Best Lesson Learnt

[muninnhuginn]

Friday evening, we were encouraging (for which read standing over trying not to shout...) Looby Loo to do her homework.[And, yes, this is a despicable thing to be forced to do to a not-quite six-year old. I'd much rather she didn't get homework until she was old enough to take responsibility for it herself--i.e. not until secondary school--and it's going to be a difficult transition to go through to make her take over responsibility for it herself sometime later. And she's just too young to have homework at all (actually I'm quite in favour of the too young for full-time education argument too). But that's a whole other post.]

The homework was maths. LL had a sheet with four single-digit numbers at the top and the instructions to make up as many addition sums as possible with them and write down these sums with their answers. This, with a little encouragement, she did. All twelve possibilities that she found. I checked them for her and in the process showed her how I'd've worked through the numbers in sequence so I knew I'd exhausted the possibilities.

Then I asked whether she could find some more. Could she add each number to itself? (There was nothing in the instructions to say that she couldn't use the same number more than once in the same sum.) I didn't suggest, although it had occurred to me, to do the sums in different numbers bases. (No there was nothing there limiting her to base 10!)

This exercise led me to thinking, recollecting. I'm contrary. Give me two choices, I'll pick the third, and then do it differently. People regard this almost entirely as a fault and when I'm being wilfully awkward I tend to agree, But, and this is where the maths homework comes in, it isn't always.

What I was vividly reminded of in the course of helping with her homework was my very first mathematics class at secondary school, a lesson that I now realise was probably one of the most (maybe, the most) important lesson I ever had. The whole first lesson was slightly abnormal. Our teacher, MM, a woman with a strong Geordie accent and habit of referring to folk as "petal" or "flower" (and this to mini-skinheads with a propensity for arson), has previously taught in one of the trendier public (note for non-UK readers, that's fee-paying and exclusive rather than state-funded) schools (I forget which: it's not the sort of detail that would have meant much to my eleven-year old brain) where her pupils addressed her by her Christian name. That was what we were to do too. So just as we were adjusting to that horrendous custom of addressing teachers as "Sir" or "Miss" (or rather those bisyllabic whines "Si-ir" or "Mi-iss" usually preceded by an "Aw") instead of the far nicer Mr X or Mrs Y we had the oddball who had to be different. A formidable and slightly scary oddball at that.

Then we got our first exercise. We were handed a sheet of paper on which were a groups of sixteen dots arranged in four-by-four grids. The top left dot in each group was labelled A and the bottom right one was labelled B. The task was to find as many ways as possible to draw a line between A and B. We diligently set to (diligently? it was our first few days; rebellion didn't start until a little later), joining the dots across the grid. After a few minutes we stopped and got to compare results. MM then proceeded to gently harangue us for our lack of imagination. Why had we all drawn lines only within the grids, and only straight lines, and only directly between one dot and the next? What was wrong with drawing a curved line around the outside of a grid starting at A and ending at B? Or doing zigzagged lines between each pair of dots? Or...? Or...? It was a moment of sheer sickening revelation. The scales fell from my eyes and I was mortified (getting things wrong always made me feel ashamed). It was a bit frightening too--all those multifarious possible answers, the infinity of different routes.

We went on to define the terms of the exercise more carefully so we could find the maximum numbers of routes subject to a specific set of criteria and we moved on.

The lesson stuck. Through the various "investigations" we did (assessed projects taking up blocks of, I think, three weeks) for Mathematics 'O' level, my first move was to see what holes had been left in the question and the narrowing down of options.

The lesson stuck. Given a list of mainly war-related literature and the subject "The Search for Glory" was there any need to cover only warfare? Or warfare at all? Hence an essay on Frankenstein, William Golding's The Spire, Graham Greene's The Power and the Glory, Joseph Heller's Catch-22, and the odd bit of Wilfred Owen's poems.

The lesson stuck. I "break" instructions and interfaces by pushing beyond the assumptions I believe others to have made. I find filling in forms almost impossible because I can see too many possible true answers even to the simplest of questions and somehow have to tell most of them to bog off.

It was the single most important thing I ever learned in school. The first week, possibly the first or second day. Anything else, any other teacher, had less of an impact. More than the wonders of science (or Physics, anyway) or the mechanics of Economic systems or the crucial lesson. Granted it fell on fertile ground: I'm both literal-minded and pedantic (and pedantically I see these as two subtly different concepts). But fall it did--and sprouted.

So (in a pathetically obvious attempt a meme creation) has anyone else experienced one of those revelatory, world-changing, moments in the course of their education?

Comments

[armb.livejournal.com]

Not that I remember, which limits "revelatory" even if not "world-changing". But my answer to "Why had we all drawn lines only within the grids, and only straight lines, and only directly between one dot and the next?" would have been "because otherwise the answer is obviously infinite, and the question not worth asking".
I was once on a project marked down for "Originality" for coming up with an answer the instructors hadn't thought of. Being marked down for taking advantage of a loophole, even if we did explictly ask if the loophole was supposed to be there and if it was ok to use it, wasn't too bad (at least it gave the other teams a chance to catch up elsewhere), but claiming that it was unoriginal was unfair.

[bohemiancoast.livejournal.com]

We had some brutal times with Marainne in infants with homework. She's now in year 3, gets homework (in quite chunky amounts) every Friday, and generally sets to it with only a little reminding as soon as she arrives home from school. On the occasions when we can't do it Friday, she's quite proactive about working out when she might do it. And although I am, like you, skeptical of giving infants homework, I have to admit that the fact that she has the habit now is helpful.