## October 29, 2010

### Has someone lost their see–through pencilcase?

Imagine my surprise when I went to get a pen out of my pencilcase, at 8am one sleeping morning in school, to find there were loads of pens I didn't recognise right at the top. It took me a surprisingly long time to notice it contained entirely pens I didn't recognise, none of my own, plus some little cards saying "f(x) = [some function]", and therefore, despite the fact it is the same case, and crammed full of pens like mine, it is in fact, not mine. So if you have lost your pencil case (clear rectangular, with a black zip), I have it. Sorry. I think I picked it up last Wednesday (core group?) or possibly Thursday (Rachel?).

## October 28, 2010

### The wrong way or just not your way?

This is something that bothered me during my observations of a few weeks ago. Also, I'm not enjoying writing my SCT2 based on said observations. In 2 of the 6 lessons I observed, pupils were told that their method (ie a method they'd invented to do something, rather than following the teacher's method) was wrong or wouldn't work. One of those observations I only saw because I was stood nearby, so I'm willing to bet there are others I missed in the other 4 lessons.

The first was in a lesson on compound interest. Pupils had to calculate what £1000 plus 5% interest was by typing "1000x1.05=" into their calculators, and got £1050.  They then had to work out what another 5% of interest on that was like by doing "1050x1.05=". One boy put up his hand and offered a different method:

Lets do 50x1.05=52.5.

Then the total is 1050+52.5= 1102.5.

He was told a simple "no, you must do..". In the teacher's defense, she may not have realised he had a valid method, as when he explained it he got a figure wrong early on and so gave an incorrect answer. He gave an answer at the start "Miss, I got something else!" and the teacher asked for the calculation, presumably looking to find an incorrect figure in the calculation she suggested, and so not expected a different method. A "listening for" rather than "listening to", I think my books class that as!

The second was in a lesson finding the sum of interior angles in polygons. They were to find these by drawing lines from vertex to vertex to split the polygon into triangles, then use the fact that angles in a triangle sum to 180 degrees. While the class were working individually on a worksheet, one girl put her hand up to ask if you could do it a different way:

Draw a dot at the centre of the polygon.

Draw a line from the dot to each of the vertex of the polygon.

Use these triangles to find the interior angle.

The teacher told her "no that doesn't work". I'm sure I heard "that doesn't work". It got to me, since I can understand that sometimes it's learning a certain method that is important, and the teachers professional judgement and knowledge of the class trumps mine any day. But...it does work. An n-gon will be split into n triangles. Total of 180n degrees so far. Some of that is used to go around the centre point of the polygon, not to fill the interior angles, so we need to take away 360 degrees. That's just as neat as the other method. It doesn't work as generally, but they were given convex polygons on the worksheet so the method was fine for that. It's not just the stifling of creativity that got to me, it was the plain incorrectness of what the girl had now learnt. How could she trust her internal logic and mathematical thinking when it lead her to this idea she saw no problem with, but now thinks is incorrect?

## October 18, 2010

### PP1 Day One

Staff are lovely.

Buildings are freezing.

I am tired.

## October 15, 2010

### TDA Literacy Test

English PGCEer's: Help!

I've been doing a lot of work towards this test as I know it's my weakest area. I've just being doing a practice test online and I've hit a brick wall about one point. There is a subtlety of interpretation which I'm missing with my sledgehammer black-and-white, right-or-wrong mathematical brain.

Here (literacy_question.docx) is the question and my answers are on the right. The last one I ticked "the encouragement of independence of thought" is wrong. The commentary on the answers says this is because while "paragraph 2 refers to how we do things individually but there is no reference to the encouragement of individual though". Yet, there is! Line 6 of paragraph 2 has the exact words "encourages independence of thought". What is it about the context this phrase is placed in which means it doesn't fit the question, because, by my logic, it's the easiest correct answer to find!

### Feeling like a pupil

I've felt more like a pupil on the PGCE course than I did doing my Maths BSc. This may seem like obvious news: we're (often) in a classroom rather than (almost) exclusively a lecture theatre, we are taught by people who are/were teachers rather than professors (and the teacherness of our course leaders is obvious in their mannerisms and ways of getting attention). We spend lots of our time doing school level maths.

I've been using the 3 weeks at uni before we start in a school to reflect on how it feels to be a pupil. I've touched on this in other posts, eg the fact that even with high quality teachers who we are motivated to work for, we've gotten restless and lacked concentration at times. There have been other things I've been wanting to talk about but they all relate to specific events I'd have to describe to make sense. I found it hard to write about them without it being obvious what I was referring to and waited until events were (relatively) far in the past so shouldn't prompt anyone's memory in the way some little incident from earlier would! I'm aiming for no-one to be able to tell if the people I am describing are my subject leaders, core leader, special guest speakers, fellow subject trainees, fellow core trainees, placement teachers, on "the classroom experiment", etc. It's such a drawback of the blog, as my only place of written reflection, that I can't speak openly.

Making pupils work at the same pace is impossible to get right.

When I was at school, this rarely happened as we worked from textbooks at our own pace. There were occasional teachers who would stop us to go through a question. This was highly irritating as I was a fast worker and so usually had done it. Or, I was at the other end of the scale, highly focused on a question that was really challenging me, and dragged out of that frame of mind to see an example far far harder and a long way ahead of where I was.

I'd pushed all this to the back of my head, filling my head with ideas about lessons with pace and multiple activities. Which I will definitely go this route, not the textbook way, most of the "multiple activities" lessons I've experienced so far have required pupils to work at their own pace. This is especially bad for tasks that basically just require writing with little thought, as the same quick writers will finish first and sit around bored, and the same slow writers will struggle, forcing themselves to go as fast as possible, and either not finishing in the time allowed, or being guiltily aware they held everyone up. Also, the questions that are more sustained and time consuming by nature, as everyone will get out of sync and to stop at some point will mean some are told not to start the next one and sit around for a few mins, and some start but only get halfway through.

I think there are two main features that stop a child from learning: if the maths is too hard or too easy, or if the teacher is irritating and they get too frustrated with them to listen as it will only make them more frustrated!

Often the frustration will be caused by the maths itself as it's very hard to accurately pitch the level for every single pupil. I want to think about how to avoid the second one where possible. I've tried to identify things a teacher may to to frustrate there pupils:

Not letting them work at their own pace (covered above);

Making them feel stupid eg by obvious differentiation in front of class, remarks about where the class "should be by now", attributing lack of written work to lack of effort;

Asking the class for a response but not allowing time to give one eg Saying "is everything ok?", "Does anyone have any questions about how this works" and moving on before the pupil has had time to formulate how they want to answer.

Explaining how something works to the class when a pupil had just twigged and is dying to tell you;

Making them listen to stuff they don't need or care about, especially conversations between the teacher and one pupil taking place in front of the whole class before the can get to work.

Making mistakes constantly and having to correct it, forgetting resources and having pupils share instead or running out of the room to get them. Other general things that make the learning inefficient. If I'm in the mood to focus and learn I want to capitalise on it while it lasts!

Running the lesson on over the bell. Noticing the class's desire to leave translating into edging towards the door, insufficient packing up, etc and making them stay behind even longer until everything is in order. The "I'm not letting you leave until the whole class is stood silently behind their chairs" one was a particular killer for me as my leaving was dependent on my classmates controlling themselves, which they usually couldn't. This made me incredibly anxious as a pupil, especially at the end of the day when my rubbish bus home contained more pupils than seats. Sometimes a teacher would come to inspect it and make the ones standing up get off and wait for the bus to complete the route and come back to school for us.

Being inconsistent or unfair!

I have never felt such a strong sense of right and wrong that I have as a pupil when a teacher does something inconsistent. Since starting this course, I've wasted hours on end studying something myself that's later handed on a plate to all of us as were weren't actually expected to follow that instruction (how my fellow PGCEers are figuring which instructions are necessary and which are optional, I have no idea. I can't tell so do everything). I've given myself a splitting headache working late into the night when I was exhausted which knocked me out for the following day (thankfully at the weekend) completing some work from scratch since we were told a version of the same thing we'd all done couldn't be adapted for it. Then some people did use just that! There was also something else I had to struggle with due to a lack of a resource, later some people on the same task were allowed the resource.

I've observed pupils looking unimpressed at a teacher's actions and when I questioned them why, I've often considered the reason to be petty or immature. Stuff like not collecting in homework when they say they will. Or not allowing a pupil to use their calculator but then later letting someone else use theirs. Allowing a pupil who has special circumstances slack in unrelated areas, especially in following the rules. (Also related is not allowing necessary slack in the rules for special circumstances. A friend at school in my tutor group was told off almost every morning for being late, and was often given detentions too. She repeatedly told my tutor it was due to having to take her brother to school first and he would make them run late and was given icy remarks about better organisation and "complain to your mother, not me". Her brother had severe mental difficulties and would be difficult to dress and get in the car to go to his special school, before she'd be brought to our school. As pupils we were united against the tutor in finding this utterly unfair!).

Not knowing how well you're doing.

This is a contentious one given the latest research and whatnot which emphasis comment only marking and avoiding giving grades. But I hate not knowing! I knew where I was all through school (near the top in most subjects, near the bottom in PE, Drama and Music), all through my BSc (about middle). I have no idea if I'm worrying the tutors with my lack of ability or if I'm flying ahead near the top of the group. We haven't got a heck of a lot of feedback on much so far, my CCT1 and SCT1 have now both been returned. The CCT1 is especially hard to judge anything from, it basically said I did vague things like "communicating" well. No points for improvement. And most definitely no grades. I think I'm suffering a little like the girls did on "The Classroom Experiment" from grade-withdrawal syndrome!

## October 14, 2010

### cos (tan x)

For those curious what that crazy graph we were asked to draw earlier was actually supposed to look like, I draw it in Autograph.

costan_x.agg

Using my mathz skillz, I'm reckoning that those big blocks of black are the cos curve doing it's usual waving up and down between 1 and -1, it's just the ups and downs are getting closer and closer together as x tends to pi/2 (or multiple of pi/2). At x=pi/2, I think it's undefined. This  is different to what y = tan x does at pi/2, which is tend to infinity. This means we're attempting cos of infinity. Picturing following the y = cos x graph along for larger and larger x values, it just does it's unchanging waving up and down. It doesn't tend to a specific value like tan does near pi/2. Therefore undefined. I'm assuming this means our graphs don't get the dotted lines that y = tan x does at it's asymptotes since it doesn't contain asymptotes.

Incidentally, I got curious as to what tan(cos x) looked like. A wierd kinda right angled thing (almost, the lines are slightly kinked). Here it is: tancos_x.agg

### Reflections on SCT1 Feedback

Follow-up to SCT 1 from Elizabeth's PGCE blog

This task was peer assessed. My group were very unclear about what was actually good or bad so found this difficult to do. We wrote some stuff that I have the feeling was utterly wrong now! Lots of other people found this too so there is a possibility the people who wrote mine found it hard to know what to say.

I'm finding it quite hard to get much out of the feedback I've been given. They liked the starter and the homework, the differentiation and the architecture examples. Areas they feel I could develop:

There was a lot to do in each task. I might want to consider timings.

I agree. Since this was assessed, there was a temptation to put all the good material in together for this one lesson, which I wouldn't have teaching a series of lessons. I intended to put "prioritising notes" in next to each activity, to indicate which can be skipped entirely, which bits can be cut down in certain ones, and which parts are key and time for them must be preserved no matter what. It's very hard to know timings, especially with a subject like maths when there is a "eureka" moment which may happen quickly, take ages, or not happen at all! I prefer to overfill rather than under-fill a lesson, it's easier to skip parts than it is to make them up on the spot! Awkward waiting at the end of a lesson implies the lesson time isn't valuable which is the opposite of what I want.

I'm going to resist putting too much into one lesson. In particular, I'm going to stop planning such multi-part lessons, with short tasks. Long sustained tasks are great too, and in many ways it's nicer for the pupils as they can work at their own pace and are given time to get into a focused state of mind.

I assumed there would be a TA to work with the SEN pupils. What if there isn't?

I found it hard to write a lesson plan for a fictionary class and decided to make some convenient assumptions. I'm finding "differentiation for SEN" hard to do at the moment: surely it is dependent on the exact SEN? This relates to something in the core session on differentiation which I'll write about soon so I'll not say anymore for now.

If there isn't a TA, then the SEN pupils will have to work without that support, and will just have mine.

Perhaps it's aimed at the wrong year group. Main task seems more suitable for Year 9's.

This was a very interesting point as it's not something I'd thought of. The nature of the task was to bring different areas of maths together, some from the other lessons in the topic (this was the last in a series of 6 sections), some they could make up, and some required by me (eg knowledge of an isosceles triangle). This is pretty dodgy with a Year 7 class at the start of the year as the knowledge they have will be dependent on the primary school they came from and so this may unfairly persecute the ones who haven't been taught it. I had the idea that I'd ask the class if they knew what it was, if no-one did I'd explain it and draw some on the board, if some did I'd get them to share it with the rest of the class. I didn't state this in the lesson plan, though.

The task could have worked very well with Year 9 as they'd have a much larger and somewhat more uniform bank of maths knowledge to draw from. It would have been very easy for me to change that little "7" to a "9" in the lesson plan too, but it simply didn't occur to me. To plan a lesson then decide who to teach it to seemed a really unusual thing to do. I figured you get a class who will have a lesson and you plan it just for them (later adapting it for other years, perhaps, but again having the class known beforehand and then thinking this would be good for them). I realised thanks to this feedback that actually, at this stage in my career, the purpose of writing these lesson plans is a) practice and b) to build a bank of lessons to draw from in the future. In which case, deciding the class after writing the lesson seems a pretty good thing to do.

Today we got the real feedback from the tutors. It consisted of a list of criteria with ticks or crosses if we'd hit the standard required. I did pretty well on the lesson plan (all ticks) but pretty poor on the topic plan (2 of 4). I'm really unsure of topic plans. Jenni recommended places on the National Standards website where I could find examples but unfortunately none of the links were working. I'll have to check again another day.

I didn't "structure using clear and appropriate learning objectives" (although I did "clearly identify appropriate learning ojectives and learning outcomes" in the lesson plan). Looking at what I actually wrote, there are no learning objectives whatsoever in the topic plan. We were given a table to fill in and I did exactly that, and there wasn't a column for learning objectives! I didn't know we could access the criteria we were marked against; it was revealed today it had been on the website for a while. If I'd seen it I'd have put some it, but I'm not entirely sure I'd have managed it well.

The other one was "linking to the National Curriculum". Again, I have no clue how to improve this. I spend ages meticulously going through the enormous first section of the NC, carefully identifying which parts are addressed in each lesson (incidentally, this activity improved my topic plan a lot, I kept thinking of new and interesting things to do based on the key processes). I didn't include anything topic and level related, from the level descriptors for the strands of maths. This was mainly because every section of the topic plan had the same vague "properties of 2D and 3D shapes" (or similar, I've forgotten the exact thing) description. Would I have gotten a tick for that criteria if I'd included that? Who knows.

I think I'll have to ask Jenni for additional feedback as I have literally no idea how to improve. I intend to resubmit it if I can to see if I can hit the other two criteria that I missed first time around.

One last thing to note is that the feedback from the tutors and from my peers didn't contain any overlapping points. I got a tick by the SEN part of the criteria, and there wasn't a mention of timing or level appropriate activities in the tutor feedback form. Does this mean I've got twice the feedback to work on, or am I now dwelling on things that weren't really an issue?

### A long long time ago…

I found this on my old soon-to-be-demolished blog from when I was an undergraduate. This was written shortly after the first ever lesson I taught alone. One teacher was ill, so I turned up at her lesson to help the supply teacher (I'd found this to be a great experience as they aren't maths specialists and most aren't confident about the material, meaning I get to take a really active role). The lesson started with some miscommunication between myself and the supply teacher, and she sat at the back with her laptop and got on with something, leaving me to do the lesson. She sent me several dirty looks during the lesson which was confusing until the end when she said "I expect better behaviour management off PGCE students on their final placement" to which I explained I wasn't a PGCE student!

It was an excellent experience to see how badly pupils will behave when they aren't given boundaries, how some will work solidly through the mayhem going on around them, and how I still very much wanted to go into teaching at the end of it! I talked to their usual teacher when she returned back to school days later, who described them as the worst class she's had in 30 years. She did say she'd terrified them into silence the following lesson when she painted me as some sort of class inspector who was highly disappointed with what they'd done! I'm not sure I could manage such blatant lying, but it sure had the maths staffroom roaring with laughter. She knew exactly which boy had caused me major grief, interestingly I saw him again just the other day, now a big year 10. He was as good as gold, even to me when I questioned him on his work.

EDIT: Highlight to read. I think my old blog had a different background colour therefore different text colour which has been automatically carried over to here. I can't find the change text colour button either...

## March 19, 2009

### I'm currently spending my easter holidays not at my parents house like usual, not actually *on* holiday (or even better on the climbing trip to Mallorca), not even revising for my really-quite-soon exams. Not even doing much on my maths essay which I've been working on for absolute ever. I'm working full time in school, as part of the Student Associates Scheme.

At the end of last year I was having a look at what modules I'd want to take in my second year and I came across IE2A6 Introduction to Secondary School Teaching. I'd sort of figured I wanted to be a teacher, I quite liked it in year 12 and it's been my career of choice unless something better comes along (4 years later, nothing has). So this module sounded pretty interesting. I have to write 6 essays on teaching (worth 24CATS in total. Scary for someone who hasn't written an essay since GCSE English but the lack of an exam is a major plus) and to write those I have to have some teaching experience. Thats where the Student Associates Scheme comes in.

It's some sort of Government organised thing. We get to try out teaching in return for "raising aspirations" of students who wouldn't normally consider going to university. Oh and we get paid £600 for 15 days work.

So I am currently getting up at 6:30 every morning, going to my school on the other side of Coventry and doing various things in each of the 5 lessons of the day (despite the fact our handbook says to expect to spend 50% of our time in lessons). We do a mix of things, plain old observing, working one to one with a pupil who struggles, walking round the class helping anyone who is stuck (which is either really dull if everyone is ok or like a game of Whack-A-Mole if everyone is confused), teaching a starter activity, or if we're feeling particularily brave, a whole lesson. Which is what I did today.

It was a year 8 class of 30 pupils, and seriously, I'd forgotten what  kids of that age can be like! It was quite tough compared to other lessons I could have taken; the bottom sets only have 12ish pupils in, plus if their regular teacher is there they tend to behave (incidentally, bottom sets, at least at this school, were not as I expected. They are full of scary looking pupils who look like they'll beat me up after school (and a couple probably would given the chance. But many are genuinely good students who unfortuantly just can't do maths. In year 9 we're currently doing addition of negative numbers and it's a struggle). I was doing a cover lesson with a cover teacher who knew no maths. According the the sheet I was given, the class had started stem-and-leaf diagrams the lesson before and were working through a worksheet on them. If they finished they were to do an exercise in the book. Sounded great, but most of the class had lost the sheet. Some weren't there the lesson before so didn't know what a stem and leaf diagram was. One boy had sized me up well and tried almost every trick in the book: he claimed he didn't understand a think and proceded disrupt my explanation at every moment. The questions not only required knowledge of stem and leaf diagrams but also median, mode, mean and range which most of the class had forgotten. The back row somehow managed to cover themselves and the desks and the floor in yoghurt. Aforementioned boy decided to object to my "picking on him" at this point and refused to see the lack of logic in his statement given he he wasn't in the back row and I hadn't talked to him at all until he joined in. Must not try to reason with pupils in the future. Almost everyone needed the toliet. The girls at the front were cutting up one of their books, in such a way to create a large loop of paper they then planned to stand as many of them as possible in. Some wonderful wonderful pupils has worked solidly through all the work and so unfortuantly had finished half an hour early. The textbook didn't have any more questions. With the advice given by the person who taught us about open questions in our uni sessions, I set them writing their own questions on some paper, then they swapped questions. Plan was to swap back and mark the question they wrote but hallelujah, it was the end of the lesson.

Luckily it was the end of the day as I was about to have a heart attack. Still, I don't think it can get much worse than that, and I imagine actually that it will never be like that once I am a teacher as I will know which requests are genuine and which are just to cause trouble. Plus tomorrow I'm going to ask how discipline works. Given how loads of the boys were whining about how outrageously unfair it was for me to ask them to be quiet and get on with their work, I didn't want to actually be unfair by giving them a detention or bad mark when the routine is to give a warning first, or whatever.

I start tomorrow with a very nice top set year 11. I'm going to prove the area of a triangle = 1/2(ab sin C). Piece of cake in comparison I would imagine. :-)

I had a very nice thing happen in my year 7 Whack-A-Mole class: a little group at the side were asking me who I was, was I a teacher, etc. I said I wasn't but would be in a few years and they asked if I could teach at their school as they thought I was really good. Awwww.

### cogs

geogebra_cogs.ggb

We had trouble making the animation work. Here is our attempt.

EDIT: I found the sheet we were given to do this task here: http://nrich.maths.org/6966. There is also a matching  interactive resource here: http://nrich.maths.org/content/id/4775/cogs.swf. While it beats ours by miles as it is actually animated, it's not quite what I had in mind. It had a button to add dots on the cogs which is useful for marking. I dotted one tooth on one cog and set the animation going. I then dotted the gap our marked tooth fitted in to and continued. I tried to dot the next gap it fitted in to and that's not possible, only one dot per cog. Shame, it makes it much harder to follow. Much better would be dotted all the gaps it fitted in to, then we could see that either all the gaps had been filled, or that it was cycling through the gaps it had already visited. Even better would be the option to number each gap in the order it is visited, then it is clearer that it's repeating the same gaps in the same order and can't ever escape that pattern to fill the others.

There is also this version (http://nrich.maths.org/810) which has much harder and mathematical wording. The animation is slightly different but has the same limitations.

### Microteaching Evaluation

My lesson evaluation for the microteaching activity.

Target 1: Write less!

I've indulged myself this time writing as much as I want as it's my first teaching activity but I'm not going to complete this course if I can't do it quicker.

yr_7_plans_and_elevations.docx

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