Why I will never use lolly sticks in my classroom.

Because, well, reasons.

I’m sure there are great reasons to use lolly sticks, or other randomisers – it creates a culture where everyone is expected to be attentive, or to articulate their thinking at any time or something. You may have great success with them in your classroom. That’s fine. Don’t tell me I have to, and here are a few reasons why.

  1. It removes my judgement as to who I need to ask about a question. I realised this when going through a re-arranging homework with a class. There was one student who had different looking answers to many questions, and I realised this when he put his hand up and answered a question. It presented a perfect opportunity for discussion about multiplication, division and the order we do steps in re-arranging formulae. It also turned out there were other students with similar looking answers who didn’t speak out. If I only selected at random and did not allow students to put their hands up, there’s a chance I miss this and two bad things happen: We miss out on a valuable learning experience and some students go away thinking their method is wrong, when it’s right.
  2. I taught a student with anxiety issues recently. Her biggest fear in college was that she would be called upon to answer a question and have to speak out in front of the class, particularly if she wasn’t certain of the answer. While it’s a good thing to help students overcome these fears, causing them misery and anxiousness because they might be called on at any point in a situation out of their control doesn’t seem like the best way to do that.
  3. An answer to the above is that I could just not include her name in my randomiser and that solves the problem. Seems like an elegant solution right? I remove the possibility she could ever be asked to answer. I also remove the possibility she could ever choose to answer as well. I essentially remove the opportunity for them to overcome their anxiety. That student above, about March time that year, she answered a question in class. A month later, she answered when she wasn’t sure she was right. If her name isn’t on the lolly stick, maybe she never gets that chance.
  4. That culture of attention and preparation, it’s also a culture of uncertainty. If you’ve ever been to a TeachMeet where they randomise the order of the presentations, you’ll know what I mean. Every time the randomiser spins you’re adrenaline starts pumping; will I be called to do my 2mins; will it go alright; will I forget my opening line, my carefully thought out response to a question at the end? By the time is gets to you 45mins later, you’re already exhausted. If it can happen to us, people who are used to speaking in front of an audience, think how it might feel for students in the room.

I guess the bottom line for me, is that I don’t find it helpful. Some people might. But like a lot of things in education, just because it works for you, doesn’t mean I should have to do it.

Posted in Classroom, Pedagogy, Not Maths, Assessment | 3 Comments

Two ways I try not to suck at formative assessment

This might end up being the content of a teachmeet prez in future, so bear with me if it’s a little scattershot

Formative assessment is hard. It’s probably up there with behaviour management, teaching a topic for the first time and having a life as one of the hardest things to do. Many people, very clever people, say its one of the most important things we can do though.

So maybe we should try hard to get it right. so here’s two ways I try to suck less at it.

Exit slips.

Exit slips are cool. SLT love them. Teachers love them. OFSTED probably love them too, but they aren’t allowed to tell us that. We all love them. I used them a lot for a while. It was great, I could sit down and confidently congratulate myself that all these students knew how to differentiate, or multiply by decimals or whatever my lesson had been on. Smashing stuff. And then a few weeks later they’d sit an assessment and get it wrong. Sometimes a bit wrong, sometimes REALLY wrong. Heartbreaking. It took me a while to understand what was going on. See I saw these exit slips as this:

exit 1

When really what they were telling me is something a bit closer to this:


Now this might be obvious. It probably is. But it took posts like this from David Didau, or this from Dylan Wiliam, and carefully re-reading his excellent book Embedding Formative Assessment. And hundreds of other little learning steps to put it together.

So now when I down and review exit slips I confidently stack up and push aside all those which are correct and use those that got it wrong to guide how I think about the class.

I wish he was there when I write Hinge Questions

src: Banthapedia

Hinge Questions.

In case it wasn’t clear from the motley collection of posts on this I’ve thrown together, I freakin’ love Hinge Questions. But they kind of fall into the formative assessment trap that exit slips do.

Student’s getting it right tells you much less than when they get it wrong. Which is why I find they take so long to write. I want to get the closest possible thing to semi-density as I can so I can make the best possible guess at what the student was thinking when they got the wrong answer.

src: Analyzing diagnostic items: What makes a student response interpretable?

src: Analyzing diagnostic items:
What makes a student response interpretable?

Which is why they are so hard, why they take so much time and why we often see the reverse – where we are only interested in the correct answer, and we collect that data and deal with those that got it wrong as one group.

Posted in Assessment, Classroom, General Maths Thoughts, Pedagogy, Something to work on | Leave a comment

Sorry, your qualification isn’t good enough anymore

So this evening I was talking to a secondary teacher friend about many things, but among those was the general uncertainty about GCSE changes, what constitutes a ‘good’ GCSE, conditions of funding in Sixth Form and the like.

Then it hit me.

There are going to be literally hundreds of thousands of young people with worthless qualifications.

And I’m not meaning a “oh your C grade isn’t really up to the standard of an old C Grade and more” kind of worthless. I mean the directly comparable this isn’t the required standard any more worthless.

Because there will be Student X who get a grade 4 after leaving secondary in 2017, or 2018. Great, well done student X, the world is your oyster. You have achieved the minimum standard in Maths. You can go study English at Sixth form, and Politics and History and go and get your 1st at university and apply for a job. And see the words:

GCSE Grade 5 in Maths required.

Because now the government says this is the minimum standard.

Poor student X you think, but hey, they have a degree! I’m sure any employer worth their salt will consider that to be more important than some GCSE from years back. And maybe thats the case. Maybe. But tell that to the History or Art graduates from the early 2000s who had to take extra Maths courses to be teachers.

What about Student? Student Y works really hard in 2018 but doesn’t get her 4, she in fact gets a 3. But she has decent results elsewhere and gets into a local college on a BTEC programme. They put her through GCSE even if she doesn’t want to, because its a condition of funding. Student Y is  late bloomer and she pulls it off! she gets a 5. Life is good and just. The hard working are rewarded. In fact she now has a better grade than her friend, Student Z, who has a 4 from school. They want to apply for apprenticeships in 2020 after getting their BTECs and Student Z is left in the cold as he doesn’t have the 5.

Because now the government says this is the minimum standard.

What about Student Q. Student Q takes GCSE in 2017 and gets a 4. She looks ahead and realises that the standard will go up by the time she has finished uni and so asks if she can retake her GCSE. Turns out she can’t, because she has the minimum and there’s no funding for retaking a level 2 when you already meet the minimum. So she struggles through a Level 3 Maths course for a year and fails. The content is too much. All this algebra she has never seen before because it was on Higher tier and she entered for Foundation. Does she try again in the second year?

What. A. Mess.

Not sure of an answer, but does anyone else feel like this has been overlooked in the mess that GCSE reform has been?

Posted in Assessment, General Maths Thoughts | Leave a comment

Some conversations.

*Any resemblance to a specific individual is unintentional. Any resemblance of traits of a group of people is intentional.

Manager: This is the most important thing to improve teaching and learning throughout this year!

Teacher: Can I have some time put aside to do it?

Manager: No. But this is the most important thing.

Some time passes

Manager: This is the priority for improvement going forward!

Teacher: Can I have some time put aside to do this?

Manager: No, but this is the most important thing.

Some more time passes

Manager: This is the best way to improve your teaching!

Teacher: Can I have some time put aside to do that, or remove some of the other things?

Manager: No, but this is the most important thing

The results arrive

Manager: Why didn’t you do the important thing I told you to do? If you had, your results would be better

Teacher: Which important thing?

Manager: The most important thing.

Teacher: OK, well can I have some time put aside to do this next year?

Manager: No, you need to prioritise your time so you get the most important thing done.


Posted in Not Maths, Pedagogy | 1 Comment

BREAKING NEWS: Good, fun not always synonyms.

People like bad movies. It’s true. I do as well. I love Starship Troopers, but its a terrible film. It’s cheesy, the acting is bad, the dialogue is poor in places and frankly its totally ridiculous.

It’s also incredibly enjoyable (for me). Another recent example is Pacific Rim. It’s a ridiculous premise, the storyline is outrageous and the characters are, well, somewhat one dimensional. I’d watch it again in a heartbeat because it was a thoroughly joyful 131mins.

There are also films that are critically acclaimed, by many measures among the best, that I really don’t enjoy. As an example; Amelie.

Unfortunately I consistently find that many people couple ‘good’ and ‘enjoyable’ in their heads. If I say a movie wasn’t good, people assume I’m tell them it’s unenjoyable, or that they shouldn’t be allowed to enjoy it, or that somehow I’m criticizing them personally.

The converse is also true. I don’t like opera. I don’t enjoy it. It doesn’t mean that somehow the talent of operatic singers or composers is diminished or that they haven’t achieved something good. It just means I didn’t enjoy it.


So what does this have to do with teaching!?


Well, I have a student teacher in one of my classes and she was beating herself up that the students didn’t all enjoy the lesson. She was worried her lesson wasn’t good because of this. My argument: the students learned, they worked hard on something challenging. Your job is to help them learn, not entertain them. If they enjoy it, then bonus. But if they enjoy the lesson but don’t learn anything? Well you might have well put a DVD on for 70mins.




It’s incredibly frustrating that teacher training, INSET, lesson observations are pushing the ‘fun’, when frankly, I feel like it’s a terrible measure of whether a lesson is good.


Posted in Classroom, Not Maths, Pedagogy | 3 Comments


Something for consideration:

Every time you ask a teacher to complete another piece of paperwork without taking something away, a bit of goodwill dies because I already find it hard to find my mouse under all the paper you give me.

Every time you add a data collection point in the year without taking something away, a bit of goodwill dies, because I already have to do 3 entries per student per collection point and that many clicks is horrible.

Every time you add something that’s ‘just 5mins per student’, a bit of goodwill dies, because I have almost 100 students and just 5mins adds up fast.

Every time you change a policy without consulting the people it will impact, a bit of goodwill dies, because I want my opinion to be respected, just like you do.

Every time you introduce or move a deadline without warning, a bit of goodwill dies, because I plan my time according to what needs to be done.

Every time you tell me ‘what Ofsted wants’ a bit of goodwill dies, especially when I know you’re mistaken.

Every time a concern about a student comes back as ‘what are YOU going to do about it’ a bit of goodwill dies, because If I could do something, I would already have done so.

So don’t be surprised when I don’t jump to volunteer any more.


Posted in Not Maths | 1 Comment

By Hand

I love Desmos, I love graphing packages. I even like TI-8x graphic calculators (Even the old, old TI-82s with dodgy screen contrast).

But sometimes it needs to be graphed by hand. Sharp pencils. Accurate marks. Slow, deliberate, calculation of points.


Because there’s something about realising that when you plot sin(x) and cos(x) they have the same value at x=45 that comes from actually drawing it. Or that something horrible and frightening and wonderful is happening as you approach tan(90). Or that cosec(x) and sec(x) look totally weird but make sense when you try to make a table of values and compare to sin(x) and cos(x).

Because in the end, if you haven’t drawn it accurately and had your hand try to make the shape, what hope do you have of sketching or visualising?

Because in the end, ‘I drew it on my graphic calculator’ won’t earn you marks.

Maybe it’s blasphemy. But tomorrow we will sharpen our pencils, fire up our scientific calculators and draw some goddamn trig functions. And, since I’m in a bit of a mood and I haven’t finished my tea, I’ll fight anyone who tells me I’m wrong.

Enjoy the smell of pencil shavings.

Posted in Classroom, General Maths Thoughts, Lessons, Pedagogy | 3 Comments

The Dream Crusher

Enrolment week always seems so hard in a Sixth Form College. It should be a time of excitement, fresh faced enthusiastic new students and positivity for the year ahead.

Then, as the week goes on the appointments get trickier and trickier. The conversations have less and less “Of course you can study that” and more and more “well, unfortunately you didn’t do as well as you had hoped so that isn’t right for you, instead why not consider this…”

It’s the hardest thing to have to tell a student that they won’t be a vet/doctor/engineer/architect/whatever else they always wanted, that they can’t even take the subjects they wanted because they missed the grade, because the school over predicted, they were ill on the day of the exam, they lost a teacher half way through the year or any of the other hundreds of reasons.

Maybe this year there have just been more students with unrealistic aspirations, but this year, more than before, I have felt like there’s a side to the Sixth Form Tutor that no one talks about, the part of you that has to turn a child’s unrealistic dream into something achievable, challenging and interesting so that they can be successful.

Sometimes we have to be the Dream Crushers. And it’s the right thing to do.

Posted in Assessment, Not Maths, Pedagogy | 1 Comment

Why One Hundred Percent is Important

or ‘The tale of why my classroom is full of students doing retests’

Students join us from a variety of secondary schools into a range of different Maths programs (we are a 16-18 provider). They come with different experiences, strengths and methods that vary hugely based on where they have come from, what ability set they were in and whether they had a specialist teacher for any, part or all of their later secondary education.

All of this compounds into problems for the start of the course. Both AS Maths and AS Use of Maths are incredibly algebra heavy courses, and as such a level of competence and speed is necessary for success. Over the years we have found getting students up to speed on algebra to be a sink of class time early in the course, and frankly unfair on those students who were competent and wanted to learn something new at their new college. So over the last two years we changed how we were to run the start of the year from:

“We will spend the first week getting students up to speed and covering in gaps”


“We will spend a fraction of time in the first two weeks checking students are up to speed and highlighting areas they need to improve. We will provide opportunity outside of class for remediation”

We put together a choice of algebra skills we expected students to come to us with from GCSE that they should demonstrate accuracy and efficiency with. I wrote 4 assessments for each skill and we asked all students to sit one per lesson for about 10mins at the beginning or end. If the student didn’t get 100% we asked them to return outside of class for help and a resit.

Doesn’t sound like anything new to people who do SBG I guess, but it was a big change for us.

The first year we had 10 skills, shown below (with slight variation later between the two courses to take into account the lower entry requirement of AS Use of Maths). All were tested at 8 questions (except AS UoM skill 10). They looked something like this:

I’ll be honest, those first few weeks were a fairly harrowing experience for students and teachers. Marking load was high, especially for those teachers with 4 first year classes, and students were frustrated with timing (too many questions on the later tests) difficulty (particularly the surds example above) and the organization became messier as the third week (only four lessons a week meant it spilled over into week 3) drew on.

So for this year we changed things. We reduced from 10 to eight; reduced the number per assessment to 6 and kept the 10min target. We also, critically, kept the bar set at 100%. As I said to my classes ‘If I ask you to write your name 6 times and you get it wrong once, we’d both be worried. These skills are just as important’.

So this is what they look like now:

We’re now winding down week 3, so all classes have tried them all once, and we have had a much better uptake on student resits. Sure, I still have students who got none of them yet, and yes I’m worried about them. But now, crucially, I have something concrete to start a discussion about support with managers, parents and most importantly, the student themselves.

The fact is; I’m not sure how to truly measure the impact here. I’m certainly not sure it would work anywhere or everywhere else. All I know is that those students who get it all, or at least most of it, done and sorted turned out last year to be the more successful, and that theres a pretty strong correlation between those who didn’t bother, and those who failed. I’m looking forward to a proper analysis once we have two years of data.

That’s all I have on that. If you want to see more of the assessments let me know.


update: actually while this was in my drafts folder, we finished up. I set a deadline and on the last day I was positively snowed under with resits. Some students still didn’t make the attempt, or didn’t get them right the last time around – what to do next for those is the next big job!

Posted in Assessment, Classroom, General Maths Thoughts, Pedagogy | Tagged , , , , | 4 Comments

Trig Wheel

As requested on the twitters here is the trig wheel I shared with the folks in the PreCalc morning sessions at #TMC14. I’m going to repeat what I said there; I found this on someone’s blog. I don’t know now who. But I stole it from somewhere. So if it’s yours, tell me and I’ll credit you – and THANKS!

The file (each student needs one circle in each of two colours):

Mark degrees anti clockwise on one circle (make sure you start at the correct line) and radians anticlockwise on the other (note that the numbers should go under the line, it’ll make sense later!):

2014-08-11 19.10.16

Cut along the zero line from the edge to the centre:

2014-08-11 19.10.41

Place the two wheels so the cuts line up and the labeling faces inwards and slide one circle into the other – this should reveal an angle – rotate until you find what you want and flip over to convert:

Enjoy :)

Posted in Classroom, General Maths Thoughts, Lessons | 3 Comments