## Microteaching

Microteaching: you know, splitting a lesson between a number of people each delivering 5-10 minutes. It was always an activity I enjoyed during my ITT course and it is something I’ve used well come revision times over the course of my career, although not for a while to be honest.

Then, on Monday when I was discussing with one of my Y13 classes the plan for this week and the work I would like them to complete over Christmas to pepare for January’s “Pre public examinations” one of them asked if they could do it. He didn’t use the term “microteaching”, he just asked if they could split up the unit we’ve just covered and each deliver a short revision session on it. The class are fantastic and I was pleased to give this the go ahead.

Today was the time for that lesson and when it arrived none of them had prepared anything, I suspected that this might happen and had brought so work as a contingency plan, but the class were keen to deliver the sessions anyway without planning. To “wing it” as it were. I was amazed by their willingness, as I know experienced teachers who would freeze on panic if they were asked to deliver even a short lesson like this without a set of pre prepared slides.

The sessions themselves were great, they led to some great discussions around the topic “differentiation”, and any errors made were picked up by others in the class. They also made some fantastix links to other topics and other areas of maths. There was also a decent amount of comedy in some of the sessions, including a little at my expense, but that just made it more interesting.

Definitely an activity I would run again, especially with this class.

*Cross-posted to “One good thing” here.*

## Where’s the Function?

This question was another question from the January 2013 C3 paper that I remember almost foxing some of my students of the time:

It’s a strange question in that it asks for ff(-3) but, unusually, doesn’t define the function algebraically. I remember the day of the exam three of them discussing the paper with me after sitting it saying “it was a well weird function question, it just showed you the graph.” That day they had worked it out, but I feel that the time taken had contributed to at least two of them running out of time later in the paper.

So on Friday when a couple of learners asked for my help and I saw they were working on this question I didn’t even need to ask what their issue was. I started by reminding them that the graph was the function and that they didn’t need it algebraically to get an answer as there was enough information on the graph to answer it. We discussed this and they realised that the y coordinate is what comes out of the function when you put the x value in.

It’s a nice question, it highlights a possible blind spot that I need to address and shows us one of the pitfalls of an over reliance on past papers in revision. Past papers are a key part of revision, don’t get me wrong. But they shouldn’t be the only part of it, as otherwise a curveball question like this, one that asks something in a slightly different way, can really throw you off.

## Effective Group Work

Last night I attended Teachmeet South Bradford at Appleton Academy and saw some superb presentations. There was one given by Andy Sammons (@amsammons) in which he was discussing independent work. He mentioned that he gives his pupils ten “sammonspounds” per group at the start of a lesson and tells them they can buy ten minutes of his time with it, but that’s all they get. This gives the groups drive to be more independent and to save their time until they are really stuck and have devised good quality questions to ask him. You can read more about the topics Andy spoke about on his blog here) This is a great strategy and got me thinking about the ways I have tried to do group work . It reminded me of one method in particular that I have used a number of times to great success and I wanted to share it with you here.

The first time I used it was with a Y11 class in my NQT year, they all had C’s already in maths and were not very motivated to get B’s. I had taught a topic on Pythagoras and trigonometry and I wanted to do a consolidation/revision lesson on it. I set the room up for grouped tables and assigned them groups on their way into the room. I selected groups so that each of the groups were evenly matched and assigned team captains, envoys, timekeepers and finance managers. It was the captains job to take a deciding vote on any decisions, the envoy was in charge of discussing with other groups, the timekeepers were in charge of ensuring they were not running out of time and the finance manager was in charge of the “money” (in this case counters!). I gave each team a float of 20 counters.

The task itself was an exam paper question based relay, there were some really easy questions, and for each one of those the teams completed they gained 5 counters, they went up in difficulty and there was 10 counter questions, 15 counter questions and 20 counter questions. The teams were told that they could buy my help for 8 counters, or they could buy help from other teams at an agreed fee, but I gave a suggested value of 4 counters. At the end of the lesson the teams cashed up and the winning team received a prize.

This worked well with that first class, they were all shrewd with the questions and only purchased help if they really needed it, it helped with independent thinking. I have now used the set up many times (not always with the same activity) and it does work. It engages them and makes them think for themselves more. And on top of that it is fun for tem and me and some teams get really competitive!

## Maths exams and how we prepare

Recently I’ve been thinking a lot about the way maths is examined and the way we need to prepare for exams, and I’m not the only one. @bigkid4 has written a series of posts on it here: http://mylifeasacynicalteacher.wordpress.com/2013/06/03/how-would-i-change-the-exam-system-ks1-5/ Dave Gale (@reflectivemaths) has written about it here and has also discussed it with Colin Beveridge (@icecolbeveridge) on their podcast here. I’ve read and heard other things too, and had many conversations about this.

The main thing that got me thinking was “that” C3 exam last week. It was really hard and seems to have thrown the vast majority of A level students across the country who sat it. When I first read it I thought it was ridiculously hard. But then I worked through it and realised the the main reason it looked so hard was that some of the questions were phrased differently to previous years. I actually enjoyed working through it, and realised that the students had all the tools to complete it, but if they had relied too heavily on past papers for revision they may have been thrown. Last year I tried to include more open ended maths questions in my lessons, and found some real beauties on some old A level and O level papers dating back to the sixties (when calculus still held it’s rightful place on the O level curriculum!). My year 13’s (among others) loved those questions that I threw in, (one said enthusiastically one lesson: “sir, these questions where you have to work out what maths to use are my favourite!”) and I’m going to build many more.

It’s clear to me that exams are moving this way, and I think it’s right that they are doing, especially at A level. Dave Gale mentions on the podcast above that S1 questions start “using a binomial distribution”, and I know S2 ones do the same with poisson etc, and this seems too easy. But as I say, I reckon the c3 exam is the first step in a move away from that.

This is a trend we are also seeing in GCSE papers. When my HoD and I went through last Friday’s calculator paper is seemed every other question we were saying things like: “that’s unusually phrased so may have thrown some of them”. I hope (and think) that I already am teaching the maths, and not just the methods to pass exams. But I intend to work on this even more to ensure in future that my pupils are ready for anything that gets thrown at them come next May/June time.

While listening to the podcast above I thought the real life use of solids of revolution to derive the volume of a frustum shaped plantpot was superb, and I’m going to use this when c4 comes around. I also liked the challenge question they asked and enthusiastically answered it afterwards (see below). I think questions like this will be key to fully developing future mathematicians.

Question: an equilateral triangle and a regular hexagon have equal perimeter. The area of the triangle is 2 square units, what is the area of the hexagon. The picture was my initial solution, but I did then realise I could have done it quicker and more simply using similar shapes…

## Whistle-Stop Tour

This year my year 13 class picked up AS level further maths on top of their A Level maths lesson. As the whole class were doing it and I was the only teacher covering C3/4 and FP1/2 we decided to do C3/4 first and they sat that in Jan, then we did FP1 and 2 for this sitting. With FP1 on the horizon the class are all hard at work revising, creating revision cards and hammering past papers. They are coming in for a few hours tomorrow and I thought it might break it up a little if I put together a whistle-stop tour of the module to ensure they havent missed anything. I have create a notebook presentation which I will use as a starting point so we can discuss all the topics involved. If it works I may try doing similar for other modules.

You can download the resource here: http://www.tes.co.uk/teaching-resource/FP1-Whistle-Stop-Tour-6338370

## Data Revision Quiz

So, following on from the success of my “pub quiz” style revision tasks for Years 12 and 13 (https://cavmaths.wordpress.com/2013/05/16/revision-quizzes/), I thought I would try some with some of my Y11 classes and see how they fared. The first one I have tried is one I have written on data topics (the class are all sitting foundation) and the resource can be found here: http://www.tes.co.uk/teaching-resource/GCSE-revision-quiz-Data-6335135

I tried the quiz with a small class of pupils who have previously been known to have behavioural issues. The quiz format worked really well for them, they helped each other out a bit with some questions, but all tried to make sure they were still winning. It was a close fun thing with the range of scores being only 4!

I enjoyed running the quiz and they enjoyed participating. The all revised topics they haven’t covered for a while and going through the answers has meant they all can now do things that will more than likely come up on their exam that they couldn’t before! all in all, a successful and enjoyable lesson was had by all. I think I will run similar quizzes next week for them and for my other Y11 classes.

## Half term revision

Today I spent a few hours at school leading Y13 on a half term revision session. It’s something that I feel I would have shunned in my days as a student, but my students were keen and who am I to quash that enthusiasm.

We spent the time looking at problem topics from C3 and C4, mainly Trigonometric Identities and Integration. They are two of the topics that students struggle with most, but they are favourite two subjects too.

The students did some recalling of facts they needed to know, and i filled in aome gaps, they applied their knowledge to challenging exam questions, both individually and as a class and I modelled some answers on the questions they were really struggling with.

It was an enjoyable day, spending a few hours talking about some of my favourite areas of maths with some great young people who are eager to do.well in the subject. Let’s hope it has a positive effect on their scores.

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