Sunday, 27 November 2011

Being a Postman

Last Tuesday me and my colleagues had a very interesting conversation. Me and another NQT were talking about the heavy workload and how we never manage to get everything we need to done. As soon as we feel on top of everything, we find out there's something else that we should have been doing all along but haven't (like emailing TAs with lesson plans and instructions. Whoops.).

We were hoping for the more experienced teachers to reassure us that after n years (where n is nice low number) you stop feeling like that and the workload becomes a doddle. To our despair, that's not what we were told.

My head of department (and mentor) raised an interesting point: that as teachers, we wish away our present and live in the future. We tell ourselves that at the weekend we'll have more time so we'll finally be able to catch up with work. Then by the weekend there's too much work to do in the time we have. We tell ourselves that during half term we'll finally catch up and even get ahead, but again this fails. We wish away every day as we wait for the summer holidays: the only time a teacher can truly relax (but not for the whole six weeks, and with relaxation comes I-should-be-working guilt).

One of the most experienced teachers in the faculty admitted he sometimes dreams of being a postman. A postman has a bag of letters to deliver. When the last lettter has been delivered, his job is done. He knows it's done because there are no letters left. He can draw a line under the working day. He then goes home and spends the rest of the day however he likes. He does not worry about tomorrow's bag of letters. He does not have to prepare anything for tomorrow's circuit. He doesn't have the pressure that a letter he delivered badly today may ruin tomorrow's delivery. He can't be held accountable for any letters' futures.

It's tempting, isn't it?

I asked him why he doesn't become a postman. They get paid less than teachers, but it's enough to live off. He thought about it for a second, and then simply said, "I just couldn't. I'm a teacher".

I thought of all the hundreds of jobs I could do instead of teaching. Some better paid, some worse, mostly shorter hours, but some with longer. I thought of having a job with no "homework", a job where you're not emotionally invested. I thought about jobs where you shut down your computer at 5pm, pick up your coat and you're instantly free until 9am the next day. And what conclusion did I come to?

I just couldn't. I'm a teacher.

Emma x x x

Sunday, 20 November 2011

The End of Starters

All of my lessons start in exactly the same way: the date, title, learning objective and starter are projected onto the IWB, the pupils copy them down and then do the starter. They know this is the routine, by now they don't need to be told.

Sounds brilliant doesn't it? You might even be jealous that I have such a wonderful and consistent system. One of my colleagues and fellow-NQT sometimes admits to me guiltily that she sometimes doesn't do a starter. She beats herself up about it, thinking she must be a failure because we all know that for a lesson to even be satisfactory, there HAS to be a starter on the board the second the bell goes. To skip the starter altogether is surely the number one teaching sin.

I discovered this week that that's a complete load of rubbish.

This fortnight at my academy is one of the most stressful for teachers: observation time! The academy leadership team have given all of us a two-day window in which any one of our lessons could be formally observed and graded. Mine has been and gone, with little stress, but for some the pressure still looms. The atmosphere in the maths faculty office has been somewhat more tense than normal. As an NQT, I'm used to being observed regularly, and I'm also used to being told I'm doing stuff wrong, so I wasn't particularly worried. But for the best teachers,  it can be very stressful.

My observation went fairly well. My pupils were well behaved and on task. We were doing about answering wordy maths questions, which is a key focus for our faculty due to the crazy new-style exams. The feedback I got after the lesson was out-of-this-world amazingly useful. The senior teacher gave me so many ideas which I know are tried and tested and easy to implement and will probably work. None of this rubbish making me come up with ideas, she actually told me what to do. Although in doing so I also came up with my own ideas. Now that's good teaching!

One of the things that I realised in dissecting the lesson (although it wasn't commented on until I brought it up myself) was how ineffective my start of lesson routine is. I had assumed that what I was doing was 100% the perfect thing. I had always been told the pupils should have something to do the second they come in, so they can start as soon as they're ready without waiting for other pupils to come in and unpack. I don't know whose stupid idea this was but I've realised now it doesn't actually work or make sense!

My pupils know that when they come in they have to write down the date, title and LO and do the starter, but they do so at their own leisurely pace. They start it when they're ready, which for some means as soon as they're unpacked, for others means after they've talked to the person behind them about the match last night. There's no clear start to the lesson, it just start of gradually blends into existence. After I think 90% of pupils have finished the starter, I begin the "actual" lesson. This can sometimes take 10-15 minutes, and most of the time the pupils have learnt nothing. How pointless!

Consider this method instead (often used by my aforementioned colleague, who feels guilty about it): the pupls come in, there is the LO on the board which they can start to copy. As soon as every present pupil's bum is on a seat, the teacher instructs the class to turn to their homework. The answers are then discussed, and some probing questions are asked and answered. Any late pupils realise they are late because the teacher is at the front talking and the class is quiet. They must walk to their seats quietly and shame-faced. Pupils always do their homework because if they don't they won't be able to participate in the first 10 minutes of the lesson. The activity you would normally do as a starter is then done afterwards, but the teacher can actually explain how to do it verbally rather than having to explain it in three lines on a PowerPoint slide.

Can you see immediately how much better that would be? The only barrier would be the pupils arriving in dribs and drabs. I say wait until 50% of the class is there and then start. As the pupils get used to this, I bet lateness would decrease. If you have the corridor space, you could have the pupils line up outside and that would solve the problem too.

From now on this is how all of my lessons are going to start. It will encourage me to remember to set homework every lesson (as is my academy's policy, and most schools' policies these days) and should also improve homework completion. It will also save me marking homework. But most of all, it will give my lessons a much more purposeful and swift start, setting the pace for the rest of the lesson.

What are your thoughts on starters? Do you find them useful? Necessary? How do you use them?

And to anyone with observations looming: remember this is a brilliant opportunity to realise things about your teaching and lesson structure that you weren't aware of. It has helped me immensely.

Emma x x x

Sunday, 13 November 2011

Thank You for the Maths: Dedicated to my Maths Teachers

As a teacher, I've noticed that although you're changing peoples' lives every day, it's quite rare to be thanked. I know I've not been in the game long, but I've yet to have a proper, sincere, thank you from a student.

I can't really complain about this though, because when I was a student, I never thanked my teachers. And I have a lot to thank them for: outstanding GCSE and A level results, a maths degree and a postgraduate qualification. They did good. (OK, except maybe my English teacher...)

So here it is, long overdue and probably misdirected: my thank you to all of my maths teachers.

When I started secondary school, maths wasn't my favourite subject. I did like it, and I knew I was good at it because they'd put me in for the level 6 paper in my year 6 SATs. I seem to remember saying that English was my favourite subject back then, because I loved reading. At some point in my school career, I went from not really caring about maths one way or the other, to absolutely loving it. Who's responsible for this transformation? It had to have been my maths teachers.

I don't remember many particularly fancy lessons. We didn't have an interactive whiteboard and the most kinaesthetic we ever got was cutting and sticking. But the care and support my teachers gave me got me through my GCSEs, A levels, and degree with good marks, and inspired me to become a maths teacher myself.

When I was in year seven I did something pretty bad. The worst thing I've ever done to this day. And my maths teacher was the victim of it. What I was so grateful for was that she put it behind us straight away and still treated me the way she would any other student. A few years later she taught me AS maths and she did a truly excellent job, delivering what I realise now is a very tricky syllabus in such a straightforward way. I owe my success in C1 and C2 to her and my other AS teacher. What this has taught me is that when a pupil does something bad, even if it feels like a personal attack, I should try not to let it ruin the relationship. Because that pupil probably doesn't mean it at all, and will appreciate everything I've done for them in ten years' time.

My A level maths teachers (2 for AS, 2 for A2) greatly influenced my life as it is today. It is because of them I chose to do maths at uni, it is because of them I chose the particular uni that I did, and it is because of them I'm now a maths teacher. A lot of the teaching techniques I use I subconsciously picked up from them. Their teaching is still helping me today, as I use lesson ideas I picked up from them 6 years ago.

I want my teachers to know how much I appreciated the comments they wrote on my work and on my reports. I realise now how long they take to write, but they really do have an impact. I still remember many of the comments they made at parents' evening, and every now and again I like to read my school reports and I still feel that warm glow of pride. Unfortunately I also still remember the time my year 9 geography teacher wrote "Is this some kind of joke?" next to the essay I'd written for homework.OK, so I'd written it on the bus on the way there but it wasn't that bad!

I wish I'd said a proper thank you when I was still in school. Not the day I left sixth form, but way back in year seven, and eight, and every year after. Once a week, every lesson, every time they marked my work, the first time they got me to explain something at the board (that was the moment I knew I wanted to be a teacher). I didn't say it then so I'm saying it now: THANK YOU!

What would you thank your teachers for if you could go back in time? What do you think your students will be thanking you for in 10 years?

Emma x x x

Saturday, 5 November 2011

My Top Ten School-Related Novels


10. Pandaemonium by Christopher Brookmyre





9. The Wayside School Series by Louis Sachar


8. The Twins at St Clare's by Enid Blyton




7. Love Lessons by Jacqueline Wilson






6. A Little Princess by Frances Hodgson Burnett



5. Prep by Curtis Sittenfeld


4. The Harry Potter Series by J K Rowling




3. The Rotters' Club by Jonathan Coe














What was the last good book you read?

Emma x x x 

Wednesday, 26 October 2011

The New Ofsted Criteria Explained!

This week we had a teacher training day focused on Ofsted. My academy will definitely be inspected this year, and the odds are it will be after January when the system changes, so the Academy Leadership Team were really keen for all teaching staff to get to know how the new system works, to maximise our chances of hitting Outstanding.

The training sessions were run by Cambridge Education. The maths, science and ICT teachers were put together in one classroom and we were led by Penny Holden, a senior principal consultant at Cambridge Education, who happens to be an ex-headteacher and ex-Ofsted inspector. She seemed to be the perfect person to deliver the training.

The first thing worth mentioning is the extremely cool free pen we were all given. Just look at it:

That's right, it has a highlighter on the end!!! How awesome?!!

Anyway, onto the actual training. The aim of the session was to learn how to observe colleagues the way an Ofsted inspector would, and how to deliver feedback in a contructive way. Through doing this, obviously you become better at delivering Ofsted-pleasing lessons, because you become aware of what they're "looking for".

We were given a handout of the things Ofsted look for when examining the quality of teaching. Here it is word for word:

  • The extent to which teachers’ expectations, reflected in their teaching and planning, including curriculum planning, are sufficiently high to extend the previous knowledge, skills and understanding of all pupils in a range of lessons and activities over time.
  • How well teaching enables pupils to develop skills in reading, writing, communication and mathematics.
  • The extent to which well-judged and effective teaching strategies successfully engage pupils in their learning.
  • The extent to which teachers secure high quality learning by setting challenging tasks that are matched to pupils’ specific learning needs.
  • How well pupils understand how to improve their learning as a result of frequent, detailed and accurate feedback from teachers following assessment of their learning.
  • The extent to which teachers’ questioning and use of discussion promote learning.
  • The extent to which teachers enthuse, engage and motivate pupils to learn and foster their curiosity and enthusiasm for learning.
  • How well teachers use their expertise, including their subject knowledge, to develop pupils’ knowledge, skills and understanding across a range of subjects and areas of learning.
  • The extent to which teachers enable pupils to develop the skills to learn for themselves, where appropriate, including setting appropriate homework to develop their understanding. 
  • The quality of teaching and other support provided for pupils with a range of aptitudes and needs, including for those with special educational needs and/or disabilities, so that their learning improves.
It is really really important that you don't look at this list like it's a checklist. You don't need to do every single one of them to get Outstanding, and getting 80% of them doesn't equal a Good.

One thing that Ms Holden kept saying which I think is really important is that Ofsted do not examine lessons, and they don't even really examine teaching: they examine LEARNING. So having peer assessment in a lesson isn't Outstanding unless the impact on learning is, so the pupils have to be seen to make more progress as a result.

Effective Feedback

I was observed recently and was given feedback from my mentor. I mentioned in this post how positive it made me feel because I had been praised and had been given some attainable targets. I feel like this was very helpful feedback. But there have been times, I must admit, when the feedback I've had after a lesson has not been helpful. I have felt demoralised and embarrassed after some. And I don't think it helped me improve either! As a proper teacher now, I am expected to give feedback to colleagues when I observe their lessons (during WOW week, for example) and I was really keen to find out how to do it properly.

Guidelines for Effective Feedback:
- Do it in a neutral place, sat at 90 degrees to each other on the same sort of chair.
- Don't hide any notes
-Never say "I liked..." You should always say ".... was good because" to make it more neutral. Basically always use the passive voice.
-Definitely never say "I wouldn't have done it that way..." or "I would have done this..." Say "You could try..." instead. What you would do isn't the best thing for another teacher to do. 
- Give evidence for everything you say. Direct quotes are best.
-Include lots of praise, even if it's meaningless like "well done you!" because teachers just don't get praised enough.
-Consider doing it coaching-style with loads of questions. However me and several other NQTs hate this! When someone says to me "how do you think you could improve x" I just want to scream at them "I don't know that's why I didn't do it!!! You obviously know so just tell me!!!" I know that coaching is effective but I do hate being subject to it.
-Most importantly, never ever start by saying "how do you think it went?" Because that's just setting them up to either talk themselves down, in which case the conversation becomes focused on the negative aspects, or talk themselves up, in which case you then have to bring them crashing down which is just mean. I have definitely been asked this before and I always respond by saying "erm...OK?" accompanied by a nervous smile. In future if someone asks this I'm going to politelty refuse to answer.

The leadership team in my academy will be observing everyone in the third and fourth weeks of next half term. It will be interesting to see whether they follow these guidelines themselves. They make it like a proper inspection, they give you a two day window so you don't know exactly which lesson it'll be. I'm quite excited about it actually, I'd like to see where I am at the moment. I was apparently an Outstanding trainee, which only equates to a Satisfactory/Good teacher as far as I can tell.

I found this training session incredibly useful and also inspirational. I got loads of ideas for lessons from watching the DVDs and from talking to colleagues. I wish I got to talk to colleagues more often and share good practice more, becaue it really is incredibly helpful.

A few of the more experienced teachers didn't find the training helpful at all though, and thought a lot of it was pointless. I suppose they've been through this sort of thing before many times. Or maybe they're more resistant to change or being taught something new? I find it funny that sometimes teachers make the worst students. For example, several teachers during the session were playing on their iPads or iPods and not listening! Someone was even planning lessons, she had her text book out and everything! I was ashamed, to be honest, some people are so rude! Even if you don't find the training helpful, you should still listen and be polite, which I know several of my colleagues did, to their credit.

If you want to know more about the training Cambridge Education can provide, visit their website. Or email me on nqtpi(at)gmail(dot)com and I can refer you to someone.

If you'd like to know more about observing and giving feedback, email me and I'll try to answer, but obviously I'm no expert! Or leave a comment below and then maybe an expert will wander along to this blog and answer it!

I hope you're enjoying half term. Time can be so cruel: slowing down during an awful lesson, speeding up during your week off!

Emma x x x

Sunday, 16 October 2011

First NQT Observation

This week I had my first official observation. As an NQT, I'm qualified to teach but I'm sort of on probation, so someone in the department has to check up on me and make sure I'm teaching well. There are also some standards that NQTs have to gain evidence towards, to prove that passing their PGCE wasn't a fluke, I suppose. My school has its own set of NQT expectations, like I have to organise a school trip, run an after school club, and be a co-tutor. I'm dreading that first one, although I know exactly where I'd go. Luckily there's a free museum within walking distance of my school. Sadly it happens to be perhaps the most boring museum in the UK (in my opinion) but the kids may like it.

Anyway, my observation. My mentor watched me with one class but his feedback I think applies to every class I teach so I don't need to give you any background or even describe the lesson. Here is the feedback we discussed:

My Strengths:

* Good relationships with pupils, good way of talking to pupils one on one and adapting my language to suit them. It's obvious that pupils like me and see me as nice, kind and friendly.

* Good questioning skills - I used more open questions than closed, and encouraged higher-order thinking and meta-cognition. I encouraged pupils to develop their literacy by getting them to explain some concepts in their own words.

*Good use of praise - I praised pupils a lot and not just general praise but specific, using names.

My Areas for Development:

* Use time constraints on exercises. Even if it's a long one, I should say you have to have done the first two questions in 7 minutes or whatever. This should give my lessons tighter pace. I can definitely see how this would help me with another group I teach, who are so slow and lazy when it comes to starting.

* Don't just ensure no one's talking before talking, but also ensure they're all listening - there's a difference!

* Develop peripheral vision and if possible eyes on the back of my head. This is difficult for me as even the eyes on the front of my head don't work particularly well! But I'll try.

* Limit the noise of the class when they're doing individual work. I should stop the class completely, tell them the noise is too high, then start them again, and repeat this. Pick out individuals who are talking and give them DTs. Don't worry too much about being fair.

After me and my mentor talked about the lesson I felt quite positive. I haven't really thought about my strengths since my PGCE. Although I'm a positive person, it's so easy to only think about your weaknesses, because I see them as the things that matter most, as you need to think how to improve them. It was nice to have someone tell me explicitly: you're good at this, this and this. I'm also glad my areas for development are things I can actually work on, as they're very specific, although the peripheral vision one I think will take many years to hone.

This week at school the maths department are having a WOW week (Watch Others Work) and I'm really hoping I can have one of my lessons covered so I can go and see an interesting lesson (the only year group I don't teach is year 11, and I'm not excited about seeing a group of unmotivated pupils work through past papers for a lesson). I'd love to see how all the teachers in the department teach and get some good tips.

I hope you all have a good week, and to all those lucky people in Leicestershire who are already on half term, please spare a thought for the rest of us who still have 5 days to get through!

Emma x x x

Sunday, 9 October 2011

All I Ever Talk about Is School

I have quite a serious social impairment. All I ever talk about is school.

Every facebook status I've made for the last 5 weeks has been teaching-related. My friends must think I'm such a loser. Most of the friends I see regularly are maths teachers, and all we ever talk about is teaching. That's bad enough, but talking to non-teachers about school and nothing else is really quite awful.

The thing is, talking about school to my teacher friends can be really theraputic, and often incredibly useful. Yesterday I met up with two of my maths teacher friends. We talked about school. A lot. But I was really inspired by a lot of the things I heard and actually took out my iPod and made some notes. I got a few starter ideas, homework ideas, behaviour tips, and some other bits and bobs. I'm going to talk about these in my next post.

But it would be nice to talk about other things. Like... See, I can't even think of something that's not related to teaching! What did I use to talk about? Back when I was doing my A levels we used to talk about: One Tree Hill, the Apprentice (when it was on), boys, clothes, music, films, books, and, to be fair, school. It would be nice to be able to talk about those sorts of things again. Now that I think about it, I would also love to start watching One Tree Hill again too. I loved that show.

So my resolution this week is to talk about things other than school. This will be difficult, but I'm going to make a real effort, just for the next seven days. Obviously my blog will still just be about teaching. I'm sure no one wants to read 500 words of me talking about Nathan and Haley's relationship and why James Lafferty is so much hotter than Chad Michael Murray.

Do you find you have the same problem? Why not try and talk about other things this week too?

Emma x x x

Friday, 30 September 2011

Mathematics in Literature

Lewis Carroll's oeuvre, Alice's Adventures In Wonderland is pretty much my favourite book of all time. Why? Because it's FULL OF MATHS!

Lewis Carroll is the nom de plume of Charles Dodgson, who was a maths lecturer at Oxford. He was actually more famous for being a children's photographer, but his maths was pretty good too. He was really obsessed with Euclid's Elements and wrote textbooks to go alongside it. He loved logic too, which is what you see most of in his books.

Tweedledee says that. It's one of my favourite quotes from the book. The best logic puzzles appear in his other books, like The Hunting of the Snark.

Here's another favourite quote (it's just as Alice is falling down the rabbit hole):

"I'll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is - oh dear! I shall never get to twenty at this rate!"

Alice's wrong calculations can be explained by using different base systems:
in base 18, 4*5= 20 = 18^1 + 2 = 12
in base 21, 4*6= 24 = 21^1 + 3 = 13
if you carried on the pattern, you'd get:
base 24: 4*7 = 14
base 27: 4*8 = 15
base 39: 4 *12 = 19
base 42: 4*13= 42^1 + 10 = 1X (where X is the symbol for 10 in base 42)

So Alice is right, she'll never get to 20!

Interestingly, it breaks down at base 42. Lewis Carroll seems to have a slight obsession with the number 42, it appears everywhere in all of his books. It has been suggested that Douglas Adams used the number 42 in the Hitchhiker's Guide to the Galaxy because of this. Adams named his chapters of the radio show "fits" which is also what Carroll did, suggesting he's a fan.

My favourite maths thing that Dodgson did though, was his work on voting systems. This is really interesting, it's got some great maths in it, and if you tackled it in a lesson you would be hitting the moral, social and ethical aspects of maths.

So if anyone asks you to come up with ideas for a maths/English connected curriculum day, suggest studying some of Lewis Carroll's work. I love it when literature and maths combine, as they are my two favourite things. Another good mathsy book is Mark Haddon's The Curious Incident of the Dog in the Nighttime, which I love, but the maths in that is very separate from the story, and I don't think it would be good to use in class.

One of my favourite authors of all time is Louis Sachar, who wrote Holes, which is very commonly studied at secondary schools. He also wrote some great maths books, the Sideways Arithmetic from Wayside School series, so if you have a year 8 class studying Holes, it would be cool to do some puzzles from that to run alongside it.

Finally, another of my favourite authors of all time is Koji Suzuki, the Japanese author of Ring, which was made popular by the abomination that is the film The Ring. There are two sequals, Spiral and Loop, and all three books are outstanding on their own or as a series. They include some brilliant codebreaking linked to genetic codes, and some discussion of meta-mathematics which is just plain awesome. I'm not saying bring them into your lesson, but suggest them to sixth formers who like reading and maybe need showing the coolness of maths. And you should read them yourself because they're sooo good!

Emma x x x

PS if you want to find out more about the mathematical life of Lewis Carroll, I recommend Robin Wilson's Lewis Carroll in Numberland.

Wednesday, 14 September 2011

Are Equivalent Fractions Really Equivalent?

We teach pupils that 6/7 is the same as 12/14 is the same as 120000/14000 etc. But is it really?

This thought struck me in a faculty meeting this afternoon. The head of maths said that the maths department had the highest proportion of U grades at A level in the school. He then said, "But we did have a much higher intake than other subjects". Everyone immediately said things like "ah, yes" and "true, that needs to be taken into account" and "well there you go". So the message I was hearing loud and clear was: if 7 people out of 42 got a U grade, that's not as bad as 1 person out of 6, and hence the two fractions aren't equivalent.

When you see adverts for shampoo or whatever on TV, it might say 70% of women agree, and then it always says at the bottom, 109 out of 156 women agreed. Now if that figure was 10900 out of 15600, would you be more likely to believe that it's a good shampoo? I would. We all know that the bigger the sample, the more reliable the findings. So the two fractions aren't really equivalent.

Of course equivalence is an undisputed term. It means they have the same value. The thing is, the word "value" can have multiple meanings. The mathematical meaning, which is obvious, and the other one, the one that refers to how much value we give to something, as in, how much we think something is worth. We think 1/6 is worth more than 7/42 when it comes to U grades. We think 10900/15600 is worth more than 109/156 when it's to do with data collection. Mathematically, of course they're the same.

Happy hump day everyone!
Emma x x x

Sunday, 11 September 2011

Getting Pupils into a Seating Plan : Activity

This week I wanted to put one of my new classes into a seating plan, but I didn't want to do it at the start of the lesson. I had two lessons with them in one day, which made this work really well, but it would still work if you only had one lesson.

Before the Lesson
I planned my seating plan (alphabetical but adjusted so it was boy-girl).
I numbered the seating plan. I have three rows of ten so I numbered it 1-10 three times.
I wrote a slip of paper for each pupil, saying group 1/2/3 and then their number 1-10.

 During the Lesson
I told the class we were going to have a competition. I told them that as I call out the register I was going to give each person a piece of paper with a group number and a secret number that they weren't allowed to tell anyone. I did this (it took quite a while) and then I told the class what we were going to do:
  • You are going to get into three groups. Group one at the back, group two at the side, and group three at the front.
  • In your group, you have to line up so that you are in number order. The first group to do this are the winners. 
  • You are not allowed to speak or mouth. You are not allowed to write, or hold up fingers to show numbers. You are not allowed to use the slip of paper I gave you.
I then got choruses of "that's impossible!" etc. But they were really keen to have a go.
When they'd finished, I told them to remember what number they were.

Next Lesson
I told the pupils as they came in that group one will sit on the front row, group two on the middle row, and three on the back. Number 1 will sit by the window, and 10 by the door. Voila, no confusion and no fuss. I can also use these numbers in the future for other activities.

Why I Thought This Was Good

I hadn't actually thought of any techniques the pupils could use to get themselves in order. I wanted to see what they would come up with. I was so impressed, all three groups came up with different ideas, and they were all brilliant. I think this exercise gets the pupils to remember that numbers are concepts, not words or  symbols. One pupil picked up a stack of textbooks behind her, and took her number from the pile. The others in her group then followed suit. This emphasises that numbers only really make sense as the size (or measure) of a set (or object). Another group used a calculator. Because they assumed that just typing in their number was disallowed, they typed in calculations that would equal their number. The last group got in order by indicating how high or low their number was by holding their hands a certain width apart. This was nice because it emphasises that numbers are about comparing and about relative size.

It was also good to do with a new class because you can spot instantly who the leaders are. In each group, one or two people took charge from the word go.

It was also kinaesthetic. Need I say more?

I hope you all had a good week. For me it was incredibly long and tiring. I need the whole weekend to recover and hence will get no lesson planning done. It's going to be another exhusting week!

Emma x x x

Tuesday, 30 August 2011

A Nerdy Day Out: Maze Algorithms

Every August bank holiday, me and my family take a visit to the Wistow Corn Maze in Leicestershire. It's a huge maze made, humorously, of maize. The design changes every year, and this year (spoiler alert) it was designed like a bee.

Photo used with kind  permission from the owner of the maze

Now it might not surprise you to hear that my family are all big geeks. Neither of my parents did maths A level, but they're both a product of an experimental system called "New Maths" which was where the curriculum suddenly completely changed in the 1970s and 6 year olds were learning set theory. My parents both know some basic group theory, and claim to have been taught Boolean algebra in year seven. My parents seem to know *everything*. They're the cleverest people I know.

One of my brothers did Physics at uni so is a slightly different kind of geek from me. The other one pretends not to be a geek with his cool metal band and all that, but he so is.

What happens when a family of geeks takes a trip to a maze? The first time we went, we took one step inside the maze, and instantly agreed we'd follow the left-hand rule algorithm. We stuck unfalteringly to this path, and looked upon families who were randomly meandering (or worse, reading the map!) with equal parts pity and disdain.

There are 12 boards hidden around the maze with pictures on, and the aim is to find these 12 boards and draw the pictures, then convert the pictures into letters at the end, to spell out a word. Naturally, my family takes this part very seriously.

Let's have some maths, shall we?

Maze Algorithms

The Left (or Right) - Hand Rule (Wall Follower Algorithm)

As long as the walls of the maze are simply connected (every wall is touching the outside wall, so there are no islands), then placing your left (or right) hand on the wall and never letting go as you walk will mean you will always be able to find an exit, or if there isn't one, the entrance. This works because (topology alert) the maze can be deformed (stretched and squished) into a circle, and obviously this rule works on a circle.

This rule fails when there are bits that aren't connected.

Pledge Algorithm

This is the only other algorithm I know (wow, how well-researched is this post!) and it works when the wall-follower algorithm doesn't (on disconnected mazes). This is how you do it: you choose a random direction and walk that way. When you hit an obstacle (a wall), you do the right-hand rule with it and count how many times (or what angle) you turn around it. When you have turned a full 360 degrees (or 0 degrees, or 720, or, ... basically when the angle sum is zero) and you are facing the direction you were when you started (not necessarily the same thing) then you stop doing the right-hand rule and continue to move in the original direction (before you stopped at the obstacle).

So what did my family do this year? Well as usual we started with the left-hand rule. My "cool" borther protested that it would make the maze less fun. But his protests lacked conviction and were easily batted away. He knows deep down that he is one of us. After about twenty minutes, we ended up back at the entrance. Darn. Follow my family's route on the map if you like.

This is the map you're given when you come in. Excuse the crumpledness.

Wistow maze is always a disjoint maze, with an inside track and an outside track. It has two bridges at opposite ends (shown on the map) for you to get from the outside to the inside and vice versa. But as you can see (if you can be bothered), following the left-hand rule means walking past the bridge in the NE but not walking across it. This is why our algorithm failed us. So we had to back track (easily done using the right-hand rule) to the bridge and go across it. Then we resumed the left hand rule until we got to the Mid Point, which has picnic tables and is a good place to stop for a Werther's Original and/or a bag of crisps.

From the Mid Point, there are 6 paths you can take. One is labelled the "quick exit" (the West path) and we came from one of them (the NW path) so we had 4 more to explore. We took the North path because that's what the left-hand rule dictates.

The twelve boards we were trying to find are not usually marked on the map, but this time they were (they're the black crosses, not the numbers), probably to speed people up as it was a busy day. We allowed ourselves to diverge from our algorithm in order to get to a nearby board, but we returned to the original path *immediately*. The left-hand rule is not an algorithm that guarantees to cover every path in the maze. Is there an algorithm that does? Obviously it depends on the maze. In graph theory, I know that you can cover each edge in a graph exactly once as long as the graph has an even number of odd nodes. I'm not sure how to translate that into mazes at the moment. I need to have a think!

School Trip???

Wistow Maze welcomes school trips and even has a lesson pack that you can email to get. However, it's aimed at key stage 1 and 2, and won't have anything to do with maze algorithms. I personally think they are missing a trick there!

I think you could do a really cool school trip with higher level GCSE and A level pupils. When I did D1 there were questions on the exam (MEI) about maze algorithms, so it would be a nice accompaniment to that module. If your school is in Leicestershire or neighbouring counties, definitely consider taking a group there. The maze is open mid July until the end of September, so it would be a good end/start of term treat.

Have you ever been to a maze? Did you geek out about it or did you walk it like a normal person?

Emma x x x

Saturday, 27 August 2011

Advice to New PGCE Students

This time last year I was feeling really excited about the start of my PGCE. The PGCE, for those of you who don't know, is the Post-Graduate Certificate of Education, which is a one-year course you do to get Qualified Teacher Status (QTS) in England and Wales. There are other ways to get QTS (like the GTP) but I think the PGCE is the most common. Our neighbours in Scotland do a similar course, but they call it the PGDE, because they just had to be different.

If you're about to start your PGCE, you might be wondering what to expect. My university gave me hardly any information about what the course was actually like before I started. Luckily, you guys have me to fill you in.

Expect to...
  • Have loads of fun in the first few weeks. This will probably be university-based and, if it's anything like my experience, you will feel like you're back in seconday school again. I loved it, especially as I made lots of new friends (hi, if you're reading this!).
  • Be asked to do lots of reading. My advice is this: don't do it. It's pointless. You learn nothing about teaching from books. You only learn from hearing other people's stories, or from being in a classroom yourself. If you get picked on during a seminar, use an anecdote from your own school experience as a pupil, rather than something from the book. The teacher will never know ;).
  • Have lots of paperwork. When you get given a piece of paper, decide imediately which of the following categories it comes under: "important" (as in, to do with you getting your qualification), "seems important but is actually unnecessary" (the details could be typed into your phone so that you can throw the paper away, the information on it is somewhere on the university's website), "useful" (an idea for an activity, the name of a good book for your essay, a website to check out),  "they say it's important but honestly I'm never going to look at it again" (an article, a PowerPoint handout). As soon as you know what category it comes under, you will know what to do with it: file it, make a note of it then recycle it, ditto, recycle it immediately. **Edited to add** Start collecting articles and things that could be used in the masters essays right from the start. As Liz pointed out in a comment below, the "post-reading" that was set us was often very good for using in the masters essays.
  • Be placed in a school far, far away from where you live. If you have a car, this means not too much inconvenience but a sudden huge rise in your petrol costs. For pedestrians like myself, it means catching the bus at 6:20am, and falling asleep on the bus on the way home. My advice: buy a bus pass, and if you're in the midlands, use Traveline's brilliant website.
  • Spend about five hours planning your first lesson, only to have it turn out a complete disaster. Hey, it's a rite of passage!
Our university sessions involved a disproportionate amount of origami.

The task was to make something that will hold five ping-pong balls. Our group made origami bunnies.
I think my most important piece of advice is to make some friends within your subject and organise a Friday afternoon pub trip every week. It's great to be able to let off steam about how annoying the course is and how terribly your first lessons have gone. Without this, I don't know how I would have survived!

I think that's enough for the first half term (also known as the calm before the storm).Good luck to all new student teachers and enjoy it whilst you can. The NQT  (Newly Qualified Teacher) year is apparently a lot harder (gulp).

Emma x x x

Sunday, 14 August 2011

Explaining the Fourth Dimension

Has a kid ever asked you what the fourth dimension is? What it looks like? Whether it could possibly exist?

No, no kid has ever asked me either. But I really wish one would one day.

Anyway, I was reading this book by one of my favourite authors, the hilarious Scottish crime writer Christopher Brookmyre. The book is called Pandaemonium and for goodness' sake don't recommend it to any of your pupils. The "c" word appears frequently, there's really really gross violence and gore, and it's just generally very offensive. If it was released as an audiobook, it would be read by Frankie Boyle.

I loved every page.

Anyway, I'll try and get to the point. There's this bit in it where CB explains the concept of a fourth dimension really nicely. I loved it so much I highlighted it and wrote a little note (I LOVE my new Kindle!!). I'll try and paraphrase it here:

Imagine there are some ants crawling across the duvet on your bed. They are only aware of two dimensions: walking forwards and walking sideways. There is no up or down for them. So if you picked one of the ants up and suspended it in the air, all the other ants would think the ant had vanished. They would have no idea where it went. And then if you put the ant back down a few centimetres from where you picked it up, the ants would all think it had teleported.

Maybe there's a higher dimension out there that we can't comprehend. Maybe there's something out there that could pick one of us up and put us down somewhere else, and it would look like we've teleported. If we could access this fourth dimension, think of the possibilities: we could perform surgery without breaking the skin.

Back to the ants on the duvet: imagine picking up two opposite corners of the duvet and bringing them together. The ants are still only moving in two dimensions, but now they can walk off one edge of the duvet and return at the opposite end, walking in the opposite direction. This involves moving their world around in three dimensions, but keeping it as a two dimensional world, and without them noticing. Could something similar happen to us? Could we walk off one "end" of the universe and end up on the other side? Is dying walking off the end? Does God live in the fourth dimension?

Well, I found it interesting.

Emma x x x

Saturday, 6 August 2011

Khet - The Laser Game

Today I played Khet for the first time (and won, natch). It's a strategy board game similar to chess, which involves moving pieces with mirrored edges around the board, and firing a laser so that it bounces off your pieces and hits your opponent's.

Obviously, there's a lot of maths to be had here. Firstly, bouncing lasers off mirrors requires some understanding of angles. The mirrored edges are at 45 degrees to the grid of the board, so the laser always hits the mirrors at this angle. As the angle of incidence must equal the angle of reflection, the laser comes off the mirror at 45 degrees, which is 90 degrees from where it was hit. So the laser beam always moves in L shapes between mirrored surfaces.

The game also involves problem-solving, as you have to consider where to move your pieces in order to block your Pharoah (did I mention all the pieces are Egyptian-themed?) and to take out your opponent's pieces. It's similar to chess in that you have to be thinking several steps ahead at each point.

The game was a Mensa Select Award winner, so clearly it's a game that can involve a lot of intellectual stimulation. But it's easy for anyone to understand enough to at least have a go.

It would be impractical to have everyone playing this in a maths lesson, but you could give pupils a situation on a worksheet and ask them what their next move would be, or ask them where the laser would point if it was fired then. Like how in newspapers they often have a picture of a chessboard and you have to decide what your next move would be.

Khet would be great for an afterschool or lunchtime maths club. It takes about 10-30 minutes to play (according to Wikipedia) so you could easily fit in a game. Obviously the school would have to buy a few sets first. It is available in many places online, including Amazon.

To watch a video demonstration of Khet, click here.

It's starting to get somewhat annoying how I can't play a new game without thinking: how could this be used in a maths lesson? Does anyone else suffer from this?

As it's the summer holidays, my posts will be fewer and further between for the next few weeks. I am aiming to blog once a week. I'm also going to be doing some re-blogging, which means I'm going to re-post some of my favourite entries from my old, defunct blog into this shiny new blog, so that they're not lost forever.

So for now I'm going to set you some homework and leave you for a week. Your homework is to watch the latest series of Futurama. There's loads of cool maths slipped in. For example: one writer created a new maths theorem just so he could use it in the show. Click here for more details.

Emma x x x

Wednesday, 20 July 2011

Lobster Fishing

It's almost the end of term for most of us, and pupils start to expect "fun lessons" instead of lessons involving actually learning anything. Of course, showing a DVD is unacceptable, unless it's related to your subject. When I was at school not so long ago, we always watched films on the last day of every term, except for in maths, which would generally be a normal lesson. We were always outraged!

What you need on the last day of term is something that is undeniably "mathsy", but still seems like a treat. For me, that absolutely has to be Lobster Fishing. I can't remember where I got hold of the PowerPoint and worksheet that I use for this activity, but google it and you'll find loads of different versions, so you can pick and choose.

It goes like this: pupils, working individually or in pairs, are given six lobster pots at the start, and £50. They have to decide where to place their pots: in shore or off shore. Depending on the weather (decided by rolling a die) the two locations give different amounts.

If you think I haven't explained it very well, that's because there are loads of different rules you could add in and loads of different ways of doing it. You can adjust how complicated it is to suit the class.

I used this activity with year 8 set 1, and they absolutely loved it. It very nicely fills a whole hour without anyone getting bored. You can spend some time at the end reflecting on the best strategies to use. You can get them to work out the EMV for each strategy if you feel like going into game theory (somehow I always feel like going into game theory, because I love it. My pupils love it too now!)

So if you're stuck for ideas for the last day of term, give lobster fishing a go. Then let me know how it went :)

Emma x x x

Sunday, 10 July 2011

Fractal Cuts

This week's resource of the week comes from Kangaroo Maths. It's a lovely practical activity which gives the pupils something to take home and show their parents, which I think is important.

It's Fractal Cuts! The very easy way of making a 3 dimensional "fractal" out of a sheet of A4 card (or paper). Google "fractal cuts" and you'll find it.

I used this activity with a class who are working at level 7, but I think it works for a huge range of abilities. I started off the lesson by showing them loads of pictures of fractals, and told them what they are in very simple terms: pictures where if you zoom in again and again, it still looks the same. Then I got them to draw a fractal (the Koch fractal, but of course I didn't call it that to them, that would be asking for trouble!) I used questioning to get the pupils to think about what is happening to the area and perimeter of the Koch as they draw more and more iterations. I think this touches on a very interesting concept: the area gets bigger and bigger each time, but doesn't go to infinity. I demonstrated this by drawing a circle around the shape, and the pupils recognised that the area will never be greater than the area of the circle.

Then it was the fun bit: making 3D fractals! I'd made one in advance, Blue Peter stylee, and the pupils were like: woah! I gave them all a piece of A4 card and a pair of scissors and took them through the process step by step. We managed to do more iterations than the document above suggests. We ended up with squares that were about 0.8cm^2. They looked so cool.

My plenary was getting the pupils to answer the following questions in their books: What is a fractal? What's special about a fractal's area and perimeter? Finish this sentence: I think fractals are cool because...

Why I love this activity:
-It's engaging and goes a long way towards ensuring all pupils are on task
-The pupils can take their fractals home and show their parents: good because it means parents then ask what it is and the pupil then talks about what they've learnt, which makes it more memorable.
-It introduces concepts of convergence and infinity in a very tangible way.
-It would make an impressive wall display (sadly I'm not allowed to stick anything up at all in my room because it might ruin the decor. I don't even have a noticeboard).

With the end of term approaching, why not try this activity as a fun lesson? It's better than showing a DVD :)

If you do use it, let me know how it goes!

Emma x x x

Thursday, 7 July 2011

Day of the Week Trick

Today I learnt something really cool: how to work out what day of the week any given date is. It's really easy actually.

 First, work out the year code as follows (here, [ ] means integer part, ie round down to a whole number)

Year code (2000 + x) = [x/4] + x (mod 7)
Year code (1900 + x) = [x/4] + x + 1 (mod 7)

Mod 7 means find the remainder once divided by 7. 

Example: 1989: [89/4] = 22
22+89 = 111
111 + 1 = 112
112 = 0 mod 7 (because it's divisible by 7).

FYI, 2011's year code is 6, and 2012's is 1.

You also need to know the month code. You have to just memorise these. 

6 (5)
2 (1)

 January and February are different if the year is a leap year.
 I memorised these pretty quickly by making up mnemonics. e.g. for May being 0 I remember mayo (which I hate by the way). For August being 1 I remember that A is the 1st letter in the alphabet.

 Once you've done that, add together the day, the month code, and the year code, and then reduce it modulo 7 (i.e. find the remainder once divided by 7).

 Then that tells you the day: Monday = 1, Tuesday = 2 etc.

Example: 4th March 2012
4 + 2 + 1 = 7 = 0 mod 7 so it’s a Sunday.

Example: 22nd February 1989
22 + 2 + 112 = 136 = 3 mod 7 so it was a Wednesday.

I can do it almost instantly for dates in 2011 and 2012. Other dates are harder because I have to work out the year code. But people are more likely to ask what day of the week an upcoming event is, so knowing these two years is very useful for impressing people.

By the way, I've edited my settings so that you don't have to sign up to anything if you want to leave a comment (well hopefully that's what I've done) so that commenting is now easier and faster. So please drop me a comment if you have a minute, I'd really appreciate it :)

Emma x x x