Monday, July 02, 2007

Observations of a maths student- day 1

The first word that springs to mind is WOW and then wow again. Once again I'm mentally unstable at the moment, however considering the amount of sleep I had, I did OK. Most likely than not, I'll be 'reporting' on what my days are like whilst work shadowing. (Just had a nice nap after starting this post. :o)

Day 1

I managed to get to the school on time which was a relief. I hate being late. Now that may seem a contradiction to those who know me from college, however I believe college was a different story altogether. The lessons were for 90 long minutes, and so either I used to go for 'walkabouts' (i.e. to the 'toilet'!) in the middle of the lesson or sometimes go five minutes late. That being said it depended on the teacher. Some teachers came late or started 10 minutes into the lesson so you could get away being five minutes late. (I only ever went on 'walkabouts' if I either didn't understand the work and felt that a change of scene was required (it helped!), or if I'd finished the set work.) The lessons that I was always on time were further maths and Chemistry. (Mr B and Dr H gave that 'look' if you came late!) Normal maths lesson were when I pushed it slightly! Although it's different in university, since if you miss the first five minutes it takes a while to catch up. I only did that in my second year of college though, and now I hate going to lectures late. (a bell in my head is reminding me of some that I did go 'late' to, but it was all under control!)

So back to today. The first thing I did was to negotiate my 'timetable' for the day. Since the number of classes are reduced I was asked if I'd like to sit in any other lesson. Naturally I said PE. The teacher's eyes did widen slightly but it was decided that PE it was. (I'm also probably going to check the science subjects and maybe other ones as well). First lesson was PE and that went so and so. Second lesson it was maths and it was a year seven set 4 class.

Now I must explain the wow- wow teaching is indeed a difficult job! Maybe not 'that' difficult but it is indeed demanding. You have to be on top form. It's different being accomplished in your subject and being a great teacher. I think it's easier to have a good understanding of your subject (which isn't easy if you follow me), but being great at teaching is harder. Teaching is really 'wow'. When you sit back and observe you realise the things that a teacher has to take control off in a lesson. I was pretty 'overwhelmed' initially, and mentioned to the teacher that teaching is indeed a challenge. Makes you appreciate the good teachers you've had and basically say wow!

The lesson was about solving one stage equations. Previously I believe the class had encountered operations and inverse operations. So the inverse of +4 is -4 etc. To begin an equation was defined and examples presented.

My question is, how would you go about explaining to an 11 year old from the lower set (set 4), how to solve: x-3= 10, and 2x=8? That is without overwhelming the students.

With the inverse operations in mind, the teacher asked what's the inverse operation of -3. The reply was +3, and so you have to do the inverse operation to the number of the other side. Hence,


I think that might have been the best way of explaining it, however I was more inclined to explain it by saying you do the inverse operation to both sides. That is you would add three to both sides. As I was going round the tables, I noticed that most of the students understood the inverse of addition, but when it came to equations like x/3=4 and 2x=8, they got confused. Many of them were doing:

\\2x =8\\ x = 2 \div 8,

and then leaving the answer like that. This is why I was inclined to explain that what 'operation' you do to one side you must do to the other. So if you're doing the inverse operation to one side, i.e. dividing by 2, then you have to do it to the other. I don't think that was understood, so I stuck to the way the teacher had explained it. A majority of them got the idea, and even if they didn't know what they were doing, they looked at previous questions or examples and worked it out.

The problems I noted with this set 4 class was the confidence of the students. Before even saying the answer most tended to say, 'It's going to be wrong anyway', 'I don't know', 'I can't do it', etc. Some did know the right answers but thankfully even though they said them negative things they still attempted the work. (The 'negative' comments are what tends to go through my head initially but after you take the first step sometimes it becomes easier). You see, as I've said previously, I've been reading Polya's book (How to Solve it), and so was trying to, rather than tell them the answers, ask them questions. Hence by doing so they could reach the answers themselves. I wasn't very good at that, but it was my first day. The main thing a teacher requires is patience. That is the key. Patience to ask the same question (sometimes) in a variety of ways without phasing the student. It's easy to get frustrated and say the answer, but I must remember the numerous occasions in which, even now I test the patience of my lecturers with 'dumb' questions. Hmmm, this patience thing might be a challenge, as it probably requires explaining the same thing to many different people.

I wasn't teaching (thankfully), and at first was a bit apprehensive when the teacher asked me to go for walk abouts around the class, but hopefully that was first day jitters. The problem in this class was that I didn't know the mathematical background of the kids and so I probably did confuse them. (Although one of them did understand what I said about doing the inverse operations to both sides). I also hinted to the students that they could and should always check the answer. If they got x=1 they could check on whether or not it was right. The hard job was to not confuse the students since a majority of them gave up pretty easily. The question then is how do you pitch it?

I think this was a loud class and sometimes in such a class it's easy to overlook the quieter members. I noticed one student looking at the person sat next to her and so I positioned myself so that I was blocking the work from view. Immediately this student started 'panicking', and I was given the 'why' look but we worked the solution out. Anyway, that's enough about that lesson- it was indeed an enlightening experience. They were year sevens so thankfully although they were loud, it was a nice controlled environment. Hehe, I was mistaken to be a teacher, and they can't call me by my 'nickname' or first name. Weird.

The second maths lesson I went to was set 3 year 8. This was a totally different experience. I probably would have gone about doing this lesson in an entirely different way. The objective was to be able to calculate the circumference of a circle. The students were asked to draw four circles with different radius and then work the circumference out and then area. What I felt happened was that the students were quite eager to draw the circles (had A3 paper etc) however whilst they were drawing they weren't listening. I did ask a few to listen, but since many didn't have a compass they were all in a hurry to draw the circles. The teacher explained the circumference whilst this happened. I asked the students next to me, 'What's the circumference?', 'I don't know' was the reply. Some already knew, and others did listen, however a majority were drawing circles. I explained what the circumference was to the table I was sat near and I think they understood it. They continued drawing the circles.

As I moved around I saw many of the students weren't actually drawing circles, but first were putting their artistic skills to use and trying to 'prettify' the title! Once student asked me whether my writing was neat! I'm sure that you would agree with me when I say it isn't, and so I insisted that it didn't matter how the title was written. (Come to think of it, I recall that using colours for titles etc was a big deal 'back in my days'- that hasn't changed much then.) Exasperated I came across a student who still hadn't drawn any circles. Yes, the writing may have been 'cool' but all this student did was talk and exclaim loudly, 'isn't this writing awesome', 'look it at- amazing' etc. I agreed (was too scared to say otherwise- the student enjoyed watching wrestling!!) and insisted that they draw the circles. Many of them hadn't put the pencil in properly and so they drew quite a few circles that weren't particularly 'circular'. That didn't matter- they were at least drawing them!

At some moment a table had gone on the board with columns labelled: 'radius', 'diameter', 'circumference,C=\pi D' and 'area, A= \pi R^2'. The students had to fill that in from the circles they had drawn.

I went back to the first table and realised that they had all drawn the circles, but were stuck on what to do next. They didn't know what the diameter was, and so I asked them what have you drawn? They said a circle of radius seven. I asked them to show me the radius on the paper and they hesitated. Then I asked them to recall what the circumference was and they were able to do this. (some had pointed to the circumference). I then once again asked them to point the radius out. No answer. I got a ruler and measured from the centre to the circumference. It was 7cm they told me, and one student noticed this was the radius and so they all knew what the radius was. I then told them what the diameter was and advised them to always draw a small sketch labelling the radius etc. Many didn't have scientific calculators and so were told to use pi=3.14. So now they knew pi and the diameter and they proceeded to work out the circumference.

Now I have to mention this other incident. On a number of occasions I've probably said that I'm slightly old fashioned in my thoughts and ideas of education. Maybe I'm not 'old fashioned' as such, but I've probably not met many people who value the idea of education and who realise that it is important to respect ones teachers. There was this one student who I shall refer to as SG. I'm not sure what to make of SG. You see SG was the type of student with a certain type of attitude. SG was friendly enough... but I can't find the right word to use. I think that many of the students probably saw me as a teacher, and sensed fresh blood. Natural instinct means you want to know more about 'beans' and so I was asked my age. Seven was my reply, but that didn't throw SG off balance. Do you go to university (clever so and so!). I noticed what was trying to be gained and was equally vague back. SG wasn't too happy as I continued to be vague in my answers. 'I'm not going to draw the circles if you don't tell me.' 'Fine don't draw the circles, then you be able to return the compass'.

It was interesting since SG managed to draw the circles but copied the table of a neighbour. I noticed this and took the neighbours work and put it at the front. They somehow managed to get the work back when I went to the next table, but I didn't allow them to copy. At the end of the lesson SG hadn't finished the table and got told off. Some form of punishment was given, and I was caught by another student (who had been on my side-hurrah) with a big grin on my face. :D I couldn't help it! SG and the wrestling person, I think, seemed to talk a lot more and do less work. I alos noticed a lot of copying- one person completed the table and then everyone had the answer. (Well not everyone, but I noticed a few many people doing this). SG asked me how long I was going to be there for, and I replied, 'forever', much to the horror of SG! *cue evil laugh* (SG's cool though (in a funny way)- do you think I should continue with this winding up SG business? :D)

Oops another thing happened that left me not knowing what to say. 'What's pi?' I was asked. For a second I was stumped -they didn't know about the approximation 22/7 and the approximation symbol! I quickly recovered and said it's a number, and indicated that the teacher wanted them to use 3.14. I did mention the approximation thing to once person but the calculator didn't have the pi button and the student wasn't interested. Another student asked me 'why do we use pi' i.e. why is the formula for circumference C=\pi D and area A= \pi R^2 .I avoided answering the question because I felt unable to give a proper answer(!), and my explanation that pi was the ratio of the circumference to the diameter wasn't taken in as well. That got me thinking though. (SG had asked the same question later about pi and obviously had to mention something about pies. I think I wouldn't have minded SG's 'behaviour and attitude' had the work been done.)

It was indeed a long day, and I was even persuaded to sit in the staff room! That was freaky, since even now I consider myself to be a kid and teachers to be on a level above me. Sitting in the staff room implied that I was on the same level as them which was weird. Previously I did work experience in a primary school and made the mistake of becoming the students 'friend'. I don't see anything wrong with being 'friends' with your teacher, but it is vital that they understand that you're firstly the teacher. That allows you to set up certain boundaries and so you can tell the students off etc. During the primary school work experience, I had naively made that mistake. I was known by my first name, and I found the idea of being referred to as the other teachers quite 'funny'. I was part of their 'gang', and I never used to go to the staff room but play football during break times with the kids. (I think that's why half of them liked me!)

I became friends with my secondary school English teacher, however the boundaries were there. I do recall stepping out of line once and being put straight but strangely, I appreciated that since I knew that it was deserved. I intend not to make the same mistake again, and although I did talk to a few students about the school (maths, football!) etc, I hope that I am able to learn from my previous mistake. I mentioned this to a teacher in the staff room and she told me that what we have to remember is that if teachers do become friends with the students it's ok, but keep in mind that the students don't need anymore friends (so basically you're the teacher first- and you shouldn't worry too mcuh about the friend business). I think there are some students out there (like me!) who want to become friends with the teachers, but still it's important to make it clear that you're the teacher- especially in secondary school. (It was slightly different in college, since it's more of a 'maturer' relationship that you have with the staff').

This post has probably increased without a bound (ahem) but today was weird (in a good way) day. During the free lesson that I'd had, I had got talking to a history teacher. We had an enlightening conversation and both of us stressed the importance of teachers. Both of us had only ever hated subjects and then done badly in them due to teachers. I don't know whether secondary school teaching is for me, but I'm intending to continue doing work experience and maybe do some in a college as well. It is indeed fascinating to teach, and although it is hard work you can't expect results straight away. I think confidence is very important as well. I'm not yet confident about myself being a teacher which is what can be off putting at times. (One thing you do not want to be is a not confident teacher!). The history teacher has already deduced that I can talk for England. :D I guess you guys already know that, but she'd only spoken to me for an hour or so!

Upon telling the history teachers (another came) that I had completed my first year doing Maths, I was told that it must be difficult. I claimed that I'm just being brave and it's difficult but that can be fun at times! Obviously both teachers preferred the humanities subjects and we ended up discussing blackboards. The school should be getting some smart boards and the history department is looking forward to this. :( I argued that black boards were the best, much to their amusement, and they offered me the board in the class. Upon loudly deciding that for the board to go in my room my wardrobe had to go out, one of the history teacher deduced that I wasn't normal. Phew. (I had kept a low profile on the maths 'obsession' but it had to come out eventually!) I got the worried look that my mum normally reserves for me, but since I was talking to history teachers I decided to show that them that I wasn't entirely ignorant of history and found it interesting. I told them that I knew some history of maths and went to tell them about the great library in Alexandria. *cue some face!* This got us talking about the history of maths, since one class had recently done such project.

OK, I'll stop waffling now. It was indeed a tiring day and I'm feeling 'lethargic' about tomorrow. It's 2:20am now, but I'm awake since I slept from about 5-9pm! (Quite weird since I'd been watching TV and then nodded off. Later on I woke up upstairs!) I'm feeling the strain of trying to wake up earlier and I think that having changed my routine quite suddenly, there are some side effects. Oh no- call the doctors.... maybe not, but I'm glad of this. :) So day one was .... wow (hehe), let's hope day 2 goes good. Morning. ;)

(I've got a bad habit of ending posts by morning or night. :( Hence this line.)

1 comment:

beans said...

I've got to mention what a physics teacher said when I answered that I was doing a maths degree,

'Good, very good that is an honest subject.' :D

(Kerching- I couldn't agree more!)