Earlier today I saw a tweet from Luke (@bettermaths) which said that the subject of those evenings #mathschat was “how should we assess year 9, in light of the new 1-9 grading system?”
This got me thinking about year 9. It’s a funny year group in general. Traditionally it falls within key stage 3, but in many schools these days it us counted as key stage 4. This year’s are in a stranger place still, as they will be the first year to go through the new KS4 curriculum and sit the 1-9 exams. And they will do this without having done the new KS3 curriculum, never mind the KS1/2 curricula. This means they run the risk of having gaps in the assumed prior knowledge where said assumed knowledge is on the new curriculum but not the old.
It is important schools address this this year. We need to ensure that we are equipping year 9 with the requirements to access the new curriculum. Edexcel have drafted a transition curriculum for year 9 that is freely available on their website. (I don’t think the other boards have, if you know they have send me the link and I’ll add it!) As all the boards are using the new curriculum with no additional content, this transition scheme should help if you haven’t yet put anything in place.
So how should we assess?
The answer here is pretty obvious to me. We should be assessing against the content they need to know, identifying the gaps in that content and using that to inform our teaching. I believe that that should be the main focus of all our assessment, particularly with this year group who face extra challenges.
I do, however, feel the question is intended to be about tracking, rather than assessment. I think it’s really asking “should we be using levels, a-g grades or 1-9 grades?” This to me is an entirely different question. And I see it as far less important. We are moving into a “life beyond levels” and I see that as an opportunity to take back assessment. To restore it to its former glory as a way to identify gaps, rather than a way to impose a linear model of progress onto learning that doesn’t take a linear form at all. I know at the recent #TLT14 event Tom Sherrington (@headguruteacher) spoke about the removal of levels from reports at his new school and recently wrote this excellent piece in assessment.
So what are you suggesting?
Well obviously we need to have some progress tracking, but does it need to have a numerical value every half term? Should we even be collecting data that often? I believe Kev Bartle (@kevbartle) spoke at #TLT14 about how he’s moved his school to 2 data collections per year, believing that this will mean more accurate data, which I think is a good idea.
So what should we use?
We know, as teachers, what are students need to know to get where they need to be. We know their start points and we know where they need to be at each step. Should we even be quantifying this with numbers or letters? Could we nit be rating them as “On target”, “Above target” “Below target”? In a post level world where progress is king (fingers crossed progress 8 moves us away from a threshold pass!) should we not be assessing against, and reporting on, progress?
#mathschat is a twitter chat which happens Wednesdays at 8pm. Follow the hashtag to join in. And feel free to comment here if you have opinions on this, I’d love to hear them.
Earlier today I listened to episode 19 of my favourite podcast, “Wrong, But Useful“ (if you haven’t listened, and like maths, then go listen quick!). Every month the hosts Colin Beveridge (@icecolbeveridge) and Dave Gale (@reflectivemaths) set a maths puzzle for listeners to solve.
This month it was Colin’s turn and he set a nice algebra puzzle:
Show that n^4 + 4 is not prime for any integer greater than or equal to two.
Have a little go if you haven’t already….
My thought process went like this:
For even n then the whole things even, but what about the odds?
Could it be solved by induction?
N=3 gives 85. N=5 gives 629. Nothing jumping out there.
I’ll factorise it, see what happens:
After a brief false start where I wrote the square root of 2 is 1 I came up with the solution, which is quite neat.
n^2 – 2n +2 is greater than 1 for all integers greater than 1.
n^2 + 2n +2 is greater than 1 for all positive integers.
Hence n^4 + 4 is a product of two numbers greater than 1 for all integers n greater than or equal to two.
A lovely little midweek puzzle.
This morning a colleague and I travelled over to Huddersfield to visit a school that was implementing a mastery curriculum in maths. The idea of a mastery curriculum is something that very much appeals to me. The crux of it is that each stage I’m the learning of maths is embedded fully before moving on to the next. It is something we are considering adopting as a school and it was fantastic to be invited to go to this other school and see how they’re implementing it.
The visit involved observing a lesson and meeting with the schools mastery lead to pick her brains about the curriculum. The whole experience was worthwhile. It was great to see a different school the set up and the layout. How the kids their behaved, interacted and were turned out. I think we would all benefit from being able to visit other schools as part of our own professional development. Especially those who have only ever worked in one school, as it would broaden their horizons and ideas.
I’m in the middle of writing a report on the visit, and mastery, so will blog some further thoughts here when I’ve had time to research and digest. But some early thoughts:
- Mastery is a solid idea based on strong theoretical groundwork (as laid out be Kris Boulton at the recent maths conference)
- care must be taken to ensure that the most able on the cohort are stretched and not left stagnant while the others catch up
- mastery is a big undertaking, and needs to be embedded from year 7.
- measuring progress in the way that has been done previously at year seven will not work, and this would need to be addressed, but this needs to be addressed anyway in a post level world.
Today my twitter feed is full of tweets from people in Southampton, at the teaching and learning takeover event (#TLT14). The event seems to be going well, and I hope to catch up on the day later via blogs and/or videos, but currently my house us full of the sounds of nursery rhymes, so I thought now might be a good time to reflect on the first half term.
Way back in August I started a new role at a new school. I’d never moved schools before, and as such was stepping into an uncertain world. That first week we went back a week earlier than everyone else which at the time was a tad annoying but is now paying dividends as we are starting a two week break.
Starting a new school is tough going. There’s a ton of new stuff to learn, new acronyms, new systems, new policies, new names for things, new colleagues and, of course, new pupils. This overload of newness hits you like a train, and it took me a while to get my head round it all.
I’ve enjoyed the first half term. There have been challenges, but I’ve learned from them and I think they have made me better at my job. I like my new classes, I like my new colleagues and I like my new role. On top of that I feel that the school are investing in my development and I am really glad I made the move.
As well as moving schools, I’ve also moved authority, and am now teaching in Bradford. The school is part of “The Bradford Partnership” which is a non-profit organisation which is wholly owned by its members (ie the schools). The mission if the Partnership is to improve education for all young people in the city and I think it’s a great initiative. There are opportunities to meet colleagues from other schools regularly and to share ideas and best practice.
This first half term is always a tiring one, as is the next, so I’m glad I’ve got two weeks off to recharge the batteries. I just hope my bodyclock realises it is the holidays, and allows me to start sleeping in a bit!
Formula Triangles, it would seem, are a much loved shortcut in the world of Mathematics teaching. You know the ones, it’s when you get a three term formula that is one thing = a ratio of two other things. They look like this:
I’ve mentioned my hatred for them in passing on the blog and on twitter a couple of times and come under fire for this, which has made me think about it them a bit deeper. I used the term “ban them” in a tweet, and this may have been the cause of the uproar – as with The Great Calculator Debate. The term is more important extreme than my actual viewpoint, so I figured I’d try to set my thoughts out here.
Formula Triangles were first shown to me by my GCSE IT/Electronics teacher Mr Walker. The formula he was teaching them for was V =IR (Voltage = Currently X Resistance if my memory serves me correctly). Mr Walker didn’t explain how they worked, or what was really going on. He said “I always have trouble getting them the right way round, so I use this triangle, and cover the one I need.” I’m fairly sure his algebra skills were a little lacking. I was good at algebra and quickly spotted why this worked. I had to explain these reasons to a number of classmates who weren’t happy with the “just do it like this” model and craved a deeper understanding.
I quite liked them as a short cut, and quickly realised they could be applied to any number of similar formula, including speed distance time formula and the trigonometric ratios for right angled triangles, or RAT Trig for short. I’m fairly sure I used these in my exam.
So what’s the problem with them then?
Well, since you asked…. It’s the way I’ve seen them taught. I’ve seen them taught in maths lessons the way Mr Walker taught them in IT. This misses the opportunity to cement the algebraic skills required to rearrange formulae, to see the links between different areas of maths and enables pupils with little to no algebraic knowledge to gain a good GCSE pass. This highlights the ineffective nature of the maths GCSE as a measure of mathematical ability, which surely it should be.
These formula triangles are taught as a replacement to algebra, the purpose of them is that you can cover the one you want and get the formula arranged the way you need it without having to rearrange. Becks (@becksta9) asked: “when finding an angle using the triangle you get sin x = o/h how do you make x the subject?” and this is a good question, unfortunately in my experience the use of formula triangles for Trig is normally coupled with the instruction “don’t forget that you press shift when finding an angle”, rather than “the opposite divided by the hypotenuse gives the sine ratio, so you need to use the inverse function to find the angle.”
Is it ever ok to use them?
I would say yes. I am fine with people who understand algebra using them as a shortcut to save time (although how long does it take to rearrange them properly? You must save milliseconds!) , I’m fine with teaching them to weaker students who have tried to learn algebra but are prone to mistakes after they’ve been shown how to rearrange them algebraically.
What I’m not fine with is the “do it like this and don’t worry about how it works” use of them. Especially when the learners in question want to go on to study Maths at A Level and beyond, it could damage their chances.
Becks, Jo (@mathsjem), Martin (@letsgetmathing), Hannah (@missradders) and Colin (@icecolbeveridge) all came to the defence of formula triangles on twitter. There was some sense that I was personally attacking their methods, and that I was making generalisations about the use of formula triangles. Neither of these were my intention and I apologise if it seemed it was. I hope this post explains what I meant better that I could in 140 characters. I was surprised at the massive response the tweet got, and the massive, seemingly emotional, relationship some had to it. I would love to here how Formula Triangles are used to aid rearranging, instead of as a way to avoid it, as is the point. I’d love to hear more views on this in general, do you use Formula Triangles? If so how, and why?
Late to the party I know, but this evening I finally got round to watching the Panorama documentary “Last Chance Academy”, which was shown back in August. The programme follows a handful of loveable rogues who are being taught at LEAP, the online alternative provision that is part if the Baverstock Academy in Birmingham.
The academy is in a deprived area, and LEAP is housed in a separate building with a separate entrance and separate staff. I’ve seen this sort of provision in varying forms in other schools, but the separation here is at a higher level than ones I’ve seen, which have all either been housed within the school building or staffed by the same staff.
I think that this sort of provision can work really well. The most disaffected learners can be taught in smaller groups, gaining a highly level of support and attention which often meets their specific needs. Personalised programmes can be implemented and back in the main school those without the same level of additional needs can enjoy and progress in their lessons further as they will be free from disruption. This looks to be a win win scenario for all involved.
I can imagine some of the arguments though, “how comes he gets rewarded for being naughty by getting half days?” etc. These would stem from a lack of understanding of the complexities at work, and hopefully through education could be tackled.
What does tickle me though, is the branding. These policies are often (and definitely at Baverstock) called “inclusion” policies. The head of Baverstock explain his purpose to be “I’m against exclusion as every child should be entitled to a mainstream education.” The obviously flaw being that they aren’t receiving a mainstream education and are being excluded from, not included in, the classes their peers are attending. I think the branding stems from the aim that these provision provide a temporary respite from mainstream while pupils are helped with their specific needs before being reintegrated back in.
I enjoyed the documentary, and see a great benefit to this type of provision. I was pleased to see the results were positive for the pupils involved. These are challenging pupils, who have deep issues, and are getting a good education despite that.
The GCSE Curriculum
The current GCSE is not fit for purpose, I’ve written before about my feelings on it, and as Jo alludes to it is entirely possible to get a B yet still be unable to access the A level curriculum. This is in part due to the make up of the course, which is being addressed to some extent in the government reforms. I feel the new syllabus ia much better and will ensure more pupils are ready for A Level maths, but I don’t feel it goes far enough. I would have loved to see some basic Calculus on the new GCSE. I hope the more rigorous nature of the GCSE will mean the brighter students can no longer coast, which will solve the shock issue many have when A level gets hard.
I’ve written before (here and here) about the damage certain shortcuts can have, and I recently presented on it. As part of that presentation I spoke of certain shortcuts that can have a damaging effect in a different way. These are shortcuts used to bolster grades without any understanding. The worst of these, in my opinion, is the use of formulae triangles to rearrange simple formulae, such as right angled triangle trigonometry and speed=distance/time. These topics provide ample opportunity to practice key stills that are essential in A Level maths, and by introducing students to these shortcuts we are robbing them of that opportunity and adding to the problem we have with the gap between GCSE and A-Level.
The modular nature of the A Level
Another thing I agree with in the recent curriculum changes is the move away from a modular system. I think this creates a compartmentalised feel to the A level when really maths is completely interlinked. The new A level presents an opportunity for us to create a truly exciting course that can show students this. The move away from modules, and the end to the January exams, means that A level students now have more learning time to really embed the skills and knowledge they need.
What do we do?
Jo asks, in her post, what other schools do to ensure their students don’t fall behind. In my last school, as KS5 Co-ordinator I ran regular drop in sessions that could be accessed by any student. This is something I have also implemented at my new school in my role as KS5 Leader. I find these are very well attended as we get nearer to exam time, but not so well attended at other times. This year we are targeting learners who need to attend and making sure they are coming.
What about the content?
Jo mentions summer work between Yr11 and 12, which is something I’ve looked into before. But this can lead to problems. Some will do it all, early, and then forget it. Others will do it just before the start, which is good if they get it right, but if they get it all wrong doesn’t really help. Others will not do it. And every year some students change their choices at the last minute so wouldn’t have received it. I’m a fan of the idea if giving core skills tests at the start of year twelve to see where students are. I also feel that we need to spend as long a time as is necessary getting these skills nailed on at the start of the A level, otherwise we are setting ourselves up for problems later.
Test them early
As well as a diagnostic tests on entry, I feel another test 4 or 5 weeks in can be effective especially for hammering home the need for working independently outside of lessons. This post from Manan Shah (@shahlock) explains how he uses an early test in a similar way.
Well, all of key stage 4 really. I think we need your be pushing our most able to cover A level topics and A level questions. This is something Jo suggests in her post that I have been doing for a number of years. This, coupled with a focus on ensuring pupils are gaining the skills necessary and avoiding shortcuts, should set them in good sted.
These are some initial thoughts on the subject, I may elaborate on some of the things mentioned another time. If you would like any further elaboration in any topic mentioned, do feel free to ask. This topic is also set to be the main point of discussion of a twitter chat Jo is hosting on Tuesday 7th October, #mathscpdchat, if you wish to contribute. I’d love to hear others thoughts on the subject, if you write anything do let me know.