## Tuesday, July 31, 2007

### Short Changed

It seems that I've finally found the motivation to get myself into gear. Now to answer the questions who, what, where when etc, I'm either looking at the fact that the deadline is in the early hours of tomorrow, or my semi-outburst at Gooseania. Well it was just me talking to myself in the way I normally do... They both have contributed, as has the fact that last night was a full moon. Erm... before we jump to any conclusions, no, I'm not a werewolf. :(

It was quite beautiful actually- turning my bedroom light off to find my room still alight. It's a shame that I was inside, but the creepy crawlies take over at night! Anyway, I had gone to bed ranting and raving which didn't seem to be a great idea- I had nightmares last night.

I'm still sleeping on the floor and in my dream there was a gigantic spider in my room- Shelob size- crawling all over my face! I could feel it's hairy legs. It's large terrifying face still burns in my head! That was enough to make me shoot up in bed and see that it was 9am. *shudders* I don't mind spiders - but on the face - no thank you. I then went back to sleep with my head deeply hidden under the duvet! The second nightmare was of a different and more awful kind.

Anyway, this is just a go between post whilst I'm on my break. I went to the post office today to post a letter (duh) and nuno wanted something. I sent it by recorded delivery and then went to the counter with a Freddo and a pound. Have you ever been short changed? A freddo bar is 15p and so I should have got 85p back. I always tend to check the change in my hand after it's given to me, having first tried to mentally calculate how much it should be. If it's 5p I don't really mind but this was my last quid! The guy had given me back 65p and so charged me 35p for which amount I could have bought a diary milk. Do you check the change you're given? I hesitated but then politely indicated this to him and he then gave me the correct change (I think this happened because he'd been talking to his friend behind the counter today). That's my adventure for the day folks - enough to get my heart beating fast!

Hopefully if all goes to plan, I'll report back on my days work.

BTW is it just me, or are all insects behaving weirdly this summer? :/

## Monday, July 30, 2007

### 'A Very Elegant Lecture'

As said by the author of 'diary of a dual major'. I sometimes post links etc to keep tabs on things I find across the Internet, and this is such an occasion. The link I've just posted is 'a lecture by Timothy Gowers on the importance of mathematics'. I haven't yet watched it, but I'm waiting for the first lecture to load up (which is taking an eternity- it would be easier to download it from somewhere!) Timothy Gowers has written a book that I have on my shelf and so his name stood out.

I haven't been feeling well for the past couple of days and at the same time I've been feeling like I'm not me. I mean I wake up do the things I do, but it seems like I'm watching myself do certain things and not being able to stop myself from doing others. It's weird indeed and you could say I'm having one of them internal conflicts again. Whenever I become ill my, throat gets badly affected since my tonsils are messed up (long story about how they ended up NOT being taken out). And so I get the most irritating cough in the world- not helped by a blocked nose. Humbug. I hope to repossess my body in the days to follow- oh what joy! Is it just me, but don't we all need periods where we want to be left alone? I don't mean alone alone, but alone! I can't explain this feeling, but having talked to Bella today, I'm glad that both of us are itching to get back. I just want to get back to the maths if truth be told- I feel like I've forgotten everything I've learnt so far. :/

A serious post has been in mind for a while but I may or may not post it in the early hours of tomorrow (well it's not so serious- just mad musings of a mad bean). Noddy really did give me a massive blow and I've yet to recover from it and find the motivation I had. The thing with me is that I see all these things working in my clouds, and then get carried away thinking that they're going to work in real life! I have a day left for my deadline to pass- even though I'm feeling deadly despondent (oohh alliteration), I hope to meet that deadline. The negativity has slowed me down considerably I'm afraid. Humbug.

## Sunday, July 29, 2007

### First Year Analysis II

Once upon a time, \sout{in a nursery rhyme there were three bears.} I posted about my thoughts on the first semester. Not wanting to 'tempt fate' I left my thoughts on the second semester till after I'd received my results. That moment has now arrived! [edit: I'd forgotten that I'd typed this up! The original date for this was 7/7/07 at 16:10.]

So I started the second semester with a blog, five maths books and a desire to learn maths as opposed to just studying my modules because I had to. I think it's this transformation in my attitude that has helped me in the second semester. I had honestly thought that I'd done worse than my first semester in some exams, since I'd lost my focus. What probably carried me through was the mistakes I'd made in the first semester, and if I may say again, my desire to study and understand the maths. Where I had thought my focus had been lost, I think it became spread over everything rather than just being concentrated on trying to 'pass exams'.

From my first post in this blog, I wrote: 'This blog may or may not enhance my love for maths, but I hope it does.' Indeed this blog seems to have proven to be a success. Towards exam time I did wonder whether this blog was a distraction, since I tended to post a lot and explore Blogistan at the same time. This was due my lack of self-discipline, but what this blog did was to show me other areas of maths that I wasn't studying. Thus I 'wanted' to know more about such areas and probably in them instances neglected my course material. However, that being said, the one negative (i.e. my lack of self-discipline at times) is really quite insignificant compared to the benifits. Yes, I started the second semester with a new found desire to learn maths and this blog proved to be a great medium for allowing that desire to grow. It was an outlet for my 'obsession' one could say, and through this I found other mathematicians. Mathematicians who had the interest maths!! (shock, horror).

I probably have complained and posted a lot of stupid random things at time. (A quick look at my post titles has me coming to that conclusion!), but for those posts that did have maths, I found that writing down what I'd done helped! Heck, I ended up waking the morning after with the right answer. This might be going off track for a minute, but without naming names, the people who have commented on this blog have been a great, massive, ginormous.... help as well. :) You could say that most of the comments kept me touch with the 'mathematical world'. Memories of my 'angry' post on sequences and series seems to spring to mind as well as the posts about my problems about doing a maths degree. This blog nicely balanced all the negativity I was having about doing a maths degree, which seemed to be seen everywhere in the second semester.

Without a doubt Blogistan (and my linear algebra) supervisor got me aware of communicating maths properly. (That video springs to mind- especially the bit about the typewriter making funny noises if the sentence started with 'f(x)', rather that 'the function'.) I think I may have taken the writing thing a bit too seriously in my exam though! I could go on forever thinking about the positives of this blog (LaTeX...), but I think it played a vital part in my second semester. Maybe I'm really still trying to convince myself of the positives, since I had honestly thought that I'd be blaming this blog (i.e. my lack of self discipline!) when I got my results! Anyway, enough of this now- onto my modules.

I talked about the workshop module in the first semester analysis, since that module ran over the course of two semester, so I'll start with Linear Algebra. I'd looked at the Internet page for this module, before the year had started and seen words like matrices, eigenvalues, eigenvectors and thought phew, at least I'll know something. It probably did start of slowly, but then suddenly a change of pace went undetected by me. I'll admit to probably doing a lot of complaining in the first six weeks of this course, since the way we took notes during the lecture was not something I enjoyed! Looking back, I realise that the lecturer did what he thought best since it can take a while to write out lots of matrices and then reduce them to row echelon form! (I can't think of an 'efficient' way of doing this, but my suggestion had been that the lecturer make a handout with everything that was to be taken from the book on it. Gaps would be on this handout so then we would be able to fill them with new information- like the first semester calculus lectures).

My problem was that I had to copy the notes up again at home (about 22 lectures it was!), and this was a tedious task indeed. I had to do this because I have to have the notes in my file organized, rather than just saying 'page 224 example 4.3 - book', everywhere. After lectures I normally try to read over my notes and try to follow them- making sure that they make sense. I couldn't do this anymore, due to the fact that all I was doing was 'copying' my notes rather than reading through them. Maybe I should have read them and copied them at the same time, but I was in a hurry to finish the copying since I'd fallen behind! [Bella and Milo seem to go home and copy the notes out again, whilst at the same time understanding them, for all lectures!] OK- you got it, this bean is rubbish at multi tasking. :o Well there are certain degrees of this so called 'multi-tasking'. I can't watch TV and talk on the phone at the same time, and if I'm sat at the computer and you're talking to me I'll most likely not take in much! My theory is that I'd rather do one thing at a time and do it properly. :o (Hence why I prefer only writing my notes out once during lectures, and annotating them if need be, which is less time consuming).

Do you sense a long post?! The concept of bases may seem 'trivial' to me now, but at the time when I was falling apart(!), span, dimension etc were alien concepts to me. (even now I'll probably struggle trying to prove that something is a subspace). I took comfort from the little that I did understand, but I think the problem was that we weren't computing matrices any longer. I could do most of the questions which had a certain 'algorithm' for finding the answer eg. the inverse, but I didn't understand the theory which didn't help. Apart from the note taking problem the lectures were cool. We used to be given a mid lecture question, and that I enjoyed.

After the 22 lectures we had a different lecturer! This signalled the end to me having to copy up any notes at home. :D The great thing about the weeks to follow was that we kind of learnt about the same concepts from the first weeks but generalised them. In this was way previous concepts which I may not have understood before clicked slightly (i.e. span!). There's not much else I can say about the lectures that followed apart from them being great! I actually looked forward to each lecture and I guess I love taking notes during lectures. There may have been things which I didn't follow at times, but now I was able to go home and read over my notes. So if I did have a problem, I could always ask the lecturer about it. (Which I did- too often I believe!)

I honestly can't think of anything I 'didn't' like about the weeks that followed! The material covered in the last week was probably one of the most important topics, but sadly I didn't follow it [linear transformations and eigenvalues!]. And as the lecturer said, we tend to start revising from the beginning and by the time we get to the last few important topics we run out of time! (happened to me). I think in these weeks I had a certain desire to understand the topics and do the problems, namely because I found the lecturer cool. I used to really enjoy the lectures- especially the stories. :D [The motivation was there so to speak, not quite like the first semester, but it was there!] Nope- I've been waffling and trying to think of anything 'bad' but I can't. I especially enjoyed discussing football with the lecturer- although I probably became annoying after a bit. Hmm, can't really think of any negatives... (I think having done some of the things before may have also made me lazy to a certain extent!)

Might as well move on to calculus and applications. This module was split into two parts- ODEs and mechanics. The only semi-complaint I have is that this course was taught by two 2-hour lectures on a Monday and Friday. This had it's benefits, but sometimes if you weren't awake or didn't fully follow the first lecture you suffered in the second one. It was good since the pace was more relaxed, but if you had a bad day then you (I) were(was) in trouble. However, I think during the first lecturers course the two hours seems to whiz by (apart from when we did oscillations!). I've said it before but the lecturer taught with a real energy about him and that was contagious. I must say that on certain weekends I actually looked forward to Mondays two hour calculus lecture!

I'm quite amazed at the turn around in my attitude to this subject. Not the module but the course content. This turn around is what is making me want to do fluid dynamics next year, but it's too risky! It's funny how when you look back onto events and other such things, the first things that you tend to remember are the things you didn't like. (i.e. the note making in linear algebra!). I can't think of anything bad about the whole calculus and applications course.... but wait, if I strain a little something might pop up for mechanics! I've had really cool lecturers this semester, and really cool supervisors as well. That has made a huge difference- especially the supervisors!

Heck- how could I forget! The worst thing possible, in the first six weeks, has got to be not getting 'the quid' from the lecturer. :D Oh yes- that quid! (I'm going to have a fun time when I'm old with my million odd cats. :o ). On a more serious note, (taking aside the 'no quid' thing), I found the lecturer awesome. He even made oscillations- my worst topic- seem less ugly, by bringing his own precious mug in for a demonstration. I'd be lying if I was to say that I didn't want 'resonance' i.e. the mug to break! Did I just write that down... erm... 'you didn't see a thing' (Madagascar style ;) ). The fact that I understand this whole oscillation business and SHM(!) is maybe what is making me more happy. However, before anyone gets too excited, I probably still won't be able to answer the questions! I really enjoyed this module and looking back, it made a lot of sense. (I did apologise to the perturbation method before right?)

Is it that obvious that I'm trying to delay talking about mechanics! I wasn't actually, but since I actually enjoyed this course I want to write more (than normal!) about it. My problem with mechanics was that although I enjoyed learning about the concepts, it wasn't clicking. I couldn't answer the questions and if you were to ask me about angular momentum I wouldn't know. Now the one thing that probably caused me problems in this course was VECTORS. My posts complaining about SUVAT equations and many other things were due to me overlooking the fact that we now employed vectors. I'd done all this resolving forces business in college but without using vectors and so it took me a while to actually see my mistake (I left it till very late).

Our mechanics lectures always tended to be good. Apart from the time I was having a bad day I enjoyed them. The best ever lecture had to be when we talked about anti cyclones, cyclones and what not. Seeing mechanics application to the 'real world' is probably what interests me more, and understanding the concepts. My understanding of mechanics is pretty 'duh' but it's a fun subject. This is definitely a complete turn around to my previous attitude of 'hating' it, which I welcome and is probably down to the lectures. And guess what- angular momentum no longer scares me! The lecturer was really friendly as well, and helped me on more than one occasion. Do you think lecturers are all trained to not show their annoyance at beans like me?! :D

For a second I had thought that I'd mentioned all the modules I took in the second semester. I seem to be forgetting one- Sequences and Series. Well, it's been a journey and a half with this module and I think, had I not started going to the Dr C's example classes, I'd safely be disliking this module and probably wouldn't have had the little understanding I have now. I know my problem and what probably makes me more dumb is that I don't try to overcome this problem. Actually this time you could say I did attempt to overcome this problem since I had consulted Dr. C about the problem. My problem is that if I don't like lessons or lectures of a particular subject or module, I tend to erm... hate and do badly in them modules. Well I might recover the ship and scrape a pass, but my understanding of that subject is rather poor.

This happened, firstly in English lessons at school (until we got a new awesome teacher), then Physics lessons, which sadly I never did get to like. I could blame my teacher but that's stupid of me since it was partly my fault. I reacted stubbornly to not being allowed to ask questions, and although I never disrupted lessons I just used to sit and doodle. (And whenever I got the chance outside lessons, I complained of hating Physics!). I also didn't particularly like stats lessons at college, since there was this group of students who 'bullied' the teacher and never let her teach. Rather than disciplining them on occasions when they did step out of line, she tried to speak over them. I didn't 'hate' the lessons, but I disliked stats. This dislike continued into university and I hated the stats module during the first semester. I hated it and that is the only module for which I've missed more than one lecture! I had my reasons for this, but although I got books from the library I never got stats.

So it seems that whenever I do find myself in them situations, I just end up winding myself up and not doing anything positively to overcome my troubles. It's my fault for being highly dependent on teachers, but I should have a backup plan! Thankfully for sequences and series I did have such a plan and it made a huge difference.

I don't really know what to say about this module since all semester I've been saying a lot on it! Dare I say too much, but I think my post 'Analysis?' sums things up nicely. Especially the bit that books don't give you motivation. Having read the 'In praise of Lectures' document again I'd say that I really enjoy lectures and *makes sure no one is looking* and look forward to attending most of them.** Consequently what probably happens is that I don't like the modules whose lectures I don't like attending, and so if I don't have a back up plan I do badly. As that document said, and I was surprised to have made the link myself in my lame artist post, lectures enable us to see the masters at work. "Mathematics textbooks show us how mathematicians write mathematics (admittedly an important skill to acquire) but lectures show us how mathematicians do mathematics."

Call me sad, but in my second semester I didn't miss one lecture. I even persevered and attended all the sequences and series lectures, when at times I didn't want to.

And there's where I'd left the post (I'm typing this today!) I think attending lectures or lessons makes a big difference and that's how I learn. I mean, I know we get loans to pay the university, but we have to pay them back one day! Before I do end this post, MATLAB has to have a mention! I think the final score in that match has to be 2-1 to beans. It has to be... well what do you reckon? I've probably forgotten most commands (even the diary one- was it diary session1.txt ?), but I did manage to hand in all my coursework that required its use.

So to conclude, (like I did last time!), I finished semester two with the blog intact and many more maths books (at least 10, thanks to the Tweenies as well), however I didn't really want the year to finish. My first year couldn't have gone any better- I made good new friends and met some cool lecturers. Most importantly my aspirations for studying maths were soaring. I think the holidays have dampened my mood about maths, but that's because of circumstances. There were certain things that I should have done but didn't, so let's hope that next year will be just as good as the first, if not better! (I hope to do the things I didn't do you see). Sadly the mss building and it's stairs will be longer be available, but I'm sure the stairs in the Sackville Street building will be a good substitute.

*I was going to make a new post but this seems a nice place for a little something. I had a dream last night in which I attended three lectures. We started of with a lecture at the university and then Milo, Bella, the lecturer and myself were in n13 (mss building). The lecturer was someone who I had never seen in my life-ever. I started talking to him and learnt that he was from Brazil! We then talked about football and maths, but then it was time for 'the next lecture', which seemed to take place in my primary school! The year four class is designed stupidly and I found a seat where I couldn't see the board, but that problem was quickly solved. Straight after that lecture we had another one by a different lecturer and it was about Hercules! Well we worked the title out by playing hangman... weird. I do remember enjoying it though and after the last lecture we all hurried back to the computer room to find out which lectures we had tomorrow- obviously we didn't have any and that is all I remember- looking for the timetable! Does this dream describe the state of my mind?

## Friday, July 27, 2007

### BOD..I mean BIDMAS!

The page that wouldn't fully load for me yesterday, has blessed me with it's insight! (It's the 'Common Undergraduate Errors' one).

In school I was taught 'BODMAS' - Brackets O.. Division, Multiplication, Addition, Subtraction. (I can't remember what the O was).

Hence, if I may copy something from that site, I used to interpret $-3^2$ as $(-3)^2$, which resulted in the wrong answer. I remember this very well since in my case the number had been -2 (I think) and it had been an integration question at college. I've just managed to locate the question and it was:

$\displaystyle\int^2_0 xe^{-x^2}dx$

I'll tell you something embarrassing- just know I tried doing the question on paper and my mind was blank. The first thought to zoom into and out of my head had been, 'integration by parts'! Don't worry, a good bang against the wall soon sorted me out. (In my defence the chapter after this one was on integration by parts....)

I might as well attempt it here in the way I did a year or so ago. I can't do substitutions in my head (since integration stinks!), so we do it the long way. I don't really know how the write this out 'nicely' so here goes.

We use the substitution $u=-x^2$.

$\begin{array}{ccc} u & = &-x^2\\*[1ex] \displaystyle\frac{du}{dx} & = & -2x\\*[1ex] dx & = & \displaystyle\frac{du}{-2x}\\ \end{array}$

Now this is the place when I made my silly mistake- changing the limits. I did,
$\\\text{When }x=2, u=(-2)^2=4 \text{ and when }x=0, u=0.$

Oops- the mistake has been made. (It's meant to be -4). I don't think I ever realised my mistake at that time and had just regarded the answer in the back of the book to be wrong. (The answer in the back of the book was $\frac{1}{2}(e^4-1)$. Please tell me that it is wrong! Since having done it again, hopefully properly, I get $\frac{1}{2}(1-e^{-4})$. I think the book might be wrong, since it says the answer is about 26 which doesn't sound right.

The question after all says -1(x^2), which I'd overlooked. Ah well, hopefully I won't be making that mistake again! BIDMAS all the way. (BTW what did the O stand for?) I'm not sure whether this is taught in primary schools, but words like indices should be made known to students at an early age.

I might as well mention a small (and unrelated to BIDMAS) thing now and expand on it later. A friend of mine has been reading a book and supposedly 'successful' people are those who are committed to achieving certain goals. They know what they want to accomplish. If you ask this kind of person what they hope to achieve, they'll give you a well thought out and concise answer. Whereas those who are not committed to anything but 'earning loads of cash' may not be as successful. Success is a result of commitment more than luck. I've asked to borrow this book, but I'm writing this since Andrew Wiles popped into my head when I was talking to my friend. He was totally focused on achieving something and he did. It's all about our attitude and approach to things that matters after all. Maybe I should take heed? (I'll be back with more after reading that book!)

## Thursday, July 26, 2007

### The art of Googling (maths links).

I don't remember what exactly I googled, but let me just check my history. Ah yes, I wanted to see if maths lectures was written with an apostrophe s. That is, is it meant to be maths lecture's? I can't have mastered the art properly since all I'd googled was 'maths lectures'!

Anyway, from this I've found some nice links that I'd thought might be useful for mathematicians and maths undergraduates. (Some have been bookmarked on previous occasions).

For undergraduates or first year students.

Maths Writing (recycled from my post on maths writing, which had a lot of preamble).

Notes and books etc
General

Don't worry, you're not expected to read them all at once - I for one didn't! Save them for a rainy day, which in my case was most of today. BTW I only discovered about four links today, and I'll save my Internet explorer bookmarks for another day!

I've ditched the magazine idea and my previous post as well! (For those who managed to catch a glimpse of it). The thoughts, 'biting of more than I can chew', seem to be echoed. In the document I'm writing I'll suggest it, but no more. You see I've decided that I only want to start this so called thing and then not take any responsibility of it. I have a hard time juggling my studies and I've never learnt how to juggle with more than 3 balls, which is a good enough reason. (Noddy has a fair point even though I've been arguing otherwise. Sigh.)

Sorry for those of you who are wondering what I'm blabbing about. Talking to myself again I suppose. Anyway, I might as well not type whatever else I'm saying to myself and so leave you with two 'nice' quotes- probably describing my mood ...

"The best way to keep one's word is not to give it."
Napoleon Bonaparte

"It's kind of fun to do the impossible."
Walt Disney.

## Tuesday, July 24, 2007

### Infinity Comes in Different Sizes

*apparates in front of computer*

Ahem, so where were we! I have been sent the following link by an email from a mathemagician, (or the opposite of that*!) and found it interesting.

"...Scientific American article on the "different" sizes of infinity. It discusses Cantor's Paradox and how this is possible.

It's two pages BTW! (You might not have noticed...)

I've finished reading the last Harry Potter book and will probably discuss it later on. (You might not have read it yet, and I do recall how I didn't like it when someone told me about the 5th one). One thing I've noticed is that Rowling's books are very similar to the Lord of the Rings. Obviously they both have a 'good vs evil' theme, but the similarities seem to jump at you. My reduced thoughts: it was a great book and it kept me from showing my face for the whole day! (I didn't read much on the weekend. Although during the night, I had sat in the lit hallway till some weird time until I was spotted reading- wasn't home you see). However, today there was no holding back. It's funny how you never realise how hungry you are when you're just sat in one place reading!

Believe it or not Harry Potter had been out of my system since the sixth book because I'd hated it! However the magic returns. (coughs). I got it for a bargain as well - £5 from Asda! BTW I've concluded that I was either under the Imperious curse or confuddled during the previous post (if indeed you shook your head at it). Wait... I need to get a life! Nah- I was just playing the devil's advocate I suppose but I'm seeing things differently now. (Not in a bad way). I still haven't read on because of the Harry Potter book, but will do.

Isn't it weird how quickly we tend to read fiction, yet when it comes to reading non-fiction we seem to take ages. (Or is that just me?) Actually I've slowed down my fiction reading speed considerably, and I think that's because now whenever I read I have to have the images of what I'm reading forming in my head. I've got all the Harry Potter book images in my head at the moment - well the way I see things. It's pretty 'cool' and maybe that's why I hate the movies so much! (I have refused to watch the movie Off Mice and Men having read the great book and hopefully won't ever watch it!)

Hopefully things will be returning to normal in the coming week, but then again one can never be too sure about these things! (especially considering it's me we're talking about!)

For those who don't know about Harry Potter, if you're not a wizard you're called a muggle. So if you're not a mathemagician, what would/should you be called? I thought 'trouble' to rhyme with muggle but poetry has never been my strongest point. And you can't go around calling 'troubles', 'trouble' unless you are indeed looking for trouble! (ouch).

I'd say a mathemagician is someone who enjoys maths as opposed to someone who has to do it. So someone who doesn't enjoy maths is called... (apart from evil!)... erm... I'll have to sleep on it! I think I also need to watch my step from now on: Protego. Haha- try getting me now. Wait- I thought I'd grown up. Oops, I'm probably still excited and so to end this post on a more sober note, what is one plus one? (This question should determine the \sout{century} year you were born in!)1

Wait if I'm a (wanabe) mathemagican then protego shouldn't work for me- drat I'll have to end up staying on the run now! We should all work together (ahem) and invent spells(?)/maths(?) that are mathemagician friendly -I vote we start on one to shield ourselves! Of course we should be wary of any Voldemort's flying around -know any?

Are there any Potter fans out there? If not, my apologies and I'll promise not to erase your memory of such post if you don't contact St. Mungos. :( (I don't know when to shut up do I? (Rhetorical question alert!)).

1 Well not really- but it'll give me a subtle indication. Again not really really... just answer the question in the way you would! :D It's a test!

PS: I really need to start providing links again.

## Friday, July 20, 2007

### Mathematics: something really ugly yet beautiful.

Is that the case with maths? Is it really this horrible looking thing, which as sometimes happens, appears beautiful to certain people but horrible to others?

'Mathematics is logically imperfect', so what is it that we find beautiful and great about it? Did the perfection or ultimate truth of it attract you? How would you feel, upon discovering that it's not really that perfect after all? At a younger age I used to like the fact that an answer was either right or wrong in maths. If it was right then you were left feeling content, and if it was wrong you struggled with the question to get the right answer- which provided a feeling of more great than just contentment, upon arriving at the right answer.

Compared to other subjects, like English and History, I was always left frustrated in them whenever I got a big red cross. Namely because I didn't know what the right answer was. The teacher used to argue that the 'beauty' of English is that there is no right answer, but I wasn't taken in by these comments. (Especially on certain exercises). My battles with the comprehension exercises and I think, the lack of tools in my English back pack, always had me struggling. Hence, the immense dislike this 13 year old bean felt for English.

It was ultimately this 'challenge' to get the one right answer, using whatever means possible, that kept me attracted to maths like a magnet. It was the desire to overcome the difficulties that lay across my path. It was the feeling of having conquered a nation by defeating the question. And the more common feeling to myself- that of having scored a goal or taken a wicket. The adrenaline rush and excitement of the victory is always immense and leaves you wanting more. Maybe that is why I end up liking the areas of maths (analysis) which cause me the greatest distress? The largest amount of joy is associated with these areas- if I'm ever to overcome my difficulties.

It is now as I'm doing some reading, that I realise that everyone has a different motivation to studying maths.

The one word that I can unfortunately come up with, to describe why I want to continue my study of mathematics, is that 'maths is cool.' If I was to strain my 'ickle'* brain a little more, I'd say that the diverse nature of maths is alluring and the satisfying pleasure of sometimes following a proof and other times constructing one myself has me hungry for more. Yes, I was ignorant of maths until I started university (as I continually say), and only now am I getting a proper birds eye view of everything. But I think my motivation is still the same. I still want to study exciting concepts and be able to understand them. To overcome difficulties.

What am I getting at? Well, I'm currently reading a book and it has a mention of Russel's Paradox. I read this during the year sometime but didn't think much of it, but today I read about Godel's theorems of undecidability. Are these the questions that everyone asks upon reading the two theorems? The theorems in question are,

First Theorem
'If axiomatic set theory is consistent, there exists conjectures which can neither be proved or disproved.'

Second Theorem
There is no constructive procedure which will prove axiomatic theory to be consistent.

I've foolishly not read ahead and decided to post this, but although we assume certain axioms when we prove, we can never be sure of them being true. As I continue my mathematical 'bull' (1st post!) doesn't that make Maths like Physics or the sciences, in where experimental deductions are used as results? Or is my arrow a long way off. Don't worry I actually like these two theorems since, like I've said, sometimes a scratch on an otherwise perfect car can appear beautiful. (As long as it's not my car :D). That example stinks, but e.g the mss building. It looks old and 'ugly' yet there is something beautiful about it. (apart from the fact I had an office there). As these thoughts swirl about, I'm reminded of the following picture:

How perfect is maths then? Or is it only the logicians how face this problem? As Russel said upon Godel's discovery,

'I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere...'

Once again, I don't really know what I'm thinking but I'm trying to splutter something out which doesn't make sense. (as usual).

What I may be getting at is the fact that when I was talking to the teachers who didn't teach maths, I said something to the effect that in maths, once you have a proof of something you can't contest it, because it is based on logical premises that are all true. But are Godel's theorems saying that step 1 of the proof may or may not be true? I know in maths we tend to 'assume' a lot of things, and say that if this is the case then something else is true etc, but should we be assuming things that haven't been proved. Tell me when to shut up, but I'm actually quite happy about 'this chink' so to speak. It's not making me look at maths in another light, but rather I'm glad that Russell didn't find the certainty in Mathematics the way he wanted.

Am I going against the 'code of a mathematician' by saying these things? I know certain axioms are obvious, like the addition of real numbers is commutative, but .... I think it's best that I carry on reading. :D This makes maths all the more interesting. Oh, and this post does not make any sense!

I've been having a week full of quotes, so why stop now:

"Wir müssen wissen,
Wir Wirden wissen.

We must know,
We will know."

That was inscribed on David Hilbert's tombstone and it sounded neat.

Internet problems have delayed this post, but is any one else getting the Harry Potter book in a few hours? Don't be alarmed if you see Voldemort around ... I'll be away for the weekend, so have a Potty one! My post on my final week at the school and overall thoughts will have to wait- don't look too happy!!

## Thursday, July 19, 2007

### Hidden.

I'm slightly disappointed at the moment having just discovered something else on the BBC website, but it's not to about maths so it's OK.(This was in the early morning BTW). The BBC site had a photo competition with the theme 'Hidden', and you could submit three photos. I didn't manage to since they seemed to have cancelled all the competitions. Worry not though- my silly pictures can always be posted here! (Brace yourselves).

Due to my commitment to something else I'd gone to sleep at about 5am this morning. It was just like in the old days- however, on this occasion I fell asleep when I shouldn't have! I just rested my eyes for a second and I was out cold. Thankfully I had done a majority of what was required. (Nothing major don't worry!) I do wonder how I managed to wake up this morning, but alas I did. Surprisingly I'm feeling wide awake now. But wait, I'll let you in on a secret- after coming home today I slept till 8ish, which explains the wide awakeness. (I'm allowed to make up words today!)

And so my placement has ended. Patrick will miss his friend sponge bob and Lennie will probably be missed as well. The one bunch of students that will not be missed is the year eights. Well a majority of them- they gave me nightmares. Even today, I tried my best to avoid them. It's my own fault, since for the students who gave me nightmares they knew they could. Ah well, I've learnt from it. If the students want conversation- give them something.

A teacher asked me whether I've not been put off teaching at schools. I haven't, but I'm not sure whether secondary school is the right level. My first 'love' (bucket please), is maths and then it's teaching. The commitment of a teacher makes it hard for even the maths teachers to appreciate and learn more about their subject, as opposed to just teaching it. I don't want that to happen- I don't want to ever stop learning maths. It might not happen, but it's given me some food for thought indeed. More about this week tomorrow. Here's another quote and the pictures that I was going to submit.

"The teacher can open the door, but you must enter by yourself."

This is a slug feasting on or hiding a snail! A snail had been stood on by someone, and the next thing we found was this yeerk wrapped around the snail! (The snail is hidden. :p)

Well it's sunny and not sunny at the same time... I don't really know what I was playing with here, but it's not really meant to be hidden, but it is sort of hidden I suppose!

I was going to only submit them to, but I've found a rubbish third 'hidden' photo which you might find amusing.

That's at the UMIST campus (north campus) in Manchester, and it's slightly off balance since I was trying to take this picture whilst walking! This always makes me laugh whenever I walk past it, and he is sort of hidden. :p

(believe it or not I'm still tired!)

## Wednesday, July 18, 2007

### A nice little quote.

Well I consider the quote to be nice anyway- rolls of the tongue in a certain pleasant way you see:

'...but of course maths is never out of date, just out of fashion.'
(My PT)

At the end of this placement I'm feeling a certain type of sadness. The one I felt at the end of the university term, at the prospect of three and half months of holidays and no maths lectures.

Shoot me.

I'm an active learner and although I was desperate for a week off during the second semester, I want it to start again. If you've not got a healthy heart then you might want to stop reading this short post. Thoughts like this by me seem to affect people in a negative way! Oh- and I hope your eyes don't roll out of their socket... (if indeed you are one of them people!)

We should do a study to see how many weeks of holiday are actually healthy for the brain- I mean rather than having a chunky six week (or 3.5 months) holiday, can't we break them chunks up and position them into the year somehow? Or is this the point where I should shut up and leave my thoughts be? I don't know whether I'd say I'm lazy *coughs*, but when you're going to university or school everyday you have the motivation to study and it's a continuous thing. Well that's the case for me- I just need to get started, which is the hardest bit. Two months left eh, let's see how productive they turn out to be. This placement seems to have sorted me out to some degree and it's a shame that it has to end.

Today I learnt that accommodation was a greedy word, since it has two m's and two c's as well as a few other handy English tips. (I was found wanting on my disgraceful behaviour of not thinking where apostrophes should go!) However- I've already forgotten one or two things that were said. Crikey, my brain is like a sieve- I think a few teachers were getting me back for my blatant 'advertising' of maths!

Now would you prefer a long post everyday about my day or an even longer one on Friday? Well it has to be the Friday option since this Bean has got to go in a minute! Let's see how good I actually am when it comes to deadlines and pressure. What a night like tonight requires, is a strong cup of tea!

NOTE TO SELF: Remember conversation with maths teacher.

## Tuesday, July 17, 2007

### Zeller's algorithm

Monday's child is fair of face,
Tuesday's child is full of grace,
Wednesday's child is full of woe,
Thursday's child has far to go.
Friday's child is loving and giving,
Saturday's child works hard for a living,
But the child born on the Sabbath Day,
Is fair and wise and good in every way.

So which day of the week were you born on? You can find out in a while if you don't know and more importantly if you want to.... (that's my rubbish attempt to sound enthusiastic. :( )

This week has been a busy one, but apart from today I'm just going to summarise my observations of the lessons at the end of the week (rather than everyday!). Truth be told I've been pretty tired and so my brain doesn't want me type. BTW repetition is not good for the brain, as says Dr Kawashima (my brain is 30 years old now- well he did tell me that sleep was important!). I think it's more of a point that you shouldn't always restrict yourself to repeating the same activity, without moving on when you can.

I was meant to plan part of a lesson for the year seven set 4 class and I had been considering asking them the same question that I just asked a minute ago- in a more enthusiastic manner of course. That lesson wasn't meant to be today, so I was going to discuss my ideas with the maths teacher during a free period. We didn't get a proper chance to discuss it, but we tried to see how we could make the lesson student friendly and more wordy. (It had too much going on).

I'll discuss the rest of the day later, but alas today I was once again attacked by the English department. :/ I had to help cover an English lesson for about 10 minutes. Thankfully the class had students who are now familiar with seeing my scary face and some know me from Maths lessons. (Phew!) I didn't want to do 'nothing' and I didn't want to do English, so I asked them the same question as well (about the day they're born on)! A few were interested and so after some persuasion we worked through the algorithm and most of them managed to work out what day of the week they were born on. (apart from those who didn't take part and glared at me for even suggesting doing some 'maths' in an English lesson!). Before I had to leave a few students groaned that this wasn't English and so I did an ickle 'syllogism' with them (did I mention that I liked them!). Thankfully I didn't stay in that lesson for long. Next lesson it was the year sevens. Set 4.

Before I describe the disastrous events that followed I will post how Zeller's algorithm works, through an example (my friends birthday). Zellers algorithm is a series of steps through which you can work out the day you were born on. It doesn't have to be for the day you were born, but it can work out the day of any other date as well. It's going to be in 'baby' language if that's OK. (Some notation before we start: [x] = the largest integer not exceeding x or 'integral part'.)

My friends DOB: 1/07/1988 (Write your DOB here!)

Date= D= 1
Month = M= 7
Year= Y= 1988

We take the year (1988) and split it into two components- 19 and 88. Call the 19 bit C and the 88 bit Y'.

C= 19
Y'=88

Then calculate:

$\displaystyle A= \left[ 2.6M-5.39 \right] + \left[\frac{Y'}{4} \right]+ \left[\frac{C}{4}\right]=12+22+4=38$

Now work out the sum:

$\\Z=D+Y'-2C+A\\ Z= 1 +88-38 +38\\ Z=89$

Divide this by seven and take the integer part,

$\displaystyle\left[\frac{Z}{7}\right]=\left[\frac{89}{7} \right]= 12$

Finally we calculate the remainder which turns out to be: 89 - (12 x 7)= 5, and so my friend was born on a Friday. *Quickly goes to check* Yep- that seems to be the case!! (If it's 1 you're born on a Monday, 2 a Tuesday.... ). Here's a more comprehensive version of the algorithm, and you might notice that dividing by 7, taking the integer part and then working out the remainder is the same as calculating 89 mod7.

I couldn't find the LaTeX code for the integer brackets properly (not that I looked hard enough!), but year sevens don't know about this notation. We did this in college but all I had from my notes was the calculations with no words. I also didn't have anything called Z or A, but to make things look 'nicer' I introduced them. However, that wouldn't look nice for the year sevens. Fair enough, I was going to write up a sheet with blanks and words describing what goes in each box, and instructions on what to do next. (I don't have my D1 book anymore, but if I remember correctly the algorithm was a set of instructions and just that!)

Originally I was meant to do this bit on Thursday's lesson, if indeed I did do it. But in today's lesson the teacher learnt that it was the last maths lesson with this class. A quiz was going to be prepared for the last ever lesson but that couldn't happen anymore. The teacher contemplated on whether to continue with angles and after some discussion I was at the front of the class all of a sudden, asking the same question again. ;(

I'm annoyed at myself for not preparing properly and even more so because I didn't react to the situation in a positive way. I just ... melted. Well you could still see my head (slightly), but inside I was shouting, 'Nooooooooooooooo' in a dramatic way as my life went zooming past. Yes- everything is still dramatic! Most students didn't have calculators and I confused many of them because I had decided not to call A 'A', and not to call Z 'Z'. Looking back I should have written sentences on the board for them to follow, but I didn't think. Some students actually did follow everything and waited impatiently as the other's struggled but the challenge is getting the students who struggle to overcome their difficulties. Apart from doing this on one occasion I messed up big time. The teacher helped a lot but I think when the teacher's present I become nervous all of a sudden. It's a weird sensation where normally my mind goes blank and I look expectantly at the teacher hoping that I don't have to say anything. (Which is why another teacher probably observed me on another occasion).

I guess it's because I feel under the light, but I was told to not pay any attention to the teacher being there, which is easier said than done! The lesson I'm afraid was awful (my bit anyway- the teacher recovered it later on). Some students were really eager to work out the day they were born on, but sadly they couldn't. The teacher told me not to worry about it too much, but I'm annoyed because it didn't go as I wanted it to. Maybe this was a stupid topic to pick after all. :( Thankfully this was the last lesson of the day, so I was able to come home and rub my wounds. Meh- I mustn't dwell on this for too long but I keep on thinking about what I should have done but didn't.

Now onto the 'beginning' of the day.

In the morning I was with a year 9 class. This is the final week of school (which signals my full time return to help Bob!), and the students were desperate for a free lesson (much to my dismay :D). The teacher asked the students who wanted a free lesson to put their hands up. All students hands went up apart from Lennie, who I mentioned last time, is my maths buddy! Another student did try and force Lennie's hand up, but Lennie was getting annoyed at the time wasting- there was maths to be done!

Since I was sat near Lennie's table and since Lennie was asking for maths, I decided to do some maths with him whilst the class discussed the free lesson. From the book, I opened the page on quadratics to see what to do. I then asked Lennie (and a curious friend), the answer for: $x(3x+6)$. They wrote: $3x+6x=9x$. They hadn't multiplied the x terms, and after asking them what 10 x 10 equals in terms on 10 (10^2), and a few other numbers, they realised it's meant to be x^2. A few other students 'mocked' Lennie, but I offhandedly mentioned to them that although they were not to quote me on anything, if you did a Maths A level you're likely to earn 9% more! (or something like that). Lennie seems to have his head screwed on straight and knows what he wants to achieve and what he must do so thankfully didn't care to much about what his classmates were saying.

By the time the class teacher had decided to do a lesson I was pleasantly surprised to find that it was to do with quadratic factorisation and solving quadratic equations. I didn't know this was year 9 material, and had only opened the page for Lennie since I thought he might find it useful in preparation for year 10. I think they had done something like this before but all of a sudden many students were confused when they had to solve the following: (x- 1)(x +1)=0. The teacher did explain this but a few didn't follow. (Why do I have a stinking suspicion that the teacher had heard me talking to Lennie about quadratic equations and then decided to do them?)

The problem I had was that I didn't know how much these students knew and what they knew. Had they encountered the quadratic graph before, and were they to know that when the graph cuts the x-axis we have a root? I asked questions to deduce what they knew but one student seemed to be having a bad day. (It was nice when the concept actually 'clicked' since I was with this group for a while.) They all did seem to be slightly more lethargic than normal and I also finally got the 'graffiti artist' student to do some questions. Woo hoo. (Although I spotted one student who had not even started the work!)

This lesson was quite good and I really enjoyed it. Now I'm jumping from lesson to lesson but let me tell you a little secret. I was going to go to SG's maths class today, and as I entered I was greeted with the site of graph paper! *alarm alarm* That was it- I quickly apologised to the teacher and said that I was with the other set today and made my get away to the other year 8 class. That wasn't much better, but better than using graph paper to do what not! I ended up sitting next to the worst table in the classroom, but I think they were playing up since I was sat there. (A lot of swearing and a lot of not nice words were said!) As soon as the lesson had been delivered and the students were told to get on with their work I was on the move, and quickly positioned myself on the opposite side of the classroom. The lesson was on transformations and a lot of the students did recklessly rotate a shape by 90 degrees and didn't check if it was correct, but they could do most of the work. Apart from the loud group the lesson went well.

The class teacher had thought I was doing my PGCSE (Post Graduate certificate of Education?)!!! So I've been mistaken for a year 10 student (15 years old), a college student (17/18), and now a post graduate (21+). No one seems to guess that I'm at university, and none of them believe that I'm seven! You could also look at my age mod 25, rather than it belonging to the group S_25 I suppose...

All the teachers seem to looking forward to the end of the week. I wonder why?!

(There's something I've forgotten but I can't remember what!! Duh!)

### "UK adults fail child's maths test."

I read this article today at the BBC website. It's only one question which makes it stupid for someone (i.e. me) to make a big hype about it, but it'd be interesting to know what problem the people doing this encountered. Were they not able to do the division without a calculator, or did they not understand the question?

You could say it's a 'duh' thing to suggest that people who went school 30 or so years ago would not be able to answer that question. The standard of education was entirely different then (better I believe!) compared to nowadays. What do we have today- technology? Hmm, I'm not trying to sound like a bitter old so and so with many cats, but what's really changed, from my opinion is the attitude of students. I don't know- my head is slightly loosely screwed today since I didn't realise that the keyboard has the keys, '[' and ']'- but it can't just be that. (I love going on about this don't I? :D)

Maybe what's missing is respect. All you hear students doing nowadays is swearing at their teachers, adults and everyone! Some swear words have become part of their vocabulary and they don't realise that swearing is not a good thing. I'm not going to pretend to be some angel- I do swear on occasions, but I tend to swear at events or things that happen. However, I know when not to swear. We had this event of some sort in my form class in school (once upon a time). If you swore you had to put 5p in a jar. If you wouldn't say it in front of your parents (bloody/crap) it's a swear. Oops that's 10p from me! One of my friend, who had a colourful tongue indeed, didn't like this restriction but wouldn't shut up, so my friend had to put 10p in the jar per swear. (The money went towards the annual fund raiser).

I've started doing that again but in my house. Hearing someone else swear makes you realise how vulgar it sounds- especially certain words! The only people I'd probably swear in front are the teletubbies and the Tweenies. The challenge for me is to control my tongue when I'm hot under the collar! I'll need small 'IOU' cards to go with the jar... It's a good scheme and when we were also younger we had an allowance. Whenever you swore 5p would get deducted and if you were rude to someone it was 50p. The aim of the game was to keep the amount of money you were to get, a large positive amount (we dealt in negatives as well- the amount carried over to the next week!) So let's see how long I can keep this up for.

I got carried away for a second but I'm not surprised at that result. The title of the article is slightly misleading, since a test does not consist of one question but I'm sure that some of the year seven students might have difficulty interpreting that question. If it said 32/8 they'd be OK, but it's the 'of' that might be off-putting!

I just asked Nuno this question who is in primary school at the moment and Nuno said 8. (Well Nuno had problems with hearing at a young age which went undetected. The problem is still there but it's known to us now and Nuno is a slow learner. Well if you can't hear, it's a bit hard to learn!) Exactly how many 8 year olds would you find answering that question correctly?

Woo- I've just ran every where and found that Lala's initial response was 8 as well! It was then corrected to 4 but....! (I'll comment on the others response when I locate them.) Didn't I warn myself to not get excited by this....

## Monday, July 16, 2007

### Slimy \sout{friend} foe recaptured!

Don't worry, there's no picture! (Not yet anyway...) The yeerk has been recaptured and it was found feasting upon a snail. :/ When I do post the picture, you'll probably be as fascinated as I was, but first it needs to be interrogated! I do wonder what I've got myself into- these yeerks don't seem to be backing down.

This weekend hasn't been a 'weekend'. The week hasn't ended, and guess what- it's not going to! Tomorrow I must rise before midday to go to school. I love saying that. I spoke to someone the other day and told them that I'm going to school on Monday- they didn't know how to respond for the first few minutes!

I've not done any real maths during the holidays which is making me feel slightly annoyed. I've been lazy in other things as well, but I can't believe that I'm annoyed at my laziness! I won't call it laziness to be exact- just not reached the right motivation. At the moment I've been 'conspiring' to do two things but it's all in my head (need to get it out of there). I think I need someone to tell me to do such a such thing for me to get myself going. In my defence the past two weeks have been unfortunately busy, what with doing two 'work experience' placements! The wallpaper is finally off the walls and I hope that means I can take a couple of days off. I'm just going to post a few pictures in this post (is it that obvious that I'm brain dead?).

BTW- I just wondered, if you love maths and teach it to secondary school kids, do you ever get time to appreciate and do maths. I mean maths for your pleasure as opposed for the students? Do you ever get the time whilst having to mark homework, plan lessons etc?

Oh, an update on my brains age- it's 29 years old now! Did you know cooking's actually good for your brain? Using a knife instead of a peeler is better since you have to concentrate more... as says Dr. K! It's a real fun game, if I may say so myself and you find yourself actually learning things. Onto the pictures now. I can't really say much about the first picture but I liked it,

.It was taken on Saturday, just after.

PM! Is that a sign of a bored person? (Well things did drag for a bit, and I was getting tired!) The sky was great in my opinion and I took a few other pictures of it much to the dismay of the people with me. :p Until we came across this that is:

Which was the final picture I took that night.

That's the 'hole' for the attic, which I had to climb into during the week. Well the ladder is no longer there, but the scary thing was when the extension leads plug got pulled out and the lamp had gone off. It was pitch black and I could feel the spiders crawling down my back. *shudders* (thankfully it was only for a short while!)
BLue= Bottom Left. BRown= Bottom Right. Hurrah, I remember something from Physics lessons! (Don't ask me which is the live one and which is neutral though...). Finally, my trusted friend...

... the steamer!

Having not done any maths has me feeling very bored. I was talking about university to 'the gang' today and I said that I missed maths. Boo hoo. Well I'm missing the daily hustle and bustle of going to lectures and actively learning maths. Hopefully at the end of this week I can do something about this.

## Friday, July 13, 2007

### Maths is BORING!

Yes- 95% of the students who I have come across feel this way. Since I've started the placement at school most students find maths boring and not interesting. They don't particularly enjoy their maths lessons. Some say they don't like the teacher and others because of the way the lesson is structured. Before I go off on another tangent I must say that maybe I'm being a bit harsh by saying 95%, but I can only count the students who were enjoying their work on at least two hands! One got a real buzz out of understanding something, and the other had good mathematical ability which helped. There are a few more but these students are outnumbered!

Today I happened to engage a year eight student in conversation:

'Do you like maths?' (me)
'No, it's boring.'
'What would make it interesting?'
'I don't know.... all we do is exercises from the book, which are hard and boring. We used to play games in the first year but don't anymore.'
'What kind of games?'
'Maths games. But not all the time- just sometimes!'
'Do you find maths hard?'
'Yes, it's very hard.'
'So if you were to sometimes play maths games, you might enjoy maths more? Do you think that'll help?'
'Yes.'

That was today, but yesterday when I had been distracting(!) students who had been drawing the posters the following was said:

'How come you don't look happy drawing posters?'
'It's boring and we did one last time.'
'What do you want to do instead?'
'Maths work.'
'Do you like maths?'
'Sometimes, but especially when 'my supervisors name' is teaching it.' (the second student said No!)
'Do you find maths hard?'
'Sometimes, but I like doing fractions and area.'
'How would you make the lesson interesting?'
'By not drawing posters!'
[the students preferred English lessons to maths ones.]

The first kid was from set one and the second from set three. Another couple of students in the set 1 class told me that they found maths boring and not interesting as well. Some of the set three students are lazy but I'm glad that at least one student who I spoke to said 'maths is areet'. (3 points if you can figure out what that is!) I've only been in the year 8 set two class once, and the same comments about maths being boring were echoed.

I've not really asked the year sevens this question directly but the class I be in are taught by my supervisor (who is a great teacher), which is probably why the class enjoy maths. (Although there is this one lazy student with whom I had a nice conversation about sponge bob square pants, so I can't say anything 'bad' about this student!) Then it's the year 9's. Students in set one tend to get on with the work and talk at the same time (well a few do), but there are some who just sit there copying. The people who copy are the ones who don't like maths and don't put any effort into their work. A few of these students know what they're doing and can grasp the ideas pretty quickly but they don't seem to be enjoying it.

When I was at school Maths lesson used to be one of the best ones that I had. That was mainly because of my amazing maths teacher, who I remember a lot during the 'nostalgia' sessions. I wouldn't be doing maths had it not been for my teacher. My mates laughed at me because of this, but my maths teacher was indeed special. There are some people who you can't help but admire. The way they carry themselves and the way they behave with you is the main factors. I could easily have been cast away and squatted like a bug by most of my maths teachers and lecturers, but thankfully where I see myself as a bug, I hope they see an enthusiastic student! (Well one teacher reassured me that when I bug lecturers with trivial questions and other things, they don't mind this but they enjoy it! How true is that? :D)

Anyway, because I've yet to dedicate a post to the real reason why I'm doing maths I seem to always jump at the opportunity to do so. I had a great teacher which brought the fun factor into maths. *gets lost in thought again*. However, I think there was another factor behind why I wasn't lazy in maths. I could never find maths boring since I tended to compare it with English comprehension lessons which were murderous. Don't worry I'm slowly getting there, but the group of friends that I had also helped. (We were quite large a group which had smaller groups operating within.) We had AB and Trevor- the maths boffins. :D AB was brilliant at everything and was always determined to understand things, whereas Trevor was more focused on maths. There was also Annie who sat next me for most of the time. Maths lesson used to be good namely because AB always got moved to the back of the class since AB and Bruno used to always talk!! AB never used to bring a calculator so I used to lend mine and then share with Annie. (yup- I remember maths lessons like yesterday and could go on. :))

So *drum roll*, I think one of the main reasons why I may have done alright (areet!) in maths is because of my competitive nature. In my introduction for my personal statement, which I will be posting in due course, I wrote:
'My interest in Mathematics stems from my energetic personality, which has fiery competitiveness etched into it. Thus I find the intensely challenging nature of Mathematics riveting. Not only do I enjoy competing with others, I also enjoy competing with myself. This ensures that I put maximum effort into everything, guaranteeing my work is of a high standard.'

I have to put my hand up and say that this has been my motivation- not only in maths but other things. You have to aim to do the best you can- always. In my school maths lesson, as I've said previously, I used to try to finish the exercise or set work before AB and Trevor. That never happened but I never stopped trying. I always wanted to finish first. Trevor and AB never knew this since they were competing which other, but there you have it! This competetion was friendly, and sometimes Annie and myself even competed. The main motivation was our eagerness to finish the set work and get more work to do! To some extent I think my dad might have had a hand in my nature (duh!). He's always told us that if you're doing something do it properly. I don't know how to continue this line of argument without making me sound like some sort of psycho and I don't really want to say much in this post since it's already in the draft of another post. Competing with yourself and pushing yourself is indeed difficult, which is why sometimes other people can help you to work at the level you should. *

You see I believe competition can be a healthy way to motivate people. Obviously it's a bit silly if two people with pH 1 and pH 14 compete but if you have a pH 4 and a pH 5 student then this competition can encourage the students. (Or even a pH14 and pH13.8 student!) I don't know whether my argument is correct, but on the few occasions that I told two students who were copying to see who can finish first, I felt the results were positive. The students stopped letting their neighbours copy and worked with more grit and determination, and less laziness than before.

Yes- most of the students are lazy. Most of them don't see school as a place where you learn. I used to love going to school and even as I say this to some of the Teletubbies an argument erupts since they hated it. Surprisingly, some of us went to the same school but my experience of it is much different to there's. I think this is because of the attitude I have towards my teachers and lessons (the teletubbies missed days of on odd occasions. :( ). I pause for a second and think to myself that it's the end of the year, but then I remember the English lesson I sat in the other day and notice the contrast. I had wanted to observe the English and History teacher, since from my conversations with these teachers I felt I could learn a lot from them. The history class are doing a research project and so I decided not to go to it but the English class were discussing how to argue etc. (The devil's advocate was mentioned and I tend to do that myself in a number of occasions!).

The students really got into the lesson and were enjoying it. You might think that this was a one off but to prove otherwise I came back to this class on two more occasions. The teacher is really great- I can't think of anything negative to say! The teacher may be a reason why most of the class seem to enjoy English but the English lessons were alive. Alive like my maths ones used to be. Students argued with each other in the way we used to argue with each other if we didn't agree with answers. Then the teacher would ask Trevor or AB to confirm who was correct. That is what is needed in a classroom. Life. Not always, but a balance of it. I thought that the students who didn't like maths and found it boring would not like science as well, however I was shocked to find that many of them liked sciences! Actually they 'loved Biology' and the other sciences. Most people I have met tend to like 'maths and science' and not like 'English and humanities' as much. I think the case may be that if you like maths you might have a preference towards science subjects but the converse is not true. Fair enough, but then how can you get students to like maths?

Maybe the scientist can be 'persuaded' to like maths through science. I don't know. I'm just writing a load of waffles but the attitude that many students have towards maths nowadays is worrying. When I was at school, from my whole year (i.e set 1, set 2 and 3) I am the only student from about 90 I think, who went on to do maths at university. From my college, which was large, only four of us went to university to do maths. I believe a large number of people have applied to study maths at university this year, but looking at the current attitudes in this school it is easy to conclude that at least no student might do maths! These year sevens and eights will definitely change as they grow older, but can't anything be done to make their attitude to maths positive when they're not 'more mature'.

Lenient teachers may be a problem or maybe it's the way the lessons are structured. It's true- apart from the year 7 class all the other students do is exercises from the book. I never complained of that because I enjoyed maths, but these students are not being shown the beauty of maths. They're being drawn away from it. Students should always be pushed. The 'I can't do it attitude' must be eliminated. If the students feel positive to tackle any questions then they're already half way there.

Sigh. I tend to get lost in posts like these since I myself am not quite sure what's happening. Quite a few students have the attitude that you can only do maths if you're clever. (well students from the lower sets do.) For many students getting the right answer or understanding a concept is indeed pleasing, but what about those who don't understand or have difficult understanding? They just want the answers and as soon as they get the answer and are asked a question regarding it, they want to move on. I'm becoming frustrated with myself because I'm not getting anywhere!

I will be at the school for a final week. This time I'm going to sit in some year 10 lessons and hopefully this will be give me a bigger picture on the attitudes. You see there are kids who are great at maths, but they don't really like it. They think 'it's OK'. I suppose that's better than the boring attitude. I had to teach again today and I felt more calm than Wednesday. It seems that when the teacher went out I felt normal but as soon as the teacher came into the class my mind went blank. :o It's all about preparation and I'm hoping to be better prepared for the year seven lesson. The topic was ratios but I didn't follow the book! I spent far too long going around and confiscating calculators and showing them how to do 19 x 5 without a calculator! Apart from that, and the chalk breaking, it probably went better than yesterday. I was told that interaction happened which is a good thing I hope!

I'm getting scared about the year 7 class since it's set 4 and I don't think the teacher is going to go out for even a minute! I'm thinking of doing 'Zeller's (?) algorithm', which will give them a chance to work out the day they were born on. (don't quote me on that- I need to check my file). I think it'll probably be the last lesson of the year so I don't want to do anything taxing, and this might be fun...? Another suggestion I've had is area, but I've got the weekend to ponder on this.

In an effort to summarise what I've written, I think that many of today's students are lazy or maybe they're not being pushed as much as possible. They're allowed to be lazy. Free lessons when the teacher used to be absent was one thing, but free lessons (i.e. poster drawing!) whilst the teacher is there another matter altogether. The students need motivation of some sort and I suggest competition. That has helped me a lot, and as I quoted from the movie Fearless, 'competing allows us to learn our own weaknesses, from which we may learn to better ourselves'. Not necessarily in maths, but generally. I compete when I play football, or when I played video games against my brother. You have to set the bar at a certain high level.

I know these kids are 11-16 years old, but are you expecting a spectacular transformation in them when they turn 16 or 17? Is there attitude going to drastically change? Then there's the matter of maths lessons. Is it the syllabus which needs scrutinising, or is it that great maths teachers are very rare to find? (Boy have I been lucky, and this luck has thankfully followed me to university!) Is maths actually being portrayed as boring? How can we show that maths is fun? Games is one idea, but my eyes keep on turning to the teacher. It's the teachers job to teach in a controlled environment and try to make sure that everyone knows the score and are listening. I don't think that I'm going to make a very good teacher :o, but sometimes I feel frustrated at having to sit there.

So what are your thoughts on this, if indeed you have any? How can maths me made interesting to secondary school kids, not college students. Secondary school kids who maybe lack some motivation and have a 'lazy attitude'- if they don't understand something then that's it. It seems that maths has to be made 'fun' at times to appeal to the students. In this day and age I suggest that we at least try to do this. Not just one or two teachers, but the department. Show these students enthusiasm and they respond! I imagine things to have been different years ago, and sometimes I do wish to have experienced such a time!

Alas- I have just remembered something! Today I couldn't help but try to convince a few other staff members that maths is 'cool'. I used syllogism to do this. What I call mathematical poetry. I began by writing 'All history teachers are ....' and then asking them for an adjective. They came up with brilliant and so I then wrote, 'MA is a history teacher', 'So MA is brilliant'. This got us talking about philosophy and maths and then I said the most absurd thing, 'We have to write sentences in maths!'. They found that amusing and had a good laugh (meh-humanities teachers!), but I was being serious!

Bleh- yesterday I said my brains age is 53 (it's 26 today!) and I got this information from Dr Kawashima. Having read this post here, I was intrigued. It's about the effect that the game pictured on the right had on a group of students. Supposedly, from the students who were made to play this game on the DS for 15 minutes a day, a dramatic increase in performance was noted. I thought of actually seeing what may happen, and so in the name of 'education' I bought the game for Po, without letting on why! Before I did buy the game I actually believed this to be a good strategy for helping students. Having played it, the activities that you do are designed to increase the activity of your prefrontal cortex. It's a 'fun' game and I enjoy the little snippets about the brain. I think that this game might actually have a positive effect on year seven and eight students. Just an idea I thought of sharing but if you look carefully you may notice that this game brings about a competitive element- that of trying to get your brain's age the lowest possible. Even the teletubbies who are older than 14 have all been competing with each other! (It's pretty fun and today I sleep knowing that my brain is 26 and there's is 34+ muhahaha... ahem!). If you compete againsts yourself, the aim is to get your brains age to 20. (Everyday you have to do 'brain training').

It seems that I have a lot of thoughts on this matter, some which may sound absurd like the game, but I've lost count of the number of students who I hear saying, 'awww, it's maths lesson next. :( '. Maybe it's because I'm 'passionate' about maths that I want to change this attitude? Also helping a student sometimes makes one feel hopeful- do I want to go down this road?

PS: I had a good day today- no year eights. :D

## Thursday, July 12, 2007

### Depression Corner.

:(

Strangely these past two days I've not been feeling 'happy'. Well, I do and then I don't and then I do.... and because of this I don't feel like posting. I'm currently in the 'not happy' state for reasons which I'd rather not say. However sometimes one does wonder that no matter what you do to please someone and make them happy, you're fighting a losing battle. Sigh.

My two 'work experience' placements are killing me! I come home and after an hours rest was off to help Bob and the gang. Most days we finish at 7pm and so I'm pretty shattered at that time. I actually felt reluctant about going today but then I did offer to help and I have to keep my word. One room remains for us to remove the paper, and after that the plastering crew will enter the building. (Hopefully that signals a few days rest for me!) My body is getting used to this abuse(!), but my head hurts.

Today one of my 'beliefs' was confirmed. That is, if you try to cause other people harm or distress, then one day it'll come back to you. I really do believe that since today whilst I was walking down the corridor, one student who saw me walking tried to close the door on me (in a jokey way I hope!). Well I don't know the intentions of this student but I spotted this and saved my nose from being flattened. We continued to walk down the corridor and in the next minute someone opened another door in the other direction and it hit said students face! I'm not laughing at the student (but I do find this funny), since it might have hurt. However, I couldn't help but point out to the student that they should be careful about how they treat others!

Yesterday I had started typing a post but because of the 'mood' I was in I didn't manage to complete it. I'll just paste that here in a minute and complete it, but I'm just going to talk about today now. Today was my 'off day' in the week. I have to have one a week and one student even asked if I was ill. I felt like replying, 'No I'm not ill dammit, I'm just sick of watching you guys draw posters all the flippin time'. I've had enough of it. A class full of students fighting over glue or sellotape at times, or even the markers. WHY?? OK, I did try to remember how I would have reacted in year 8 if I had to draw a poster and guess what, maths and poster drawing doesn't click in my head. Now if you told me to draw a poster for English, History, Geography etc. then I'd get creative. Don't get me wrong, I wouldn't mind drawing a 'maths poster', but one is enough. And I wouldn't want to be drawing one on fractions. Sigh.

I'm learning a lot from this placement and one thing is that posters mean that the teacher has either given in to students pleas for 'free lessons', or doesn't know what to teach next. Seriously I was bored out of my brain and instead distracted a few students by talking to them. In my defence they didn't want to draw any posters as well. :o (That was SG's class BTW- year 8).

My tactic for SG was to ignore. MT told me to not do that since SG wants my attention and if I'm ignoring then SG will not stop but rather go up a notch. I hadn't thought of it this way before and it makes sense. I should try to get SG on my side since SG basically controls a quarter of the class! I think I've been letting my annoyance show to the students who keep on saying 'whatsup'. How many times do I have to say the ceiling for them to understand that they won't be getting anything else out of me! For the first few times I was OK with this, but ..... .

Ironically, in the morning the first class had been year 9, set one. That had been a great lesson and I'd helped two students do a ratio question which had me worried for a few minutes as well! (There had been a mistake in the question). I felt really positive after this lesson and had even said to another teacher that teaching is good! Now I understand why this teacher hadn't been particularly excited by my comments, since even I had changed my mind after the year 8 class. Maybe I was frustrated because I felt that much more could have been done rather than 'just drawing posters.

The year seven class was much better but I think what did it today was that I had to help cover an English lesson!! And guess what.... they were year eights. There is something fishy about the English department at that school (well apart from the staff!), since whenever I walk down that corridor I end up having to do something I don't want to. I obviously couldn't say 'no' since I don't want a bad reference but it was painful. They had to write a horror story- the best possible thing ever, yet the ideas were thin and rare. One student had an excellent idea for a plot if I may say so myself, but due to less work and more chatter not much work was done. I sound like a right old git! It's just that once again I wondered how I'd been at that age, and it was very different. Speaking to my supervisor, this belief was confirmed. I don't hate these students, but I hate the way a few behave. I know things obviously change but I've never been a fan of drastic change. 'Beans they're year 8's- chill out!'

OK- I'll get over that (did I say I've been having a bad day? :( ). I did end up talking to two teachers today who I hadn't previously chatted to. Should I be pleased that I don't look \sout{nineteen} seven? I am supposedly 'confident', an opinion which I quickly corrected (well it depends on the scene). I just erm... like talking (not always in a mumbo jumbo way!) and meeting new people. These teachers have a wealth of experience and each of them gives me different advice and different takes on the same matter. So, yes, I do try to talk to them!

Now onto yesterday and 'my first ever lesson' (the not so long version I hope).

Wednesday 12/07/07

'So how did the lesson go?'

My heart pounded ferociously as I approached my supervisor for the days timetable. Standard form was in my head. 'Hey, I've reconsidered yesterday's offer. Well I'm reconsidering it at the moment but might still change my mind.' I had to leave the back door open for myself. And so I was helped to draw up a 'lesson plan'. The teacher just told me what topics should be covered and guided me along. I looked enviously at the back door. :( It was the lesson in the afternoon and so I had all the time in the world to change my mind. Something told me that I wasn't going to.

The lesson structure is split into three. The starter, the middle bit (can't remember it's fancy name!) and the plenary. I had decided to recap writing big numbers in standard form during the starter since they had done them yesterday. Sometimes with other classes a maths game might be played, just to wake everyone up I suppose. I was going to put a recap question on the board just to 'wake' them up and then start the lesson. You're also meant to write down the 'objective' of the lesson near the beginning, so the students know what's on the menu. I did that and not in a particular neat way. As I was doing this my heart was racing- all eyes were on me. They thought that I was a member of staff- I knew otherwise. Having wrote the objective I then started talking about writing small numbers in standard form. Well I tried to ask them questions and see how much they knew since I was told that they had done bits on this topic.

The lesson feels like a blur at the moment. So much seemed to have happened but at the same time it didn't. I ended up going a bit fast... actually I could hear the students telling me to slow down! Hence I finished my bit before I intended to and the teacher persuaded me to continue. It was one of the weirdest experiences of my life, yet I'm glad of it. Most students at the end of the lesson understood how to write numbers in standard form (I hope), and so I was relieved. I think the million questions are inevitable but since these were year 9's they weren't as persistent as the year 8's and 'none of your business' seemed to be an OK answer!

What I learnt from the lesson:

Don't talk too fast, although that happens naturally when I become nervous.
Make sure that I always prepare work for the students who finish first- I had thought that they had text books but that wasn't to be!
Don't be nervous!
Make sure that no one is talking when you are.
Don't say 'you in the corner' more than once. :o

I won't ever forget that lesson, but it was indeed nerve-wrecking. Towards the end my mind went totally blank on one question and I had no idea whether the answer that I was told was correct. I asked the rest of the students whether it was, and there was some disagreement. Thankfully the 'real' teacher stepped in then and saved me!

Sorry for the disjointness about my first ever 'formal' lesson, but my brain is in reverse at the moment, and so I must stop this random nonsense before someone gets hurts. The teacher has now asked me to prepare a lesson for the year 7 set 4 class. Any ideas on what I can do? In the first five minutes I want to play a maths game with them, so they have cards and have to match them up etc, but I don't know what topic to choose. I've been allowed to choose which does seem to make it worse! This year seven class is rather tough, and so I told the teacher that I'd prepare the lesson but may still chicken out. Area? Nah- I want something simple that will keep them all into the lesson and maybe they'll enjoy it. Seems like a tall order for me at the moment, but I'll see what I can think of.

Shame I can't say 'phew it's the weekend', since I'll be going 'down South' then. (well South from where I'm at). What joy. BTW supposedly my brain's age is 53! When we're sat idle or watching TV the least amount of activity is happening in our brains. However, when we do Maths or English puzzles the amount of activity increases dramatically. (In the prefrontal lobes). The brain is a muscle after all and needs a good workout! (The students didn't believe me :D). More about this will be revealed in due course... I did on occasions say I felt 'old' so I can't say that this wasn't been on the cards. ;) Biology is darn awesome, especially stuff about the human body!

*It seems I'm trying too hard 'not' to be the students friend.