All entries for November 2010

November 22, 2010

How to give instructions?

I struggled again today. In the last few lessons with Year 7 I've experimented with verbal instructions (bad move: in one ear , out the other/ not listening at all/ etc) and writing them on the board (bad move: pupils do not bother to look at the board). Today I used the differentiated worksheets that I spent ages creating, which had very clear instructions at the top and a worked example. It should have caused fewer problems, not more! The other worksheet I've used in a lesson was a 10ticks piece, which I chose pupils questions from. Some had problems understanding which questions they were supposed to do, even when I told them individually and wrote it on their actual sheet. It's a mixed ability class so I do personalise the activities where I can, and tell pupils to do or not do certain questions depending on whether they need it at that stage or not. After an initial comprehension of the instructions, and a check from me, it somehow gets lost. By the end of the activity they have done something far removed from what I asked. 

I really don't know what to do. I tried asking someone to repeat the instructions back once but they seemed patronised by this. In any case, it only checks that that random person understands, and only checks they follow at that minute. Given how quickly instructions seem to leak away, this isn't a useful activity at all! 

I'm also getting irritated by so many of the pupils lack of initiative. They cannot write the date and title unless given to them. They won't underline it with a straight line unless asked (and in many cases, lent a ruler). They can't do a question unless given an identical answer. If they can't do it they shout, in increasingly loud and annoyed tones "Miss I can't do it! I need help!" then "What so I have to wait, *not learning anything*, while you do something else?". They won't try. I can't tell if it's because they are used to being spoon-fed or if I'm being a pushover. 

In previous lessons it's gone pretty well and the level of help needed has been manageable. They put their hands up, and sometimes they'd gently and tentatively say "Miss?" to make sure I'd noticed them. It's descended into loud and aggressive demands for my attention. Much of it is that they want me to read the question to them. 

Today we did the angles in a triangle. There was a somewhat long and confused starter cutting up triangles and rearranging the angles into a straight line (lo and behold, 180 degree total!),  confused since they weren't given step by step instructions, we just did one together with my giant sugar paper triangle on the board. I thought they would be able to replicate what they'd just seen and been involved in. Heck no. 

Then was my carefully differentiated worksheets, tailored especially to them, containing all the information they needed, instructions, an example, hints on the questions which combined angles-on-a-line with angles in a triangle. Simply couldn't start, as no-one could read the example and then replicate it on the first question, deliberately chosen to be the same question with different numbers to start them off. They needed me to read through the example for them. I literally read out my own writing! 

Then, after a series of questions giving two angles in increasing wonky strange triangles, and find the unknown angle (deliberately putting it in different corners), there was a question with a triangle and one side extended with the exterior angle given instead. AKA use facts about angles on a straight line to find the interior angle. Then you have two angles in a triangle like the previous ones. Impossible. Even with a hint which said "use facts about angles on a line to find this angle first". When I read it out, they could tell me the angle on a line. But, as more than one girl informed me rather angrily, that doesn't work here as the angle given in the triangle and the exterior angle given elsewhere added to 195. Obviously, they just wanted to blindly add the two angles then take away from 180 degrees. At least they noticed that 180 -195 doesn't give a valid angle in a triangle. Several of them told me this meant angles on a line don't work here - as if the angle on a line only sums to 180 in certain, triangle free (planar) environments!? Shame they usually insist that either I'm wrong or maths is broken, no-one *ever* says "Miss, my answer can't be right because xxxxx, but I can't see where I went wrong". 

My feedback was to give an example of how to do it before each different variety of question. I'm going to next lesson. I'm in the maths computer room, where I wanted to do an awesome Geogebra activity. Here is an (isosceles) triangle. Move the points in the corners around. What do you notice about the angles/lengths. Repeat with equilateral triangle. Next:  names of the triangles. Can you accurately draw some of your own? Can we have two sides match but not two angles? And two angles match but not two sides. 3 angles/3 sides? Plenary: Mini whiteboards. What were they called again? What does that mean?

But we don't have Geogebra. I'm told the maths department have been asked IT for some dynamic geometry for a long time and it's a no-no. I stand no chance of getting it by Thursday. All I have at my disposal is Autograph, which isn't ideal for angles in triangles. In any case, it's only available on computers which aren't in the maths computer room (logic!). 

Also, so far these pupils hate to be given a "think about it for a bit" task. They want instant answers. If it doesn't occur to them, they ask me and I am expected to provide an understandable and near-instant solution. "Just play around, see what you notice" is not an acceptable start, no matter if I later add questions to help them. I can't imagine them trying. They start class-wide "it's tooooo hard! I don't get it!" yet won't accept class-wide support, they want their own. 

What was successful last lesson, which was a surprise at it was at the frazzling end and was the first time together, was a mini-whiteboard plenary. I asked for angle sum in a triangle, angles in a right angle, etc then "Give me an acute angle. Any number of degrees which makes an acute angle". After an initial "huh?" I added that there were lots of possible answers and some of them really went for it. I had lots of 45 and 30 degrees but also some 1 deg, 89.9deg. Yet if I'd give them such angles they'd freak about how hard it is! Definitely a good move. I then asked everyone for an obtuse angle, to one decimal place. Lots added .0 to the end of their angle. I quite liked that answer. It satisfies the question and demonstrates they knew they could just use what is effectively their previous (and correct) answer. Bonus points for mathematical corner cutting. 

So my plan next lesson may not involve computers (depends if I can find a suitable non-safety-blocked activity - I've got one awesome "here are a ton of triangles, put in isosceles/equilateral/scalene piles") and will probably only involve them a little. I'll give very exact instructions, slowly and in multiple formats. I'll give an example of equal hardness to the questions I'll then set. I think open questions are my way in to independent thought, as I can set questions which can have easy answers. Perhaps I'll do the Geogebra demo I planned on the board, with the angles and lengths appearing next to it in a list. Which equal each other at the start? Keep an eye on them. Do the numbers change? Do the pairs of sides/angles still equal each other though? Then: these are the angles and sides which match up. Draw this one. Colour matching sides and angles. Check they copied correctly. Is this (incorrect triangle) allowed? Accurately (pencil, ruler and protractor) draw your own. Label angles and sides. Swap with partner. Check it. Do again. Then mini-whiteboard plenary of properties of the various triangles. 

I'm not accepting all this calling out and demands which are bordering on disrespectful anymore. They also dawdle their way through simple instructions they used to be good at doing. Seems my requests to be ready in X amount of time are meaningless. Especially as they'll call out for individual help/reassurance at this point when it's clearly whole-class time. The fight for individual attention really is intense. 

Lets see how that goes. 

Reflections on Week 7

It's been a long and tiring week. I keep track of the hours I work each week, last week was a new record at 62hours. I suspect, thanks to the many 13 hour days I did this week, I'm going to beat it. 

I've now taken over my classes and taught 7 hours last week. Should have been 8 but I was struck by a sickness bug on Friday and spent a fun day starving hungry but unable to keep anything down while feeling very guilty about leaving the lovely Year 7 class teacher in the lurch for the Period 1 lesson I was supposed to take. 

I'm not doing too badly at this teaching lark. Fewer, and different, mistakes this week. Pitched too high with recurrence relationships for Year 12. They really *aren't* hard, finding a term-to-term rule is often way easier than nth term! (Fibonacci, anyone?), it's just the notation that throws people, plus they really like to be given an algorithm to follow then follow it for some examples. I didn't do that so I'll need to at the start of next week's lesson. 

My Year 7 class are adorable. It's going really well with them even if my tasks are a bit unsuitable at times. I'm struggling with resources. We're doing angles. I have a girl with a broken arm. She can do the work on Geogebra (I love Geogebra) but this is only available on my personal laptop, not the school ones. If I give it to her, I can't use it on the board. Also, I teach them Monday, Thursday and Friday which means I have photocopying to do with no notice for the Monday and Friday lessons, which annoys the photocopying lady (since all maths teachers have Yr 7 at this time, there are loads of us all at the same time!).

I tried avoiding this by drawing questions on the board but this was rubbish as we all had to work through at the same speed and I talked too much. It's clear from their books that only a few followed it all. Yet, they didn't say! I ask if they understand and they smile and nod. Why can't they be truthful!?! After that, I tried a mixed difficulty worksheet, photocopied in advance then chose questions from it nearer the time. Didn't go down well with my mentor as there were excess questions on there. I've made beautiful tailored worksheets, choice of 3 for differentiation, for tomorrow's lesson. Hopefully will be an improvement. 

I set homework for the first time ever and therefore marked books for the first time ever. Struffy work, no titles or dates (how am I supposed to know what those random numbers scattered across the page are referring to?). Random sheets lost or stuck in random pages. Sometimes they stuck the wrong side down and therefore obscured a load of their work. I know it's about the maths not presentation, but seriously, I can't assess them effectively when it's unclear what they've done. Some of them didn't do the homework to the expectations of the class teacher (show working; see me if lose it/unsure/it's too hard) and so I'm going to have to talk to them about that next lesson. I'll do something nice after that so it's not a mean teacher, doom-and-gloom lesson. 

My Year 10's are a bit of a handful but nice girls under all the attitude! They panicked big time the first time I taught them, they'd had an unfortunate experience with a trainee teacher only last term (as in term 3 last year) which had left them a bit traumatised by the thought of losing their highly effective class teacher for hopeless trainee. My first activity went much better than I expected, it was ordering negative numbers. I pitched low to built confidence and that was a hit. I'm thinking they need a confidence boost every lesson or will just say "no I can't do any of it, I can't do maths, it's all too hard" and then are stuck there all lesson!

I do the first bit of the lesson and the class teacher does the rest. It's tough starting. They start arriving 5 mins before the lesson begins (it's after break). The first time I accidentally thought that was the start of the lesson (well, there was a bell!) and they didn't take kindly to that. The second I left it until the start of the lesson and they deliberately tested me with a slow start. The teacher suggests I do what she does, which is go around the room giving out books and asking individuals to get ready. It's a bit of a tall order at the moment as I don't know everyone's names yet! Some girls only show intermittently so there was a new face last lesson. The time before there were loads of new faces - girls who'd come in for a chat and who were supposed to be next door! How was I to know? 

They're not too bad though, one girl appeared in the doorway and shouted "Are you a cover teacher?" to which one of my class replied "Shut up, she's nice". Awwww. 

I've utterly neglected reflections this week as I've spent so long planning. As an experiment (in the context of "outstanding trainees experiment with their practice" :p) I've going to do scruffy, bare minimum planning for all lessons expect my formal observation which will be some super multi-page typed up thing. Thus leaving time to reflect, file my work, do my essay due tomorrow at midnight, read more of AfL, and possibly even sleep. 

Which reminds me, Essay. Argh! We must read our school's safeguarding policy. I finally got a reply as to where to find this on Wednesday, after my last PPA until Friday last lesson. Quickly attempted to get a copy and found I'm denied access. So I need beg for access tomorrrow. I've got registration (I do Mondays solo with my tutor group), PPA/Observations in the morning, Solo Year 7, Team Year 10, Support Year 11 then afterschool Department meeting then my parents are passing through and are going to take me out to dinner. If my PPA/Observations are Observations then I'm in trouble! 

November 09, 2010

Starter 1

And here begins my cataloguing of the lessons (or part lessons) which I do at my PP1 school. My first activity, a starter, ended up not existing because I had to go to a meeting, but here is the plan. 


Year 7 Class 7





No. Of pupils


Lesson time

11:25 - 12:25

Topic: Angles and Bearings

Previous work: identifying acute/obtuse/reflex angles and estimating the size of given angles

Next work: angles in triangles

National Curriculum References

Estimate the size of an angle using 90 and 180 degrees as guidelines (level 5)

Name acute, obtuse and reflex angles (level 5)

Pupil Learning Targets

To recall and consolidate previous work on angles

Personal Targets

To monitor progress of individuals, not just get a “general idea”

To use incorrect answers as a learning opportunity without embarrassing the incorrect pupil


Mini whiteboards (in pupil planners)

Whiteboard pens x16 (plus spares)

Tissues to clean whiteboards






Pupils arriving, sit down and get ready to begin. Whiteboard pens and tissues given out, pupils asked to find the whiteboard page of their planners.


Drawing acute/obtuse/reflex angles (Look out for interesting "borderline" angles, as a learning point eg acute angles can be tiny or almost 90 degrees. Is likely most diagrams will be 30-60 degrees)

  1. "Draw me a right angle...and hold your whiteboard up"

(If there are incorrect answers, chose someone with a correct answer to explain to the class what a right angle is. Ask incorrect pupils to have another go and hold it up.)

  • "Don't rub out your right angle, draw on that diagram: an acute angle"

(If there are few incorrect answers, do as above.

If there are many incorrect answers: probably have some which are obtuse. Borrow an acute and obtuse whiteboard from pupils. "We have some answers like this [acute] and some like this [obtuse]. Which one is right?" "Why?")

  • "Draw me another right angle and an obtuse angle on the same diagram"
  • "This one is tricky. Can you draw a reflex angle?"

(If there is confusion ask "who remembers what a reflex angle is?", take answers from class, then they can draw it)

Can pupils recall what it means to be acute/obtuse/reflex?

  1. Repeat acute/obtuse/reflex if there were incorrect answers. (To save time, could draw all three on one diagram and put a A, O, R next to each one)

Have the ones who previous got it wrong got it right this time?


Drawing estimates of given angles

  1. "Draw me a right angle, and write next to it how many degrees there is in a right angle".

"How many degrees are there in a right angle?"

  • "On that diagram, draw a 45 degree angle. I'm not expecting it to be exact, just do an estimate".

(With incorrect answers: draw on the board an estimate of the ones I've seen (far too big/small) and ask class if they accept those as around 45 degrees? Why/why not? How did they draw their (correct) ones? (Aiming for 45 is half of 90 so should be about half of a right angle))

  • (Unless diagrams are very messy) "On the same diagram: draw a 30 degree angle".
  • "Ok, rub all that off. Now draw a 180 deg angle."
  • "We'll finish off with one tricky one: have a go at drawing a 135 degree angle. "

(Expect them to struggle. While they think about it, write 90 deg + 45 deg = 135 deg on the board. Draw class attention to this and ask "How could this help?"

Can pupils estimate simple angles? Can they explain why?

Can pupils estimate angles as a composite of simple angles?

Spare time

Estimating the size of a given angle (less interested in precise accuracy, more interested in justifications.)

If class find drawing estimates of angles unexpectedly easy and have some spare time: draw random angles on the whiteboard. Ask pupils to write an estimate on their whiteboard. See range of answers and pick interesting ones to be justified to class.

IDEAS: 55, 15, 120, 340 Remember that angles don't have to be drawn anticlockwise from horizontal.

Can pupils justify their estimates, using simple angles as guidelines?

November 06, 2010

A Mathematician's Lament

A long time ago I read something that really summed up the dire state of Maths education. Happily, I came across the exact same thing quite recently. Please, read this:

It really explains so well what has gone wrong. I still, although I'm quite used to it by now, get shocked by how few people think they can "do" maths, and how "difficult" maths is perceived to me. If I had to sum up the process of "doing maths" I would say it is 

1. Pattern spotting

2. Conjecturing

3. Proving/disproving the conjecture.

Humans are naturally great at 1, just watch an episode of "Deal or no deal?" to see the ridiculous and elaborate patterns people have spotted and are basing their decisions on. 

2 is also very easy. All you have to do is make up a rule. Doesn't have to be true and you don't have to give any evidence whatsoever towards it being true (that's part 3). 3 gets nasty, yes. It requires a great deal of creativity and perseverance. For research mathematicians, they don't even know if their conjecture is true or false, so may spend ages attempting a proof that is doomed to fail simply because their conjecture is false. And you can't tell from the conjecture how easy the proof will be either. If you're given something to prove that is at the right level for you, then proving stuff is great. You have to be so creative, much of the time you end up bringing in areas of maths that seem totally unrelated. It gets really frustrating ("character building!") when you can't do it though, which is why I think part 3 is something to be thankful that someone has done for you.

This is why maths shouldn't be seen as "difficult". Maths is reliable, it always works. If some conjecture has been proven then you can use it, build all sorts of things on it, and it won't fail you. In science, gradually new theories replaces an old ones (the earth is flat, anyone?) so what you're learning isn't concretely true like maths is. Plus if you're unlucky, something will be changed while you're still around (Pluto isn'ta planet!?). Maths doesn't get outdated, like media or technology or ICT might be. Much of the maths we learn is very very old. It gets built on and added to, rather than be replaced. In short, the fundamentals of what makes maths maths are awesome and everyone should have a natural affinity towards it. 

But what we learn, and teach, in school rarely fits into one of those 3 catergories. It's what could be put as 

4. Applying the theorem. 

(Conjectures get an upgrade to theorem when they are proven to be true.) Applying a theorem is what much of school maths seems to be. Here is Pythagoras' theorem. Now apply it to all these very boring little triangles. If I'm really trying I'll make you find a variety of sides, vary the notation, and perhaps even draw some triangles at funny angles. I'm going to try really hard with my teaching to do more of parts 1-3 (especially 2, who can'tmake up any old wild claim?). 

Reflections on Week 5

It's been a long and tiring week. Monday was INSET. It was on assessment (hello, Master's topic!) and focused on the importance of formative assessment. Much was made of Black and Wiliams findings and suggestions. I didn't learn much about assessment itself, having spent the previous week studying this stuff, but that didn't bother me at all. I completely buy into formative assessment so I was far more interested in seeing the school's take on it and see if the Maths Department supported it. Everyone was enthusiastic about it - my Professional Mentor even has a stash of traffic light cups and lolly sticks to borrow if I want to try them out. 

After the whole staff sessions we went into Departments to discuss how to implement it. Some of them have been doing peer-assessment already as part of their previous CPD. Lots of them liked the names-on-sticks idea but will make laminated versions to save money, or use a random name generator on their laptop instead. I'm going to do names on sticks, probably with my Year 7's. I also love mini-whiteboards so I'll be using those where I can. I'm debating using the traffic light cups with my year 7's since they behave well (there will be a temptation to mess around/break them) but I'm afraid of accidentally not noticing someone sat with theirs on red and them getting upset with the lack of help. 

I've been given the task of taking past papers for the final GCSE exams and splitting the questions up into categories. It's a big o'task but right up my street - I used to do it myself for my own exams. 

On Tuesday and Wednesday I was back in uni. More of the same really. Some more peer assessment. There was what I can only describe as a sales pitch by some calculator company. I'm quite morally opposed to that sort of thing, though, given what it was, it was done very well. It was by a current maths teacher who uses the stuff himself (it's some sort of fancy calculator which can draw graphs, do dynamic geometry, spreadsheets etc. It could be wirelessly hooked up to the teachers computer which was nice - so the teacher could take screenshots of everyone calculator to monitor progress). The teacher running it was excellent and gave me some excellent ideas for teaching. 

The main idea he used was the idea of much of maths being special cases. For example, Pythagoras' theorem is a special case for squares attached to a triangle, when there is a 90 degree angle. So he'd give them some dynamic geometry and ask them to find out when the sum of two of the areas (which it calculated for you) equals the other. Then get them to discover it's when there is a 90 degree angle. I really liked it, it gives far more meaning to the theorem as just a string of letters doing stuff. It also hopefully avoids the misconceptions that Pythagoras works for any triangle, and emphasises which sides it is which are added. (That came up on the INSET day actually, we had a question "For which of these triangles does a^2 + b^2 = c^2 hold?" with a load of right angled triangles with the a, b, and c labelled in various ways. Lots of staff said they all do because pythagoras holds for right angled triangles, overlooking the fact that c must be the longest side.)

At my school, classes get to spend one lesson a week in the maths computer room so I think later in the term I'll write some special lessons to do in there with these sort of ideas. I'm not interested in used the calculators (we can borrow them from the company if we want to) since I could spent that time getting better at the software I have access too - I doubt I'll ever see those calculators again so I'm not going to waste that time getting used to using them. 

Thursday and Friday were back in school. It's quite daunting to know I'll be there until Christmas now with no breaks, also quite saddening that I'll be leaving there in such a short space of time. I've got more involved with the classes now, I haven't be actually given anything to do with them yet but managed to sneak a bit in anyway. I went to a Year 11 class for the first time, their teacher wasn't in. By lucky coincidence I met the (maths-phobic) cover teacher on the INSET day and she happily let me take a bigger role in the lesson. They were doing past papers for their imminent exam. I marked them as and when they finished (don't know if I was supposed to, oh well) which was very useful for me to see what they are asked to do in this exam, and how good they are. Some of them finished in half the time, and got full marks. Some of them only missed a few marks. I wrote comments on them like "ask xxxx to explain how she did this" (xxx being someone I'd marked and they'd gotten that question right) next to the empty question boxes, but the girls were just looking at the front page and saying "12/15 is good enough"! Not impressed! They'd also been allowed to work together which meant I marked the same incorrect answers time and time again. One of them didn't even make sense which makes it look like they just copied it down without even thinking. They also finished early and were told to get on with homework. I felt bad about this but could hardly contradict what the cover teacher had said, in any case my ideas (more practice papers; go through the worst done questions on the board) wouldn't had benefited all those who got full marks, which is most of those with nothing to do. One girl saw me specially to ask for more exam practice so I got her another paper. I felt really bad for her being in that situation. I'm used to having to try to chivvy pupils into the mood to learn, to have someone ready and willing to learn but prevented from doing do was sad to see. 

I saw my Year 12's again and I feel more comfortable with them now. I've found with all new classes, as a teacher or as support, there is a period of time where I have to prove myself before they will accept me as good enough. I know I did it as a pupil! It was frustrating enough to be stuck enough on something to put my hand up for help, let alone to have the student teacher wander over, not understand what I'm saying as quickly as the teacher would, then sometimes not even be able to help so I'd have to wait for the teacher anyway. What a waste of time! I got more involved this time providing help and it's made me very thankful for my maths degree and the confidence it gave me with maths as "easy" as C1. I don't like to read through a pupils' answers at that level since the answer is long and spotting a mistake in a long piece of maths is hard. Instead I work through their method next to them without looking at their working. I get them to follow what I say out loud, confirming they have the same answer as me at various "check points" in the method. At some point, there is a discrepancy and we can then look back through the lines to see what happened. In this lesson, there was a tangent used instead of a normal, a x value substituted in for a y value, and someone taking something= -2/17, multiplying -17 across and leaving -2. Worryingly, in the last one, she didn't think that was a mistake (in the previous two there was a "oh no, I've made a stupid mistake" moment). As long as she's sat in the same place (learning names and faces is really hard!) I'll check on that idea again. 

Next week is a busy week and hence this weekend will be a busy one. The more I do now, the earlier I can go to bed in the week! I'm doing a starter on Monday with my Year 7's. I'm running after school revision classes on Wednesday and Friday for the GCSE exam (I'm well excited about this). I have to make a poster to advertise said classes (less excited about this - computer designed posters are not my forte. I might give up and make one by hand with my paints and scan it in). I need to plan my Year 12 lessons to roughly divide the material between the lessons I have. I have two 2-hour lessons with them to do C1 sequences and series. It's less time than I was expecting but it's not that hard a topic, so as long as I present it in a way that's not scary (mental blocks against a bit of maths is far more effective at preventing learning than lack of ability) all should be ok. I'm really lucky that my mentor is happy to accept late planning. The way I like to work is to have a vague plan of concepts that need to be taught over a certain time frame. I put them in order and divide it up roughly. But I can only do a full lesson plan after the lesson previously, in order to match to what they need next. I also like to mentally note misconceptions and mistakes which are being made and check up on them next time (like the -2/17 girl in my C1 class). This way I can pose a similar question to the class in a "make sure you can do this type of thing" way rather than a "someone here made this mistake, all tell her she's wrong" sort of way.  My mentor is happy for me to give her one lesson plan at a time, which makes for some tight turn arounds when I have the same class the following day!  I'm so very lucky for this to be the case, one trainee has to have in plans 2 weeks in advance!

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