Jamie Frost @ Mr Barton’s Podcast

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.

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Explicit Instruction

Three months into my foray into the world of blogging / twitter, I realise that my choice of handle 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.

Aspirin for a Headache?

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?!

 

Flippin’ Heck

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 blog title suggests, 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!

Inquiry 2

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?

DIY Homework

Virtually all of my teaching ideas are stolen, but I think I came up with this one myself last summer.  Maybe that’s a bad sign.  I’d love to hear from others who have tried something similar…

It’s not exactly complicated: students choose their own homework.  Obviously they require some guidance. Click here for the document I show the students outlining my advice.  The basic structure:

  1. Students must choose questions which they can check the answers for (so I’m expecting that they’ll mostly work from the textbook, which has answers at the back – and this has turned out to be the case)
  2. I suggest a minimum of 90 minutes per week for most of my classes, rather than a specific number of questions.
  3. Students should try to challenge themselves, and find questions with which they struggle.  If they’re doing the final few (most difficult) questions from each exercise fully correctly, that’s fine, but otherwise I expect to see mistakes and (attempted) corrections, with questions for me if they can’t get to the correct answer.

I should point out that this is not very different to my usual expectations for homework.  I have always asked students to check their own answers, so that I can focus my time on helping with the problems with which they’ve struggled.

What Went Well

The quantity of work done has impressed me – normally more than I would have set. I obviously can’t tell if a student has actually spent 90 minutes but in general, I think they have done so and many have done much more.

There has been much better differentiation in the difficulty of problems tackled: some students have tackled drill problems from the starts of exercises, others more varied problems from the harder end, and some have extended themselves with Olympiad or university entrance exams.

There has also been differentiation of the topics covered: students have spent different amounts of time on different topics, according to their needs. Some students have also varied the topic they’re working on, and worked on topics covered some time ago, giving them a chance to constantly revise.  I continue to encourage all to do this.

It has encouraged greater reflection and independence: I’ve seen more evidence than before of students learning from their mistakes, and many have engaged in very useful written dialogue with me, asking specific questions about how to tackle a particular problem and letting me know exactly what they don’t understand.

Even Better If

As I discovered in my end of term report, some students have found it difficult to choose questions and hence haven’t enjoyed the freedom as a result. I feel that this issue will diminish as they get more used to the approach. I do suggest a set of questions on each topic during classwork, so if they really don’t want to use initiative, they don’t have to!

A couple of students wanted to be more frequently in a situation where they weren’t able to look up the answers, so that they are forced to check their work more carefully. This is a fair criticism and so I’ll balance DIY homework with occasional ‘assessment homework’ next term.

It is taking me a little longer than previously to give written feedback, as I have to look through a variety of different topics and often have to find the relevant questions for my reference. I don’t mind this too much as I have enjoyed the process of engaging with my students more than writing repetitive comments on a set of near-identical work.

I’ve been keeping a record of which questions each pupil has struggled with, and so far not many have been good at returning to these questions in future homework. I need to continue to encourage them to do so, and this term I’m going to set up a shared spreadsheet to check their progress on them.

Overall

It was probably a bit much to go for this approach with all my sixth form homework this term: when I have a new idea, I do tend to go for it in quite a big way!

However, I do feel that the WWW’s outweigh the EBI’s and so I will continue to use it for at least half of sixth form homework time, probably more.

I’d love to hear from anyone else who has tried something similar and has suggestions on how to make it more effective.

My End of Term Report

I’ve used surveys before. This is the first time I’ve written up the results publicly; I’m hoping that it will help me remember the key points. I’ve decided to present the data, a selection of comments and my responses for each questions I asked.

You can see the original survey here

Inevitably when you ask formative questions, it can feel as if the feedback is quite negative, and I have had to remind myself that most of the data is positive!

Mr Pearce’s lessons have been _________ other lessons.

much more interesting than 5%
more interesting than 41%
similar to 36%
less interesting than 16%
much less interesting than 2%
More field trips please! The difficult extension questions are really interesting – could we go through the answers more often.
More practice of exam style questions. Less time spent proving and understanding why things work. – This sentiment was repeated by 2 others.
Maybe more interaction like going up to the board and doing this interactive
More math-robics please! It makes me concentrate on the task at hand.
More really generic examples we can look back to for if we are stuck

I phrased the question as being ‘relative to other lessons’ because it was the best way I could think to make it meaningful.  I teach in a very good school with outstanding colleagues so I’m surprised that it came out positive on average.  There is probably a ‘being nice to the teacher’ effect – I imagine that all lessons would be more interesting than average.

My y10 class suggested more interactivity – my recent inquiry lessons would have been an excellent opportunity to do this: I could have asked pupils to present their contexts for the time-graphs on the board, rather than writing them up myself.  I’ll try to be more alert for such opportunities.  I’m glad they have enjoyed my math-robics, it’s a nice way to break up a double lesson in the afternoon, but I don’t think I’ll be using it any more regularly!

Three sixth form students would like more exam practice in place of “understanding why things work” – I’m dubious about whether this will really make lessons more interesting?! I think they answered the substitute question: “what do you want me to do differently?” which I’ll come back to later.  A suggestion of ‘more generic examples’ is similar.

The request for more time spent on ‘difficult extension questions’ comes from a mixed class with some incredibly high achieving pupils – as much as I’d love to spend more time discussing the STEP problems I’ve been offering as extensions, I don’t think that this would be a good thing to do with the whole class, as these questions are not suitable for others.

I feel ___________ comfortable to work hard and make mistakes in Mr Pearce’s classes than in other lessons

much more 8%
more 38%
similarly 49%
less 5%
much less 0%
you react in a friendly manner and i do not feel pressured to get it right and therefore i try to work without the teachers aid and only call him over to check my answers or when i am totally stuck and my partner is too
Mr Pearce allows us to be open in class & is a much better teacher than my previous maths teacher!
Good class atmosphere – feels like more of a discussion.
Should be allowed to ask for help more
Again, the fact that the lessons generally are aimed towards the top 3-5 in the class. Fear I may seem stupid asking some questions

Generally quite positive, which I’m sort of surprised about, as my friends often joke that I’m far too harshly critical to be a teacher – I’m glad to see this doesn’t come through too strongly!

Even so, two people are unhappy: One of my y12 pupils thinks that the lessons are aimed towards the top end of the class, so I must make sure I’m differentiating more carefully.  The other doesn’t feel that they can ask for help, which worries me slightly: my classes are generally small so I always have lots of time to help.  I guess I should keep repeating pleas for pupils to ask and targeting particularly quiet ones.

The balance between independently working things out for myself and Mr Pearce telling me how to solve problems has been…

much too teacher-led 0%
too teacher-led 0%
about right 71%
too independent 27%
much too independent 2%
Often the maths is not fully explained, so I get stuck. Making notes on a topic with explanations of how to solve different kinds of problems would also be very useful
Too much time focusing on derivation of equations etc not enough making sure they are securely in our head and that we have an understanding of their applications
I don’t think the methods are sufficiently discussed in class, as generally we cover them too quickly (or not enough questions) and then I am not completely confident in the method.
Sometimes I feel like it takes me too long to work things out for myself and by the time I do we have completely moved on to a different topic.
When I am stuck, a lot of the time I don’t know how to continue

As the author of a blog called ‘discovery maths’ it’s not surprising to see that no pupils think that my lessons are too teacher-led. I also teach in a relatively traditional school, which makes my teaching stand out more than in my previous job, and so I feel that 71% of pupils saying that my balance is ‘about-right’ is quite surprising.

There are clearly a significant minority of pupils who are not comfortable with my approach, so I need to tone it down a little, with certain classes in particular. I agree that there are definitely certain topics where I need to provide more/better guidance. Similarly, sometimes I should move the class more quickly to generalise, allowing more time for application of rules. Finding the right balance in these two areas in one of my major aims as a teacher and I’m constantly trying to improve my decision making and target it more appropriately for individuals and classes. Next term I’m going to try to provide more back-up guidance, such as ‘gap fill’ worksheets for pupils who are stuck when trying to generalise.

Additional, I will try to sometimes offer alternative options to pupils who are particularly set against discovery, such as studying examples in their textbook. I also need to make sure I always conclude the process of discovery with a summary and example: I think I currently do this 95% of the time but apparently not often enough.  I’m also trying to make my notes clearer by typing them (now that I’m quite fast on equation editor!) and ensuring I include discussion notes/annotation as well as just the mathematical process.

Finally, not knowing how to continue when stuck is a common problem and one I should definitely try to address. Several years I had a big push towards instilling some of the problem solving strategies from Thinking Mathematically, but I need to constantly remind myself to bring these ideas into classes every time I teach a new class.

Mr Pearce’s written feedback is helpful.

Strongly agree 18%
Agree 77%
Disagree 5%
Strongly disagree 0%
Sometimes set your own questions so there is no way of checking that the answer is correct before submitting it, so it enforces rigorous checking of the work beforehand.
A much more formal prep structure would be helpful to gain an accurate assessment of how we’re doing periodically.
I find it hard to identify which questions to do so would appreciate if more specific ones were recommended
Please could you send us the solutions to the extension problems set the week before.
It would help if you gave a worked solution for a question that i struggled on.

I had a new idea in August, so as usual went with it wholeheartedly: allowing sixth form pupils to choose their own homework.

Generally I think it has been effective. Most pupils have targeted their work carefully to tackle their weaknesses. There has been much better differentiation in the difficulty of problems tackled. It has encouraged greater reflection and independence: I’ve seen more evidence than before of pupils learning from their mistakes, and many pupils have engaged in very useful written dialogue with me. The quantity of work done has impressed me – normally more than I would have set. In fact, the only negative from my point of view is that it is taking me longer to give written feedback!

However, some pupils clearly aren’t enjoying it! One pupil doesn’t feel that they can choose appropriate questions so I need to spend longer explaining how to do so. (I’ve already dedicated a fair amount of time to this and I do give a suggested list of questions for each topic so I’m surprised, though it’s useful to know).

A more legitimate concern is that a couple of pupils don’t feel they are getting a sense for their progress. Personally, I’ve never found homework to be a particularly useful summative assessment tool: the variety of effort exerted and assistance sought means it rarely gives a fair impression of a pupil’s understanding. Instead, I use it formatively and set fairly substantial tests in class to get an idea of progress. Next term, I’m going to set more regular mini-tests (inspired by Colleen Young) which should hopefully address this.

Another good point was that a pupil wanted to be in a position where they couldn’t look up the answers, in order to enforce them checking their work more carefully.  I can see the advantages of this, especially as we get closer to exams, so I’ll set one or two assessment homeworks later this term.

Two other comments request written solutions to problems. I’d rather not give these out directly, as educational research and personal experience tells me that they won’t help pupils to remember ideas in the long term. However, I must remind my pupils that if my hints / solution starters are not helpful enough, they must ask me in class (or on the next homework) for further assistance.

Wow – this ended up being quite long, so I summarised the main points here.