minutes. What is the velocity?

I thought it might be interesting to work through this problem but to also explain, in terms of cost, why I personally would use particular math techniques.

I know this is probably going to sound geeky but the elegance of algebra really appeals to me. Expressing a problem in algebraic terms is going to be, for me, the most cost effective. Once I've translated the problem into algebra I'm going to continue with the algebraic approach and solve any equations I can construct to find the unknowns.

What about the less algebraically inclined? Well, if you got as far as coming up with equations you could plot them and see where the lines or curves (or whatever - I don't know yet) cross. That, of course, depends if you're more graphically motivated.

If you happen to know that speed/velocity (there's more on the difference further on in this post) is given by dividing the distance travelled by the time taken to travel that distance then there is yet another good way... but, unless you're lucky, it could take you some time. That is the way of trial and improvement (basically trail and error): take a guess and work in small steps from there until you get at least a good approximation to (or at best the exact value of) the answer.

For those that are interested here are the steps I took:

1) The units aren't SI units. Convert distances into metres and time into seconds.

90km is equivalent to 90000m
15 minutes is 900 seconds
5 kilometers per hour is 5000m in 3600 seconds. That simplifies to 25 eighteenths metres per second.

Reason: well, basically that's the professional physicist in me. If you want to know what happens when people who really should know better don't convert their measurements to standard units then read this.

2) Use speed equals distance divided by time relationship...

We rote learned this one when I was a budding young physicist in science lessons at school - so one could argue that either you know this or you don't.

Reason: two aspects here to consider. One is that experience tells me because this is a "speed/distance/time" question so use the "speed equals distance..." relationship. Second is that I also rote learned two unknowns takes two equations.

This is knowledge in my head. How it got there was, as I say, and rightly or wrongly, rote learning.

3) ... to construct two equations

Firstly... assign some letters: 'v' for velocity and 't' for time. My two equations are

t=90000/v

and

(v+25/18)(t-900)=90000

Reason: That takes an understanding of rearranging equations, for example v=d/t can be written as vt=d. To do that we just need to understand that '=' means everything on one side is the same as everything on the other and, because of that, everything you do to one side you've got to do to the other. Emphasis of this last point is criminally (I think) missing from a lot of basic math teaching in the UK.

3) Substitute the first equation into the second

Remember that, although I have two equations with two unknowns, what ever the values of v and t in the first equation they have exactly the same value in the second equation. They are, in the trade, simultaneous.

Now I have just one equation... with no t in it, just v:

(v+25/18)(90000/v-900)=90000

Reason: I'm in my algebraic comfort zone.

4) Multiply out the brackets

How long have you got? There are lots of different ways of multiplying out brackets. There's FOIL (first, outer, inner, last), the "box" method - where v+25/18 is the length of one side and 90000/v-900 is the length of the other and the area of the box is the area of four smaller boxes added together (if you're familiar with it you'll know what I mean). My method of choice is "happy smiley face"... I guess because *cough* I'm a happy, smiley kind of guy...

I end up with

90000-1250+125000/v-900v=90000

which, with a bit of algebraic tomfoolery, I can manipulate that into

900v2+1250v-12500=0

Why write it in that form remembering that I can write it however I like?

Reason: now it's a quadratic I can solve it using the quadratic formula.

5) Put the numbers through the quadratic formula

In fact I end up with two numbers, one positive and one negative. Can I can ignore the negative velocity? (Your author puts on his best James Bond 'Q' immitation) Now pay attention 007...

A negative speed doesn't make much sense but a negative velocity might. Speed is a scalar quantity but velocity is a vector. A negative velocity means you're going the opposite direction. However, in the context of this question the negative solution can quite happily be ignored.

So...

If you substitute a=900, b=1250 and c=-125000 into the quadratic formula you end up with a positive answer of 11 and 1/9 metres per second. That's the equivalent of 100/9 times 3600 metres every hour, or... to cut a long story short... 40km per hour.

Don't just give the answer. If you have time (and more so if you're not feeling very confident of your result) justify your answer.

How long will it take to travel the 90km at 40km per hour? The answer is 8100 seconds.

How long at 45km per hour? That works out to be 7200 seconds.

That is a difference of 900 seconds, or 15 minutes. That gives us good justification that our answer is correct*

Conclusions

How did you get on with Chris' problem? Which method works best for you? How do you measure the cost of a given mathematical process? I'd be interested to know what you think.

Is measuring the cost of choices before you in a project your method of managing a project? I'd be interested to hear about your experiences.

*Note that I'm not going to claim I was 100% correct. I might have made a mistake in my justification that wrongly proves an incorrect result. Again, it's the scientist in me: by showing you my working I'm hoping that any mistakes will be picked up by you - my peer reviewer, as it were. Don't hesitate to let me know if you think I'm wrong.

## Friday, 6 August 2010

### Target Your Audience

I was in a fascinating conversation yesterday with the group marketing manager for one of my clients. We were talking about the design of web pages.

He was outlining how they were monitoring web traffic so that sales could target specific clients with specific information. For example, imagine I'm trying to sell you Moodle services. I want to target you with information on how I can help your school. So I create a web page with links to examples on using Moodle for teaching different subject areas. You click on the links to see what I'm offering. As a supplier, once I know which subject areas seem to interest you, I could target my sales pitch accordingly.

For instance, I've included an image of a 3D representation of a molecule that's taken your interest and you've clicked on it. Are you interested in multimedia? We can create another page containing more information on including multimedia content in Moodle. In subsequent interactions we can find out if it is actually science you are interested in by monitoring what pages you have visited, what links you have clicked on, even how long you have spent on a particular page.

Of course, why not just ask the question "are you interested in teaching science with Moodle?" Well, there are a number of problems with this approach. For instance, I might inadvertantly offend cultural sensibilities - especially when dealing with a worldwide audience. I might come across as being too blunt in my approach (it's easy for your motives to be misunderstood at the best of times but seemingly more so when the interaction is online). More importantly from a sales point of view, however, is that our potential client who's being asked that question might not actually be aware that they are interested in teaching science with Moodle. In other words: if you were that potential client then you might well be interested in the tools to teach science with Moodle... you just didn't realise it yet.

For example, I'm a theology instructor (which I'm not - I was just trying to think of a discipline that wasn't science but it probably isn't a good example) teaching about evolution: I dim the lights slightly and use the Moodle Jmol plugin to display a large, slowly revolving 3D representation of a water molecule on the interactive whiteboard. Then I start to teach...

"What is truely remarkable about that molecule on the board is that the angle between the hydrogen atoms is exactly 104.5 degrees. That means that when water molecules join together they form a solid (ice) that is less dense than the liquid. This means that if water freezes then it doesn't sink: it floats. If ice sank then everything living under it would die. Do you think the water molecule looks like that by chance [I point back to the large, slowly revolving water molecule on the board] or by design?"

See what I mean?

If you and I were trying to sell Moodle services then you can see how this approach to designing and managing our online presence is going to be far more successful than just putting up a few web pages telling our site visitors how great Moodle is and then crossing our fingers.

To discuss the care with which this particular client studies, and follows up, the interactions that take place between their online presence and their (potential and current) clients was extremely informative (in all honesty, it's probably that level of attention to detail and presence of thought that might help explain why they lead the world in what they do).

Are you a teacher running an online course in Moodle? If so check out the Reports link in your course administration block.

In exactly the same way my marketing colleagues would want to drill down to see how clients interact with the online collateral and target their sales pitch accordingly, you too can see how your pupils are interacting with your teaching materials and provide just the right kind of support and guidance.

Stick with me a few moments more because another fascinating point came out of this discussion: I was thinking about @Moodleman Julian Ridden mentioning in the excellent Moodle Mayhem podcasts (here) about tackling a teaching colleague on having lots of animated GIF images in her Moodle course (if you haven't heard those podcasts then you really must: there are two and they're excellent).

In fact what the guys in marketing have also been investigating is how their clients interact with static images and animations on web pages. For instance, they've found that if you have a static image of a book, clients are far less likely to click on that than if the icon was animated - e.g. the pages of the book start to flick open by themselves. They've also been looking at delaying the animation, e.g. for a second and a half or two seconds after the page has loaded, before the book flicks open. Then users are much more likely to click on the book.

Can we likewise take our students on a particular journey through our courses by the clever use of "visual cues"? Would we want to?

Do we, by using visual or audio cues, inadvertantly take our learners to specific resources without realising it? This is just one of the questions that has come out of the work of Dr Richard Clark (learn more here).

Have you tried investigating how your students interact with your courses using the Reports function in Moodle? Have you tried using visual cues to guide your students through a Moodle course? If you have then I'm interested to hear your experiences.

## Thursday, 5 August 2010

### Moodle Chemistry

Today I've been prompted to write a short post on how to render complex (i.e. math and chemical) notation in a Moodle quiz.

@lasic retweeted a question from @betchaboy:

"Way in Moodle to use rich text in m/c [multichoice] quiz answer choice? Need to offer chem. formulas with subscript as option."

You would be forgiven for thinking it looking at the relatively small edit box you use to specify your multichoice answers but (as the developer responsible for Moodle's quiz engine @tim_hunt later confirmed) you can actually type HTML in there (the only reason why the HTML Editor isn't displayed is that a pretty long page web page would be rendered even longer - the multi-choice scroll of death becoming even more deadly). The image below demonstrates what I mean about the small edit box...

My solution, rather than using HTML, would be to use LaTeX.

Those of us of a certain age (*cough*) predate these new-fangled "what you see is what you get/WYSIWYG" text editor whatsits. We had to use a typesetting langauge. The language of choice - certainly in the science and math community - was (and in some instances, thinking of University of Birmingham here in the UK, still is) LaTeX.

LaTeX is pronounced "lah-tek" or "lay-tek", depending on who you speak to (more details here).

Speak to your server/Moodle administrator about getting LaTeX installed on the server and the Moodle TeX filter enabled (see http://docs.moodle.org/en/TeX_filter for details). Make sure you have TeX properly configured. Check that your LaTeX isn't being rendered using the Mimetex filter - for no better reason than Mimetex only recognises a subset of TeX and the output can look a little jagged. See this discussion thead on in the Mathematics Tools forum on Moodle.org for some tests you can try: http://moodle.org/mod/forum/discuss.php?d=120418. For the more technical readers, you'll also witness me having a strange configuration error on one of my servers.

Here is a multi-choice question on the Haber Process:

How did I write those equations in the answer edit box to make them look so neat?

Well, the correct answer...

...is actually written in the answer edit box like so:

\$\$\textrm{N}_{2(g)} + 3\textrm{H}_{2(g)} \leftrightharpoons 2\textrm{NH}_{3(g)}\$\$

That may seem horribly complicated (and I'm challenging you with a technically difficult example) but, rest assured, once you learn some of the basic typesetting commands it can become extremely powerful way of arranging/typesetting your text. Check out http://docs.moodle.org/en/Using_TeX_Notation for more details.

For more details on LaTeX, how to set it up in your Moodle, and how to typeset complex notation using LaTeX then definitely visit the Mathematics Tools forum on Moodle.org (http://moodle.org/mod/forum/view.php?id=752).

Are you a LaTeX user? Do you find it easy or difficult to typeset mathematical and/or chemical notation using LaTeX? I'm interested to hear from you.

PS I don't want to be accused of plugging one of my books but I go into detail about configuring Moodle to support complex notation in Moodle 1.9 Math - including how to integrate the excellent DragMath drag-and-drop LaTeX editor into Moodle.

## Tuesday, 3 August 2010

### Smile... Changing Moodle's Default Emoticons

Just following up from my previous post about engaging learners and Richard Clark's keynote at #mootustx10, I have been pondering the use of emoticons in Moodle courses. When I'm giving Moodle training sessions I always make a point of showing delegates Moodle's emoticons and here's why...

A few years back I had to give some pastoral support to one of my students who was in tears because of something that was said by one of her friends on her Facebook wall. My immediate reaction was to tell my student to give her friend a call on her mobile. "I can't do that - not after what she's said" was the response. The situation quickly resolved itself when we could bring the two girls face to face. I can't even remember what the Facebook conversation was about but what caused all the upset was just two words: "yeah right".

Try saying "yeah right" to yourself positively - with a sing-song, shrill intonation.

Now try saying "yeah right" negatively - with a deep, sarcastic intonation.

Very different.

Do the same but now also imagine looking at a happy, smiling face (say a close friend) happily saying "yeah right" and a dark, angry face (perhaps someone you don't particularly get on with) for the slow, sarcastic, negative "yeah right".

The contrast between the two is even more pronounced: it's very, very different

One way of overcoming this problem is to use 'smilies', or 'emoticons', in your text :)

The only issue I have... and I guess this is personal preference... is that Moodle's default smiley set is not very expressive. I have a set of animated (but not too busy) emoticons I use in my Moodles and I'll describe now how you can switch over to using them - or, of course, a set of your own.

1. Locate the folder containing the smilies Moodle is currently using. This is usually the /pix/s folder. Note that custom themes can also contain custom smilies so you might need to also look for /pix/s in the theme folder for your custom theme. Make a backup copy of the 's' folder (e.g. 's_back') and replace the emoticons with your set.
2. You might have guessed that the emoticon file names are used to identify what the icon represents so the next step is to rename the files accordingly (you can specify the names in Moodle's source code but this way is easier).

You might need to resize the Insert Smiley dialog. Here's how:

1. Look in /lib/editor/htmlarea/ for the file dialog.js and make a backup of this file.
2. Search for the line beginning case "dlg_ins_smile": x = and alter the x and y numbers accordingly (check out the copy of dialog.js in the sample files and see how this differs from your original dialog.js

Do you want to include extra smilies in the Insert Smiley dialog?

1. ...if you do then it is best to copy your new emoticons to /pix/s. We'll definitely need to make changes to Moodle's core code (don't worry: it's not complicated) and that will pick up files from /pix/s - as well as in custom themes - if you switch to using one of Moodle's standard themes, e.g. standardwhite.
2. Look in /lib/editor/htmlarea/popups for the file dlg_ins_smile.php and make a backup copy of this file.
3. Search down dlg_ins_smile.php for the line \$emoticons = array ( 'smiley' => ':-)',
4. At the bottom of the \$emoticons array add references to the extra emoticons you want to include (again, see the example file for details).

If you're complimenting Moodle's smilies with some of your own then you'll also need to modify the help files for your language:

1. Look in /lang/*your language*/ - for example /lang/en_utf8 - for the file pix.php. This contains the emoticon "tooltips" - the helpful text that appears above an emoticon when you hover the mouse over it. Make a backup copy of this file.
2. Add new tooltips for your extra smilies to the end of pix.php (the the sample files for an example).

If you already have the HTML editor open in your browser then refresh the page, press the insert smiley button and your new emoticons will be displayed. Try inserting them into some text:

Reconfigure the HTML Editor

The editor can recognise ASCII emoticons and replace them with GIF images. We can, if we wish, include our newly specified smilies.

1. Ensure you are logged in as a Moodle administrator. From the Site Administration block click on Appearance HTML Editor.
2. Add your new emoticons to the list. The desired ASCII smiley is specified on the left and the name of the GIF image (not including ".GIF") is specified on the right
3. Press the Save Changes button at the bottom of the page and you're done!

More ideas

In December - in the run up to the festive season - I switch to using a "Santa" smiley set - bascially the emoticons you can see in the previous screen captures but all wearing Santa hats.

Further Thoughts

Have you ever had experience of your students reading a comment online and taking it the wrong way? How was the misunderstanding resolved?

### I'm Listening... Creating a Rapport

There is yet another great article on Moodle News (if you haven't signed up for their tweets/feeds/emails then you really must). This is a recap of Dr Richard Clark's Texas MoodleMoot keynote speech "Failure of Constructivism", here.

I found the issues raised by Dr Clark absolutely fascinating. Two items caught my eye. Take a look at the list of 11 tips for increasing the effectiveness of online learning. Item 10, "human voice is always better than mechanical narration" is one. But the statement I've been reflecting on is:

adjusting instruction for different learning styles does not increase learning (accommodation = fail)

Tomaz Lasic has just today asked this question on Twitter:

If there were a 'scientifically proven' best way to teach but clashed with your style/values, would you change? Why (not)?

To which I answered that it basically depends on my audience. I'll change my manner of teaching depending on the rapport I have with the class. What do I mean by that? I'll try and explain...

I was involved in some sales training when I was younger and I found it interesting that salespeople (at least those in the UK) tend to have a standard approach when meeting new clients. Here are the standard steps:

• Full-on stare your new client in the face and say "Pleased to meet you I'm XXXX [complete as appropriate]"

• Quickly follow up wide-eyed stare with (usually over-) firm handshake

• Thrust business card over to client

• Immediately proceed with demonstration of product (either virtual - read "PowerPoint" - or actual)

It's not particularly slick and it rarely works. So how should you do it?

As any successful salesman will tell you, the very first step is engage your potential client in an interaction, usually a conversation. If it's a conversation you've started then you can then look for the predicates in the sentences they use - specifically looking out for visual, auditory or kinethesthetic (emotive/emotional) representations. Don't worry: this isn't Neural Linguistic Programming, but the deep underlying principle is roughly the same (based on work by Chomsky, Jung et al.). Let's see how this might work in practise.

Imagine the following interaction:

Pupil: Sir, I was listening to what you were saying earlier but I didn't really understand what you meant about denominators. What do you have to do with them?

Teacher: Have a look at the board. Can you see how I've multiplied them together?

Pupil: Erm... not really. I couldn't quite hear at the time so I didn't know what you meant.

Teacher: Look at the numbers on the bottom. Can you see that you need to multiply them?

Pupil: No. It doesn't matter. I'll have another go. Thanks anyway.

The pupil feels let down by the teacher because they don't feel like they've been understood. The teacher is left feeling frustrated that they didn't get their point across. What went wrong in this interaction?

If we were a salesperson then we'd be thinking about the language the pupil and teacher used. Have you noticed that they are, at this moment, using completely different representations - the pupil is hearing what the teacher is saying, the teacher is looking towards what's represented on the board. Personal chemistry between the pupil and teacher aside, there is very little "linguistic rapport" in the language the teacher and pupil are using to interact with each other. If the teacher had used auditory words rather than visual ones would the teacher have been better able to put their point across?

It seems to work for me but I'm not sure how you'd test such a pragmatic approach scientifically.

The best salespeople will sell you something you didn't know you wanted at a time you don't need it.

To my mind that very much applies to being a teacher.

So... have you been paying attention at the back? Here's a test:

What kind of language have I used in this short piece? Is it visual, auditory or emotive? What would be the best way of attempting to sell me your idea? As ever: I'm interested to know what you think. I'll post a followup on this later in the day.

## Monday, 2 August 2010

### In Pursuit of Happiness: Open Learning in Moodle

Have you read the latest post on Dave's Educational Blog? If not then you should. It's here. Like Dave I am very interested in the notion of open learning and how groups of students learn together (on-line or in the classroom).

If you've read Dave's post then Hypothesis 7 I found particularly interesting: "Print controls our learning". The assertion is that the "historical roots and technologies of print have a profound and controlling influence on how we see education".

What intruiged me about this assertion (putting my Chomsky hat on for a moment) is the visual nature of the language used to express it. To the central point: is print a barrier to learning? As ever, that depends. As anyone reading this or Dave's blog using screen access software (e.g. Windows Narrator, JAWS, Supernova, etc) will tell you: you don't need to be able to see print to gain access to information. You need access to the technology. The printed word, after all, is a technology. Yes, there are ways of representing language in touch (Braille, blister paper) but - certainly as far as the UK is concerned - Braille readers represent a small fraction of the visually impaired population. Those visually impaired students I work with learn by being spoken to and from speaking to each other. The only communication medium available to many is language, thoughts, truth and logic represented in speech (often US English speech to boot). To the use of lanugage to express the sentiment: I'm wondering if it would be better using the word "experience" rather than "see".

Can there be such a thing as an "open" learning platform? How vital is an instructor to the learning process? This had me thinking about...

The Three Steps to Open Learning and Eternal Happiness

Step 1: Yay! My college runs a dedicated happiness course...

I'll click on that now.

Step 2: The secret to eternal happiness is only a click away...

Nirvana here I come...

Step 3: Oh hum...

How do you resolve the contention between providing a truly open learning platform and wanting to manage users in your Moodle? What do you think? Have you managed to create a fully open learning platform? I'm always interested to hear your thoughts.

## Friday, 30 July 2010

### Can't See the Wood for the Trees

Yesterday my colleague and I were contemplating general web design - in advance of designing new Moodle themes for a Moodle hub we are working on. The conversation ventured off into looking at web themes in general and he showed me the wonderfully elaborate theme on Web Designer Wall. We wondered if this was a WordPress theme or not...

And we searched and searched the page and couldn't find mention of WordPress anywhere.

We both looked at each other convinced that this must be a WordPress blog. When we looked back at the screen there it was: a large WordPress icon in a box about half an inch high by an inch and a half long - containing "WordPress" in big letters.

How did we manage to miss that?

Have you ever lost a piece of paperwork on your desk only to have a colleague come along and point to it right there in front of you? I don't mind admitting that it happened to me the other day. How did the paperwork come to be invisible (at least to me) until someone pointed their finger at it?

I've had a long interest in cognitive psychology - and especially the design of user interfaces both screen-based and otherwise.

If you haven't listened to the interviews with @moodleman Julian Ridden on Moodle Mayhem then a) you should because Julian knows his stuff and they are fascinating listening and b) Julian talks in detail about the design of the Quantum Riverview E-Learning Portal. Umm... should that be a), b) and c)?

What interested me about the Moodle Mayhem discussion is that Julian mentioned he'd put all the blocks on the right and the main content on the left because English readers have a left-to-right reading order (as above). That set me thinking: would this affect the way a user would interact with the site?

I'm a big fan of the research carried out by Donald Norman - author of one of my favourite books The Design of Everyday Things. Basically Norman asserts, based on his research, that users seek "cues" (typically "visual cues" but they could be audio cues) based on the task they want to carry out.

Then there is the notion of actually reading from left to right...

Those who know me will be aware that I worked for a time with the blind and the visually impaired. Braille readers are actually few and far between but the remarkable thing is that in just the same way we read ahead as we read a sentence (less confident readers don't manage this as well which is why children's reading sounds... so... stilted) so Braille readers will actually read with two hands - the leading hand reading ahead. I guess the same is true with music sight readers (hats off to my mother-in-law who can play the piano like this). Check out the interesting work done by Thomas Wolf in the 1970s here. Wolf suggested there are (I guess obviously) lots of cognitive processes going on - perhaps the most powerful being pattern recognition, interestingly. Though again, with music, this is left-to-right reading order.

Have you tried speed reading? If not then the idea is that you open the page of a book, place your finger in the very middle of the page under the first line and focus your sight in the middle of the page as you drag your finger down it (your eyes following your finger down the page). The idea is (and I'm not sure how efficacious this actually is) that your peripheral vision will recognise word patterns - or the sense of the patterns - and you'll be able to get a feel for the content without having to read it properly. That doesn't involve scanning from the left to the right.

But there is a deeper level at which Julian's very interesting point about left-to-right reading order works extremely well - and that is the relationship between the visual and a description of the visual, read from left to right. I'll try and explain what I mean...

I don't know how many readers are familiar with UK television "celebrities" Ant and Dec?

Ant and Dec are both very popular here in the UK but, with the best will in the world, neither Ant nor Dec individually have too recognisable TV personalities (I'm sure they're wonderful company in real life). To overcome that tricky problem all their publicity photos have them stood, from left to right, in the order Ant... then Dec.

If you don't believe me then do a quick Google image search for "Ant and Dec" to see what I mean.

Are you a Moodle theme designer? What metrics do you use to judge usability? Have you carried out any usability studies? For example, there's a great thread on Moodle.org here.

## Wednesday, 28 July 2010

### Not what you know but who...

Followers of mine may be aware that I'm currently working on the design of a world-wide network of Moodles for a group of international schools. The first Moodle is to be implemented in Poland, a country with very strict data protection laws. The upshot of those laws is that it's far easier to install the server in the Polish school. So we've identified the hardware and, for the sake of consistency across the rest of the group, we're going to be installing RedHat. We receive some pricing strategies from RedHat and as we're checking over subscription costs there is mention of "2 sockets" - in brackets - on the quote.

Not that it mattered particularly but my colleague and I wondered what, exactly, "2 sockets" meant in this context. So we did the obvious: have a look on the RedHat website, followed by Wikipedia. Neither really helped so we then we widened the net to generally Googling for any information on sockets. Not surprisingly we just got a lot of information on TCP sockets and electric wall sockets (and we were guessing it wasn't anything to do with those).

The next step of our quest interested me from an educational point of view: we had a competition between us to see who could get the answer first. My colleague went immediately to Skype to speak to one of our technical guys in Poland. I went straight onto one of the IM chat rooms I'm involved in (Prosody, in fact). I happened to learn only yesterday that one of the regular visitors to the Prosody chatroom works for RedHat and he was able to give me an answer straight away. Our guy in Poland knew the answer, too.

As it turned out (and I guess lucky for the sake of office harmony) we both got the answer at about the same time.

What's the point to this story? Well basically that the two of us sat in the middle of England had no idea what "2 sockets" meant with regard to a RedHat server installation but in our social group we managed to get an answer within about 60 seconds. What I am thinking is that this is, I suppose, a pretty clear example of learning in a peer group.

Then this afternoon I read a recent blog post on the new TDM blog (here) in which Derrin Kent mentions "We CAN learn without any teacher / course, though. We CAN learn without a formal course. We can do this alone or in peer groups." Which is true... because we did this morning.

Derrin also says "But…. we are unwise to learn without recording what it is that we are learning." Which is also true... but that isn't necessarily why I'm blogging about it now.

But I'm also minded to mention that there is nothing new in this idea of learning in a peer group. As the popular saying goes: it's not what you know that's important. It's who you know that matters.

Is it true that it's not the social group itself that's important but who is contained in it? How is it possible to ensure that your social group contains the person who is going to know the answer to the problem you haven't had yet? What do you think?

## Wednesday, 21 July 2010

### The Certainty of Chance

I was struck with an interesting thought I heard on the radio the other day: if you want to be lifted from poverty then it is a good idea to play the lottery.

What might be a morally corrupt statement is mathematically sound because if you don't play the lottery then you have no chance of winning it. For those of you interested in a little bit of further reading (which I'm sure you all are) then take a look at the excellent article here.

I've always been facinated by chance. Here is a true story I use in my teaching... which by chance is very similar to a scenario Derren Brown describes in his book Tricks of the Mind.

When my youngest son was born I was approached by the paediatrician asking if they could take a blood sample because they had performed a test and it seemed he might have Thalassemia. This is a disease that effects 0.1% of the population and the test is approximately 90% accurate. His test had come back positive and they wanted to retest.

The question: should I be worried?

Well... assuming that 0.1% of 60,000,000 people have the condition then that's 6,000,000 people. If they were all tested then 90% of 6,000,000 people would get a positive result. That's 5,400,000 definite positives.

However, 10% of 54,000,000 people would also get a positive result (albeit a false positive) - so that's 5,400,000 people who definitely don't have the condition but are told they have.

So in fact there is a roughly 50/50 chance of my son having the disease.

Odd, isn't it?

However...

There is a postscript (as there tends to be with my teaching). When he was older we finally got access to his medical records when it transpires that my young son was actually being used as a control for a piece of medical equipment that the lab technicians were worried might be giving false positives.

Statistically-speaking, was this a sensible test for the hospital to carry out?

What do you think?

## Monday, 19 July 2010

### Planning for failure

I'm currently helping with the design of an international virtual learning platform network (a network of Moodles). The Group IT Project Manager has asked me for some estimates of how long I think particular tasks will take. And that set me thinking...

My assumption, of course, is that the people executing those tasks know what they are doing, won't fall ill, won't do it wrong, won't have a mishap, etc, etc. Every task you plan has what accountants call "a cost" (and that's not necessarily a financial cost). Before embarking your team on a particular task you have to weigh up the costs. It is an important exercise because sometimes the least obvious course of action is the one with the smallest cost.

We're obviously building in some contingency... but how much contingency? There are some rough rules-of-thumb that project managers use (true cost of a human resource roughly equals salary x 2, for instance). But what about when something happens to your project that you just haven't legislated for?

I was set thinking on this path on Friday last. We had our family evening planned when I had a phone call from home to say my wife was stranded at the local hardware store because she had lost her car key. This is an innocent mishap that then has a cost (financial: more wear and tear on my car; more fuel needed for my car to fetch the spare key, and practical: late back home means late supper; late supper means late feeding of now irritable family members which means... and so on).

Like my plans for Friday evening, project plans assume everything is going to according to that plan. But that's not always the case. We're in a period when the world ecomony is still parlously close to crashing around our ears and one of the reasons put forward is that economic models assume that people behave in rational, sensible ways... which, of course, they don't. It's called the "efficient-market hypothesis".

When I'm reporting my timescales for tasks in our Moodle project I'm working with what one might call an "efficient-project hypothesis". I guess what I mean by that is that not only do we assume that all the players work in the most effective way possible but also (and possibly more importantly) that any project will only be as successful as the information available at the time (in fact EMH comes in three flavors, weak, semi-strong and strong - essentially to do with the amount of information available).

If I assumed that everyone working on the project didn't know what to do and everything that could go wrong did go wrong then how long would the project take to complete?

Erm... if I did that would I still be in a job?

Gulp.

I am interesting to hear your thoughts.

## Friday, 16 July 2010

### Respect My Authority

For this post you'll need to know about math operator precidence so very quickly: the basic math operators are add, subtract, multiply and divide. You have to be careful to use the operators in the right order. Here's an example so you can see what I mean...

What is 14 x 2 + 3 ?

Well, 14 multiplied by 2 is 28. Add 3 to 28 gives 31. Easy.

But I speak English and we read from left to right - called a "left to right reading order". What about languages that have a right to left reading order? Then you would add 2 to 3, giving 5... and then multiply 5 by 14 giving an answer of 70. Ahh... now we've got two completely different answers. Who's correct?

The solution is to have a worldwide convention: carry out operators in a certain order then we don't get different answers. The convention is Brackets, Indices, Division, Muliplication, Addition, Subtraction... BIDMAS. If everyone carries out mathematical operations in that order then we'll all get the same answer.

So I'll pose my students the same question: what is 14 x 2 + 3 ?

"So you say the answer is 28 and I say it's 70. So who is right?"

And, invariably, with some hesitation, they'll tell me I'm right.

When asked why I'm right the answer, invariably, is that I must be right because I'm the teacher.

I'm completely wrong, I've told them the reason why I'm wrong (but, of interest to me, I haven't explicitly told them I'm wrong). They know I'm wrong - but they can't bring themselves to question my authority: "You must be right because you're the teacher".

I close this aspect of my math teaching with a bit of sage non-mathematical advice: always have the courage of your convictions.

I'm very interested in exploring the pupil-teacher relationship - the nature of authority and respect. Is this something you've tried exploring in your teaching? I'd be interested to hear what you think.

## Thursday, 15 July 2010

### Reflecting on Reflecting - PRINCE2 and issue logs

Of course there's nothing new under the sun, and whilst filling out an issues log this morning (for a PRINCE2-supported project I'm currently working on) I was taken to writing this short post on reflective learning.

I don't know how much you are aware of PRINCE2 but if you are going to be working on a UK/Westminster government contract then it is pretty much expected that you will follow the PRINCE2 method. If you're interested then take a look at the UK's Office of Government Commerce (OGC) website, here.

One aspect of the method I'm particularly keen on is the issues log. Anyone involved in the project can add an issue to the log. These are the curve ball problems from colleagues - can often come at you from nowhere and bring a project to a dead stop until they are resolved.

Issue logs are simple affairs, often just a spreadsheet with columns for description, target resolution date, &tc. The column I'm most interested in (from an educational point of view) is the oft-forgotten one at the end: Closure Comments.

Closure Comments is the project manager's opportunity to reflect - hopefully sensibly, coherently, and with a critical eye - on how that issue came to be missed, how it was resolved, and why, if necessary, the target date for resolution was missed.

It's the part of the job of project management I find the most interesting and challenging: having to justify to everyone - including myself - the decisions I make.

But it's a very powerful teaching technique I also apply to teaching math (if you've Googled me then you'll realise I wear lots of hats - hence the name of this blog). For instance, I could ask: "why did you factor a quadratic that way?" or "tell me at each step of adding two fractions together what you are doing and why you are doing it".

Have you tried this technique in your teaching? What have been your experiences?