All entries for Thursday 14 October 2010

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.


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.



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

EDIT: I found the sheet we were given to do this task here: There is also a matching  interactive resource here: 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 ( 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. 


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