Tuesday, July 10, 2007

Two sides of a coin.

Before you break into a quiet panic, this isn't going to be a post about cartoons! Believe it or not, I've been waffling away my thoughts on the second semester at the same time but my waffling hasn't finished yet. Simply because my second semester was 'mathematically' great. Since I have no intention of being awake after 1am, I decided to post about my day now and then tomorrow chug away at the other post.

At the end of today I was asked, 'Beans, do you want to teach a lesson tomorrow?'. My natural response would have been to shout NO, and then slowly back away from the teacher. I did take a step back but then 'laughed' out the words 'me- no! You've got to be joking!'. It seems that a teacher is going to be absent tomorrow for a year 9 class. They're doing standard form. The thing is that if I was told to 'teach'(!) how to solve a system of equations using the Gauss elimination method then I'd be able to do that. If it was about finding the radius of convergence, or convergence in general I'll probably be able to do that. Heck, even if it was the first semester stuff on modular arithmetic and the euclidean algorithm, then although it'll be a struggle I'll manage. Ah, but I'll only be talking about them things to mainly university students and there mathematical background is sort of similar to mine.

I do know about standard form and how to write large numbers, or really really small numbers nicely, but teaching that is another thing. Inside my head I see it all. I see myself being there at the front 'doing my business'. Sadly, reality is much different. I feel that this opportunity may not come again and I'm seriously contemplating on saying yes. The teacher is obviously going to be there, which is making me feel nervous and calm at the same time. If I mess up, back up is there. I won't have to 'force' the children to listen to me. Something inside me is telling me to do this. It's screaming for me to go for it, and yes I might mess up (most likely) but I'll regret not doing so. How many times have I sat in lessons imagining myself doing things? An 'uncountable' time. :p

Sadly, I have a feeling that I may decline this wonderful offer. The main reason being that for my own 'experience' I'll probably deliver a rubbish lesson and these students will hate this topic forever. OK, that's more hyperbole for you, but somethings not falling into place. At the moment I'm all for it. Yes- I'm going to be at the front! Gah- that sounds quite scary to be honest. :( And then I want to be a teacher? Pfft. Anyway, I'm going to brush up my knowledge on standard forms from a GCSE book in a minute (just in case!), but the best solution is for me to do part of the lesson only. If I survive to tell the tale I'll let you know. (I really should be called chicken little you know!)

Today's lesson were great. SG- whose SG? Hehe, I think the discussion with the teacher might have positive results. The reshuffle is actually working *touches wood*. SG and mate got on with the work today and I was only subject to the lines, 'haha blah blah blah.' Yep- I can't even remember! Fifty cents was actually better behaved today (for what reasons I don't know) but there was no disruption whatsoever in today's lesson (I mean major disruption). The class has been split into three sections, each with a balance of loud and quiet students. I'm actually quite pleased that YW has been doing the work in the past two lessons, as well as another student. It seems that these kids biggest enemy is laziness and not being pushed all the time.

You should never let the kids feel content with what they have accomplished, but always move on and show them what can still conquer. If you don't push them they become bored i.e. one reason to be disruptive. I know you have to pitch work at certain levels for different students, but don't pitch it at their level, but one slightly above. The students had done some sort of national assessment (don't recall doing it in my day!), and they've got some good results. The lazy attitude is apparent in all of the maths classes I've been to.

I was also in a year 9 class today and they were doing something about square roots. (Gosh- my memory is going worse!) I enjoyed this lesson, walking around picking up calculators when I saw them being used, from students who wouldn't attack me! There was one student who had finished her work before the lesson had started and had been doing a different subjects work, whilst waiting for the answer sheet. I took this from her since her neighbour had been doing this other work rather than the exercise. After much protest I gave in since she had a point that she'd completed the work. I continued on my rounds and came back to her again. She was still marking her work. In the book I noticed an extension question which hadn't been done, and asked the student to give it a try. Naturally I was met with 'no- I've finished the work, I can't be bothered'. I once again insisted upon this and eventually said I'll do the questions with her. This seemed to be OK with the student.

I'm kicking myself since I didn't present the solutions in a clear way. :( We had a rough paper and the work on the paper was not orderly and if you were to read it you'd probably get the shrek look!! :( My lame excuse could be that quite a few other students were asking for help at the same time but that's lame. :( The kicking will continue until I see the student again and see whether the work was understood. This question had an important concept of maths hidden in it. Proofs. It was an 'investigate' question and to do with square roots. From a few of my supervisors and lectures I've learnt that if you've got an equation you have to work with, first stick a few numbers into it and see if you can get the general idea of it. In this way you might even be lucky and find a counter example.

So I told the student to do the same and she gave a number for A and another for B. We plugged them in, and got 7=3. The next question gave something absurd as well, but then the questions which I'd left till the end were the 'correct' statements. We did an example like before and this time the answer was something like 1=1 (ie. something correct). I asked the student whether this is correct for other numbers and the student slowly replied yes, it's true for whatever number you choose. 'How would you show it?', 'Put all the numbers into the equation and then you can show it.' This was my cue to explain that in maths if you want to show that something is false a counter example will do (thankfully!), but to show it's true you have to prove it. This is when the kicking myself bit comes into place. Verbally I may have made sense, but from my experience having something written down helps a lot. We managed to get through the question (and I may have cheated and suggested 'squaring both sides' :o), but the work had been understood. At the end I further highlighted the difference of a proof and just saying that something was true, and this student seemed to be listening!

The problem is that when you find a student responding like this you(I) want to tell them more! I did stop myself in time, but that's not the first time this has happened. I have to be careful not to confuse anyone as well. That lesson was good, and I eve argued with a student that maths isn't boring and full of lots of symbols everywhere. Well I couldn't deny that symbols and numbers did tend to crop up ;), but I told the student to look at the small parts first and move on.

This was a set 1 or 2 class I think, and the students were all able to do most questions of the book. Some needed help but they got the idea. As a teacher you have to make sure that you cater for all students needs. What separated these students from each other was their attitude towards work (and maybe maths). Those who were determined and wanted to do their own work got on with it, and those who were lazy and couldn't be bothered just copied someones answers. Care has to be taken to push the lazy ones and at the same time push the ones who are not lazy. Another student had finished the exercise as well and I'm sure that all this student had done was talk. (OK- it is the end of the year, but still!)

Overall I must say that today has the been the best day so far. The year seven class were great as well (ad Fibonacci popped up much to my amusement). And guess what- I didn't for once think about my secondary school maths class today! I think some of them understand that I'm there as a teacher and not there friend (thankfully) which is a positive. The key to how well anyone probably does is how hard they're pushed. So maybe other peoples expectations (like teachers) are a good thing after all? I'm switching of at the moment but will surely discuss this laziness problem another time! (talked to MA about it today).

The bob the builder work wasn't too great today i.e the other side of the coin. I had to go up into the attic and did a lot of running up and down the stairs. I'm feeling quite broken at the moment, and in need of repairs. I spotted quite a few spiders, and thankfully the sensation of one crawling down my back was imaginary. We've nearly finished removing the wall paper now and I have to do some lifting and loading work tomorrow. What joy. This is like a second work experience it seems but I no longer have time for a cuppa after school! That being said I'm grateful for this change to my previous routine. So to teach or not to teach...

WHY DO WE HICCOUGH?!! I don't normally get them but it's been a nightmare today! (Yes you guessed it- they've returned again. :/)


Jake said...

Standard form?

Is that what I know as 'Scientific Notation?'

beans said...

Yes, I believe it is. Wiki says: 'In British English, standard form is the more common name for scientific notation.'

I hadn't heard of scientific notation before, although SI did pop up somewhere!

Jake said...

LOL. I thought it was the other way round; I had heard of 'scientific notation' but don't remember the term 'standard form'

SI, or Systeme International, is something different. It is an international standard for systems of units (all metric). It is the most common system of units used in the world of science and includes things like kilograms, litres, seconds, amperes, moles, etc. It is also responsible for the prefixes indicating orders of magnitude

e.g. mega- = 10^6
nano- = 10^(-9)

so I suppose it is linked to scientific notation in that it offers a standard naming convention for orders of magnitude in base ten and is probably taught alongside scientific notation in schools. I mean, I guess that is the main point of scientific notation, to put things into a standardised format that is easy to read.

beans said...

I guess that is the main point of scientific notation, to put things into a standardised format that is easy to read.

Scientific notation and standardised format in one sentence again! :p It's pretty handy having a convention as such and I recall being introduced to SI units during M1 lessons. (ms^-1)

(I've also heard standard form being called index form).