Classic Blog

I chose to listen to Jamie’s appearance on the Podcast as a friend and ex-colleague Peter told me that his resources were good. I wasn’t disappointed: there were lots of good ideas in on the podcast. I’ve since investigated the resources and I agree with Craig – they are consistently very high quality and contain some great ideas.  Here are some of the points he made on the podcast

Teach general ideas, not specific methods
I think this is an excellent point: rather than getting pupils to follow a specific method like “finding the zeroth term”, encourage them to understand how they can find a constant term by thinking about making the sequence ‘fit’. Crucially, general ideas like this extend much more effectively to more difficult problems (in this case, non-linear sequences).

Traffic Lights
A classic idea from AfL. I bought a class set of red/amber/green cups and trialled them for about 6 months but they proved unpopular. I teach in a school where the students don’t generally lack confidence and are very mature. They said that they would rather just put their hand up and they found it a bit childish. But I’d love to make better use of them in future. Tips, anyone?

A lesson doesn’t necessarily need a plenary
I totally agree: when I’m circulating and checking individual work constantly, I agree that sometimes I’d rather just maximise the lesson time with pupils challenging themselves more individually than bring the whole class back together.

Prime Factor Buckets
A really nice visual idea – imagine the prime factorisation like a bucket of prime factors, which you draw from to find LCM or HCF as required. I wish people would share more of these kind of ideas in teaching. There are a lot of people blogging about general teaching principles, which I do find useful and interesting, but I’d love to read more blog posts sharing ideas of how to teach specific topics.

Work-Life balance
Jamie’s sounds quite bad – mine is “better” – the inverted commas are necessary because Jamie appears very happy with his. If you’re keener to have more time for life than work – I’ll write about how I achieve this soon.

The M-word
I’m glad to hear that Jamie avoids using the word minus. In my younger classes, it’s a banned word and pupils can earn / lose reward points for using subtract and negative / misusing the m word!

Subject Knowledge for Teaching and Learning
Jamie talked about how he has gained this in his first few years of teaching. This is true of all teachers and I’ve heard a lot of Craig’s guests say something similar, but I think we should promote better sharing of this, so that you don’t have to pick it up through experience but can learn it from more experienced teachers. My previous school offered new teachers 2-3 hours a week of one on one meetings with a more experienced mentor within the department. I found this invaluable in my first two years and then enjoyed giving back to the process as I became a mentor myself. I suspect that this is very unusual but I wish it were more common.

Grammar-School Specialist
I’m currently also specialise in teaching high attaining, but unlike Jamie I’m not sure I want to remain like this for my whole life. It’s a difficult point: I like teaching further maths every year and plenty of A-level, but I went to a comprehensive school myself and I’ve seen the statistics: they seem to be better for social mobility.

Homework platform
I had a bit of a go on the trial section of this and it looked really impressive. I’m excited to see  how it develops.

Overall, it was another cracker of a podcast. Thanks Craig and Jamie.

Three months into my foray into the world of blogging / twitter, I realised that my choice of twitter handle (@discoverymaths – now changed!) is more controversial than I thought! Whilst I champion guided discovery, explicit instruction still takes up more of my lesson time than discovery.

One time when the Head of my previous school observed my class, he saw a pretty standard lesson involving only explicit instruction. He said that he was impressed by my questioning and pushed me to think about how to pass on ideas to the new teachers I was mentoring. Here are my thoughts:

Everything is a question
Only add something to the class board notes once a student has said it, so all the ideas have to come from the class. Constant questioning means that you’re less likely to overestimate understanding and that pupils have to remain alert as they may be asked at any time. And on that matter…

What did Sarah just say?
This is one of my favourite questions, deployed in almost every lesson with larger classes. If you ever sense that someone isn’t listening to their peers, ask them to repeat what was just said. They’re usually pretty embarrassed if they can’t. Even if they can, it helps to reinforce important points and encourage listening skills.

Personalised
Target questions according to understanding to challenge all students appropriately. Break down the problem into many more steps than an experienced mathematician would.  This enables you to ask lower-attaining students to make small logical steps and higher attaining to come up with bigger ideas.

No opt-out
One of my mentors used to say “You have to have an idea. It doesn’t have to be a good idea, but you have to have an idea”. If you reach a total block, ask a simpler question which will help, either to the that or another student, before returning to the first student with the original question.

Bounce back
Hopefully your students will be inspired by all the questions you’re asking to ask their own. How to respond… Can you use your expertise to ask them an easier question which will help them come to the answer themselves? If not, pass it on to another student to keep all involved.

Pause / Think-Pair-Share
Pausing to get all students to individually think about or have a rough go at a question you have posed (and then discussing in pairs if you wish) during a period of explicit instruction is a good way to break up the time and give pupils a chance to refocus.

Subject Knowledge for Teaching and Learning
What really helps you ask good questions is knowing the misunderstandings that students often have and how to break your questions down into smaller steps or re-frame them in a different context to overcome these. As Jamie Frost emphasised on Mr Barton’s Podcast, this is not just about knowing the subject, it needs to be learned.

I really like Dan Meyer’s metaphor of presenting maths as the solution (aspirin) to a problem (headache), simply because it reminds me that I should start a lesson by making clear in some way what the problem is, before diving in to introducing new ideas.

I like it so much I was talking to some (mostly non-teaching) friends about it the other day. It went a little like this:

Luke: …isn’t that a great metaphor?

Alice: It sounds a bit negative.

Becky: It sounds as if you’re saying that maths is a headache.

Luke: no, no, no…

Alex: Yes, but I don’t want to have to take Aspirin.

Alice: I never take Aspirin anyway, even if I do have a headache. I think that’s more of an American thing?

Luke: Have you got a better version?

Alex: You want to undertake a journey but there is a river in the way. Maths is the bridge you need to cross the river.

All: *wretch*

So, I’m sticking with Headaches and Aspirin for now… anyone have a better suggestion?!

I’ve very much enjoyed several of Craig Barton’s podcasts recently and they are the highest quality audio source of ideas for Teaching and Learning I can find. I also like radio 4’s the educators but it doesn’t seem to be producing new programs, or at least they are very rare. If you know of any other podcasts that you think are similarly great, please comment below.

The title of this post refers not only to Craig’s most common response to his guests’ ideas (which makes me feel at home as a northerner!) but could also describe my overall response to the most recent episode with Greg Ashman.

Firstly, I love the sound of Greg’s department. It sounds very similar to the department at Highgate, where I worked for seven years. From my experience of other schools, I think it’s pretty rare to find a department where all the teachers work together so closely and come to agreement on the best approaches to teaching, but I think it’s a great idea and wish it was more common. From my own experience, it gives the students a very consistent year-to-year experience even if they change teachers, and encourages levels of discussion and debate amongst staff that just don’t happen without it.

I’m also a big fan of Greg’s behaviour management strategy of pointing out students that are doing what you’ve asked, instead of those who are not. I encountered this idea a couple of years ago in the form of “doing the politician” (when politicians come on stage they often point out their supporters) and it has been incredibly effective.

Then we come to discovery learning. Flippin’ Heck!

I’ve never heard of Cognitive Load Theory before reading about it through Greg’s blog, so I’m no expert, but this application of it seems relatively intuitive: students ‘working memory’ is limited and quickly becomes overwhelmed. I definitely agree with this and have regularly witnessed the problem he describes: students working memory is taken up by sub-tasks required as part of the discovery and so they fail to make the required discovery.  This can definitely be frustrating for me as a teacher and some pupils find it stressful.  It’s for this reason that I spend much of my planning time providing a variety of different levels of scaffolding (best case scenario, I admit!) and design resources which aim to reduce the cognitive load during discovery. Furthermore, I have put a lot of effort recently into improving the clarity of my follow-up explicit instruction and I’ve reduced the proportion of lesson time spent on discovery tasks, as I am to some extent convinced by the research evidence to which Greg refers. I also enjoyed the toilet fixing / beer tap installation anecdotes, although I personally very much enjoy discovery DIY!

Why am I not willing to stop entirely?

I’m a little worried that I’m suffering at the hands of the backfire effect, but I have another major reason for using discovery: motivation.  I find that a large majority of pupils are excited by the joy of discovery and feel empowered as mathematicians; my lessons almost never contain the games, frequent changes in or variety of tasks used by many teachers to gain attention but as one of my heroes Michel Thomas said,”it’s the learning process itself that motivates these kids, not the material used”. Also see Dan Meyer’s blog: “if math is basketball, let students play the game.” Greg does go on to talk about problem solving, and how he uses it after explicit instruction, but is that really playing the game of maths?!

I’d also say that as a team of 20 teachers at Highgate, we found that our students seemed to gain a better understanding using these approaches, as measured by teaching them in later years. Although this isn’t hugely scientific, they also did better in the UKMT maths challenges (the best test of problem solving skills I know) relative to students of similar ‘ability’ (Midyis scores) elsewhere. NB: sample size = 2 schools.

Overall, I like to think that my approach isn’t actually as different from Greg’s as my former blog title (discovery maths) suggested, as I am a proponent of more research-based approaches in schools, would like to do further study myself and am very envious of the quality of his writing.

Having trialled the inquiry approach with a small group, I was ready to unleash it on a full class in year 10.  You can see everything that went on the board in the inquiry here.

The pupils chose repeatedly to spend time on creating contexts for the graphs. I felt that this was partly them rebelling against the idea of inquiry – they wanted to turn it into a more traditional question – but discussing their contexts as a whole class revealed many misconceptions and tackled them before they ever got close to doing any calculations.

This part of the lessons was very engaging for the majority of pupils and as in my first inquiry, I felt that understanding was shared well between the class, as they debated (argued?!) over which context was the most realistic.

In terms of practicalities, I had learned from the previous inquiry and so gave examples of which ‘card’ they might choose the first time round before asking them to decide (but I still haven’t created actual cards!) I found the management of a larger group a little stressful at times; at times it felt a little fake, as if I were saying ‘you decide the path of the inquiry’ but then making final decisions myself. This will be much easier when I feel comfortable running a more open inquiry, allowing different groups to take different paths.

Finally, after around 3 to 4 lessons of 40 minutes, they decided to ‘practice a procedure’ and I was able to set them the questions I’d planned! This inquiry did use quite a bit more class time than a traditional approach, so I won’t be able to do it too often.  Next step… how to choose the most appropriate topics for an inquiry?