A Consuming Experience: learning

Showing posts with label learning. Show all posts

Monday, 13 October 2008

Pink elephants, numbers, & the spaces in between...

A confession: the single hardest thing for me in trying to learn computer programming, specifically loops, is one very, very basic issue - counting.

That's right. I can't count properly.

All my life, I've had problems with the difference between numbers, and the intervals between numbers. Even though I have A's in A Level Mathematics and Further Maths, and I passed the Mensa IQ test. It just shows how meaningful test results are, eh?

1, 2, 3. That's 3 numbers. But, there are 2 steps between them. What are we talking about: how many numbers, or how many steps there are between those numbers? I always have to stop and think about that before I can carry on. The difference is not instinctive: I actually find it very confusing, and I often mix them up. Even though it's basic arithmetic.

So when I'm looking at an example of a loop, or trying to write a loop, I have to work through a couple of actual instances before I know whether it should be < or <= (less than, or less than or equal to), or if it should be > or >=, simply in order to get the correct number of repetitions.

Interestingly, I'm not alone. When I admitted this to my best friend, she told me that in fact she has exactly the same issue.

When she was 4 or 5 years old, she drove her teachers mad. They lined up cardboard pink elephants to illustrate addition and subtraction, and she just couldn't grasp that X number of elephants minus one elephant produced a particular number of remaining elephants. She was more concerned with the interval between the final elephant and the one that had just been removed - what had happened to that? What happened to the space between two objects if you took away one of them (as if the elephant were a bookend), did the space "fall out", where did the space go, doesn't the removal affect everything else? They had to tell her to shut up and stop worrying about that - just worry about the elephants!

And she felt that intervals had properties, and that numbers had "directionality" - that the interval between 2 and 1 is not the same as the interval between 1 and 2. Surely the interval between 2 and 1 isn't 1, it's minus 1. (She also wanted to know: where did the elephant that had been taken away go, what had they done with it, and why? Surely that might have an impact on the elephants that remained? But they weren't interested...)

I must admit I didn't go quite as far as all that, myself. But still I have a problem with things, and the spaces between things, and boundaries / limits - when do you count the thing itself that's at the upper or lower boundary of what you're dealing with, and when do you not.

I think that maybe my friend and I both visualise numbers as actual objects, locations in 2D (or perhaps 3D) space. I'm not sure if that's an example of us both having a kind of number form synaesthesia, or if that's just a child's way of trying to grasp abstract concepts like arithmetic by unconsciously using a number line.

Like, what happens exactly when you add and subtract? What are you doing, what are you counting? The numbers, or the spaces between them?

Does 3 - 1 = 2 means there are 2 steps between the number at location 1, and the number location 3? Is that how subtraction works?

But hang on, what about addition then? 1 + 3 = 4. How does that work, in terms of spaces between locations 1 and 3? Confusion...

Solution: aha, you're counting the number of steps away from 0 that a number is. Addition is just adding up the distance the first number is from 0, to the distance the second number is from 0. And subtraction is the difference between the two distances.

Got it. Sort of.

Oddly enough, I don't have the same sort of problem with multiplication, division etc - probably because I've just memorised the multiplication tables, 3 x 4 is 12, and that's just the way it is.

So effectively this means I've never understood the fundamental hows and whys, why things are the way they are - I've just memorized a few set things, and then I apply them; I can do that at least!

If I could just figure out exactly what I need to memorise for a basic loop - this structure gives you that type of counting / number of iterations, this other structure gives you that other type of iteration - I think I'd be there, at least for the basic stuff.

Relationships, proportions and different types of things

I have also always had a problem with relationships or proportions involving different types of things.

You know, things like, if 3 elephants are equivalent to 20 chickens, how many elephants would equate to 50 chickens? The only way I managed to get through all that (and I still have to do this today), was to be utterly mechanical about it.

I worked out a formula. You line up the "like" things (elephants) on the left, and, in the top line, you put the other thing that you know about on the right.

Known_type2 equates to Known_type1
Unknown_type2 equates to WHAT?

And then I'd know the answer was to go through 2 sides of a triangle which I'd memorised by rote: Top right x Bottom left ÷ Top left. Seriously.

20 chickens = 3 elephants.
50 chickens must be 3 x 50 ÷ 20 elephants.

If they gave me the number of elephants for the second time, I'd have to line it up differently but use the same formula, similar things on the left:

3 elephants = 20 chickens.
8 elephants must be 20 x 8 ÷ 3 (top right x bottom left ÷ top left).

To this day, I've never developed an instinctive feel for what goes with what and how you put them together.

I wonder if all this says something interesting or profound (or not!) about me and my friend compared with other people, or about the concept of numbers, or how children learn to conceptualise numbers - and if so, what on earth that would be.

Are we alone, or do other people have similar issues?

My friend of course looks at it another way. She said, when they asked her: "If it takes 3 men each using a 2.5 litre bucket X minutes to fill a pond, how long would it take 2 men using 7 litre buckets?", she thought - I really don't care; why can't they just use a hose?

Saturday, 27 September 2008

Cyberbass helps singers learn choral parts more easily

If you sing in a choir, Cyberbass is a useful growing online "note bashing" resource for choral singers to study and learn their own part more easily.

It provides free MIDI files (playable automatically on most modern computers, but their FAQ includes troubleshooting tips for Windows) which will play out each individual section's part or line against a metronome click, in some cases with the accompaniment in the background. You really need to listen to it in stereo - the selected part will play out of the right speaker or right headphone, a bit more loudly than the other parts.

It has .MID files for soprano, alto, tenor and bass parts (including splits e.g. soprano 1 and soprano 2), for almost all of the most popular oratorio works in the modern choral repertoire - from the Faure Requiem, Bach's Magnificat, Handel's Messiah, Mendelssohn's Elijah, Mozart's Requiem, Orff's Carmina Burana and Verdi's Requiem, to (perhaps more usefully, as they're rather less commonly performed) Britten's War Requiem and Vaughan Williams' Dona Nobis Pacem. (No Allegri Miserere, though?).

Check out their list of major works, by composer, and the full music index (by composer, with a Christmas tree symbol for "good for Xmas"!). Not all of them are 100% complete and the site's a bit basic in design, but hey it's free.

It's the usual - click on a link to play it live, or rightclick to download to your computer. A lot of mobile phones and MP3 players can also play MIDI files. For some pieces you can even play back all parts at once and try to sing your line in context, by clicking "Tutti"; or change the playback speed (tempo) if you have Microsoft's Windows Media Player 11.

They make money from ads & affiliate links and selling learning CDs for the major works, or from donations. Cleverly they provide free concert listings on the site - but only for choirs that have learned their lines for the forthcoming gig using their service!

Very useful if you can't read music or don't sight read well - or just to help you learn your part by playing it over and over again in your earphones on the train.

If the use of technology for music interests you (or just singing generally), see also my other posts on music and on singing, including:

help on pronouncing words in French, German or Spanish by creating a sound file to download your computer
free virtual piano keyboards to help learn notes
how to find a good singing teacher
some tips on voice health and vocal care
check out Pavarobotti!

Monday, 11 August 2008

"Interactive" training only works if properly planned

Increasingly, people seem to push interactive, participatory learning as a panacea: "To teach or train people properly you gotta make it interactive, man!"

Don't get me wrong, I think active learning is a good thing, and I can see the point of constructivist teaching methods based on constructivist learning theory. But even those techniques hold that "learning should build upon knowledge that a student already knows" and should promote "a student's free exploration within a given framework or structure", and they note that "While it makes sense to use these techniques as a "follow up" exercise, it may not make sense to use them to introduce material" (my emphasis). In constructivism, the teacher's role as facilitator is vital. Furthermore, critics of these methods point out that "due to the emphasis on group work, the ideas of the more active students may dominate the group’s conclusions" and that "instructors often design unguided instruction that relies on the learner to "discover or construct essential information for themselves"".

If the statement I recited rather irritatedly above is applied too simplistically as a mindless mantra without proper work or, more disappointingly, thought behind it, it just results in people not being taught or trained anything useful at all.

Participation, schmarticipation

A story. When I started using the Web a few years back, I didn't even know what a link was. I went to a formal evening class because I thought it was the quickest way to find out about this InterWeb / World Wide Web thang. (Yes, I was born before there was a Web, I'm that old.)

The first thing the tutor did was tell us to go find X on the Web, without having explained what links are, what they do, or how to find them (i.e. blue underlining, the mouse cursor changes to a hand if you hover over a link), let alone explaining what search engines are, how you get to them, and how you use them.

Without giving us that foundation, without explaining those essential basic paradigms, he might as well have told us to go walk around in circles muttering. Which is pretty much what I did, in virtuality.

I could try doing what I liked, but "participation" in itself does absolutely no good unless you already have the base level of knowledge that's needed before you can "participate" properly, before you can try things out in order to cement something you've just learned. (To top it all, he tried to hit on me.)

"Interactive" groups, pah!

It's the same with "interaction". Interaction simply for its own sake - which seems to translate to "Yeah man, let's make it 'interactive' by splitting everyone into lots of discussion groups, woohoo!" - is a pointless waste of time, and insulting to the attendees at worst.

Even so-called problem based learning requires that the group be given a specific problem to discuss and solve, and to be effective it requires motivation, feedback and reflection. One reason it works is that it "taps into existing knowledge". My emphasis, again!

Many people worship the "learning pyramid" and cite it to say that in terms of teaching methods, "discussion group" (supposedly 50%) is much better than "lectures" (supposedly 5%) for retention of information. However, investigations into its origins show that in fact there is no hard research behind those frequently cited figures.

Undoubtedly, there's a grain of truth in it. Learning actively by doing, when you're given exactly the information you need, in context and at exactly the time that you need to use it, does help boost retention when compared with memorising things by rote in abstract isolation.

But in relation to discussion groups, it all boils down to one simple but critical thing, which many organisers / speakers ought to but don't always consider: What's the purpose of this session? What are you trying to achieve, exactly?

Do you just want the attendees to admire the speaker's wit and wisdom? To be mindlessly entertained? Do you just want them to be able to say they went to a session on X in trendy surroundings (in which case all you need do is entitle the session "On X" and leave them to it)?

Or do you actually want them to learn something, so that they'll come back when they want to learn more things or other things?

If you want them to learn and retain something, then you really need to think about what that is: what are the 3 key points (certainly no more than 5) that you want them to take away with them?

Another issue is, are you trying to teach them what they want to know, or what you think they need to know - which may be quite different! And in either case, again, what is that exactly?

The latter is particularly important in a business context. My previous day job involved a fair element of training, in the sense of trying to make sure certain people know the things the business needs them to know (whether or not they think they need to know it, and even if they think they already know it. More often than not, in fact, they don't.)

So I have some practical experience of training and teaching. And that's the number 1, to me: What's the purpose of the session? That has to drive everything - who you get to speak, the way you run it, everything.

Now back to "interactive". Interaction in the sense of a discussion group can definitely help people to learn and retain more. But just saying "Now go into groups and discuss this issue", even when coupled with "Then come back and report on what you think", is, without more, an utter waste of time - unless of course the purpose isn't for people to learn anything but just to get them to socialise or to listen to the witterings of other non-experts who nevertheless think they know everything.

If the point is for them to find out what other people's opinions are on a subject, fine.

But if the point is for them to learn something about the subject that they'll remember more than a few nanoseconds later, then the discussion needs to be:

Carefully planned, in detail, in advance, and
Facilitated or led by someone who:
- understands the subject sufficiently
- has a list of the "learning points" (pre-planned, and not too many of them: the famous 7 points +/- 2 principle (or myth?) relating to how much the human memory can hold, to ensure the cognitive load isn't too heavy - it may possibly be just 3 to 5 points) that need to be brought up during the discussion to ensure they are indeed raised and understood, and
- is able to "pick on" people to get them to answer questions and participate (it's not a discussion if they won't volunteer to talk, is it?).

Herding people into random groupings without facilitators who know what they're doing, and expecting them to organise themselves into a group that can conduct a coherent discussion on a subject they know little about (otherwise why would they bother going to the "learn all about X!" session?), is as bad as sitting someone who's never used the Web before in front of a browser and telling them to go find X. Or worse. They're not likely to learn anything, and may even be put off.

Wouldn't you be fed up if you attended a session in order to learn about a subject you're interested in, only to find yourself dumped into a group of equally ignorant attendees and forced to listen to people who know as little about the subject as you do, or even less, dominating the proceedings by virtue of egocentricity, pushiness and loudness rather than actual expertise in the subject matter?

Yes, I'm talking about Dana Centre events, yet again. If they want to annoy people they're going about it the right way. Some friends I'd previously persuaded to go have never been back, and they haven't bothered to tell Dana why, they've just taken themselves off Dana's radar. I've been giving Dana another chance, and another chance, in the faint hope of another talk like Baroness Greenfield's, but so far nada.

For a single evening session where time is limited, by far the best format is talks by experts (or a channeled discussion amongst panel of experts) before an interested audience in a single large room, followed by audience Q&A. The Royal Society for the Arts clearly know this (and the format works well for an all-day session too, when properly facilitated e.g. The Wealth of Networks 2008 conference on digital economies and the next generation internet) - but equally clearly, the Dana Center don't.

There is a place for small participative groups, but only if they're properly planned and led (which takes days or weeks of preparation time, and requires enough properly-briefed experts to facilitate each group separately).

(As for making people trek between groups from room to room including up and down stairs while trying to balance plates of food, that's just a ridiculous waste of time as well as an unnecessary inconvenience, especially when the journey time (which may add up to 15 or 20 minutes total, or more) would be much better spent allowing (static) speakers to expound on their themes more fully to the (static) audience.)

Thursday, 24 July 2008

Online virtual piano keyboards: free way to learn notes!

A tip: virtual piano keyboards can be useful if you're a singer trying to learn a part from a score (whether for choir, opera, musical theatre, pop or rock) but you don't have access to a musical instrument. All you need is a computer with soundcard and speakers or headphones / earphones.

Here are some examples of free online piano keyboards available through your web browser via the Flash technology or a Java applet (which all modern web browsers can handle); two can record and play back a series of notes, one of them can even be downloaded to your computer (whether desktop, laptop or notebook) and then played offline without any internet connection! They're meant for educational games, teaching piano rather than choral or vocal lines, but are in fact very handy for vocalists too.

(For those who don't play the piano, there are lots of diagrams on the Net of which keys on the keyboard correspond to which notes on the music staff, see e.g. this pic or this more comprehensive one)

1. Ababasoft

Virtual keyboard and free downloadable Flash version (just rightclick that link to save it to your computer; in future, doubleclick the saved .swf file to access the keyboard).

You can click on several keys in a row (including rests if desired) and they'll show up in the stave below; the Play button then replays all of them - good for learning a sequence of notes, and Loop will repeat it over and over to really get the pitches into your head. Temp. is self-evident, you can set the speed so it plays back faster or slower. Sound's a bit too sustained for my taste, but that's just a quibble.

Ababasoft also have a "chord piano" (again downloadable) which lets you hear your part against other people's (in vertically stacked boxes) - click in a box, then click the keyboard to set the note for that box. Double left or right arrow buttons move you along horizontally one stack at a time, and what you hear is always what's in the middle stack at the time.

2. Flashmusicgames

No music stave but the Flashmusicgames piano (again downloadable) lets you set the duration of the notes played, in milliseconds (default is 100 ms), if you prefer less sustain per note than Ababasoft's piano.

3. Apronus

Bare bones Flash pianoforte, no way to record and replay a sequence so it's "live" only, but it gives you 2 octaves and a more realistic piano sound.

4. Pianoworld

Wai Man Wong's Java applet synthesiser keyboard (with piano sound), don't be surprised if it plays you a back a fast run while you're waiting for the page to come up!

2 octaves, hit Rec before you play it in order to record, Ply to play back what you recorded, Clr to clear the recording. (Not figured out Mem, it just plays a B - as does clicking anywhere on the synth picture above the keyboard other than Demo or Drum..)

Bonus fun bit: click "Drum" to hear a random drum sound; you can even intersperse your recording of notes with drum sounds, but sadly when you play back the recording you can't accompany yourself with the drum live!