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Understanding students’ ideas

June 7, 2016 Leave a comment

I read a really interesting article today entitled “Teachers’ evolving understanding of their students’ mathematical ideas during and after classroom problem solving” by L.B. Warner and R.Y. Schorr. It is a great report that looks at three teacher’s responses to their students’ solutions to a problem, and it discusses in detail how the teachers reflected on them together. It is well worth a read for all maths teachers.

The teachers were middle school maths teacher and they were presented with a problem to solve by the researchers they then presented their classes with the problem and debriefed afterwards. It was clear that the teachers didn’t have the thorough subject knowledge of a high school maths specialist and this lead to them failing to pick up some misconceptions and not allowing students to explore their own methods if they didn’t understand it, rather moving them on to a method that was more familiar to the teacher. The reflections of the teachers are interesting, they all appear to become frustrated with themselves when analysing their responses and are able to reflect on this by offering alternatives. It does show that deeper subject knowledge is important to allow that exploration to take place. The study showed that in this context when the teachers just told students how to fix their mistakes, rather than question students as to why they had made them, this led to student confusion. This suggests that we should be striving to understand our students thinking whenever possible and using that to combat their misconceptions so they don’t fall into similar traps again. This will also allow students to see why they are coming up with these misconceptions.

There are many teachers who, at times, fail to understand the lines of mathematical thinking taken by their students when solving problems. This can lead to not giving the proper amount of credit to valid ideas and it can lead to teachers failing to spot misconceptions. Some students may have a perfectly valid method but as the teacher may not see where they are going they can sometimes block this route off. This has deep links to “Flowery math: a case for heterodiscoursia in mathematics problems solving in recognition of students’ authorial agency” by K. von Duyke and E Matusov , which I read recently (you can read my reflections here). I feel that it shows that deep subject knowledge is important, as is allowing students time and space to work through the problem on their own. Rather than saying, “No, do it this way” we should, be encouraging students to follow their nose, as it were, and see if they can get anywhere with it. It is always possible to show the students the more concise method when they have arrived at the answer to bui8ld their skill set.

Warner and Schorr believe that subject content, as well as pedagogical content is vitally important to teachers to enable than to know how to proceed when a student is attempting a problem. They look at relevant literature on this and quote Jacobs, Philip and Lamb (2010) who suggest that this is something that can be achieved over time and Schoenfield (2011) who says that teachers tend to be more focussed on students being engaged in mathematics and replicating the solutions of the teacher rather than allowing students to meander their own way through so the teacher scan identify their understanding and misconceptions. The latter would, in my opinion, be a much better way of developing, and I agree with JPL that this is a skill one can develop over time.

References

Jacobs, V. R., Lamb, L. L. C., and Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, pp 169–202.

Schoenfeld, A. H. (2011). Toward Professional Development for Teachers Grounded in a Theory of Teachers’ Decision Making. ZDM, The International Journal of Mathematics Education, 43 pp 457–469.

Von Duyke, K. and Matasov, E. (2015). Flowery math: a case for heterodiscoursia in mathematics problems solving in recognition of students’ authorial agency. Pedagogies: An International Journal. 11:1. pp 1-21

Warner, L.B. and Schorr, R.Y. (2014). Teachers’ evolving understanding of their students’ mathematical ideas during and after classroom problem solvin. Proceedings of the 7th International Conference of Education, Research and Innovation, Seville, Spain, pp 669-677.

On-the-fly

February 6, 2016 4 comments

The best laid schemes o’ mice an’ men, Gang aft agley – R. Burns

There are many reasons that a lesson goes awry, and being able to deal with that is key. During teacher training a lot of weight is put on planning, pikes of lesson plans are produced by student teachers and often they are very helpful and certainly aid development and allow us to consider the subject we are teaching, consider the questions we need to ask and what exactly we want our students to take away. But the heavy emphasis on planning can make some teachers too reluctant to deviate from said plans.

I remember during my NQT year being told about hinge questions and how I should include them in every lesson, a deputy head said I could come to his y11 class and see how he used them, but I was left underwhelmed as the result wasn’t any different to how the lesson would have been without it. He just had a “hinge question” in the middle and carried on regardless. Hinge questions are useful, but only if you then have 2 separate paths for the students to take.

Similarly starters that check prior knowledge are good, they’re useful for filling in gaps and they can aid a lesson,  but you need to be ready to change your plans on the fly if needs be.

This week I had a lesson planned on cones and spheres, some of the questions towards the end of the lesson included cylinders and prisms as well as spheres, cones, pyramids and frustums, so I set a couple of cylinder and prisms questions in the starter. I was met with blank faces. Totally blank. I hadn’t taught them this before, but I had assumed they had met them in previous years, but they hadn’t  (or at least if they had they’d lost their memory of it). At this point I jettisoned my plan and started over.

I talked through some examples, explaining how they had got it and then set them off on some tasks I had saved on my hard drive while circulating to check the understanding. It was an enjoyable lesson and the students now have a good grasp of cylinders and prisms, plus I have the added bonus of one less lesson to plan next week now.

It can be terrifying when this becomes necessary. During my NQT year we lost all the power from sockets in the school – the lights were still on but the smart boards were unuseable. When they went off I was 5 minutes in to a year 10 lesson on constructions with a class who had a reputation as the worst in the school. It was my first time being without the presentation I’d planned and my first time teaching construction. I did my best to demo on the boards, then set them doing simple constructions while circulating and teaching the more complex ones. It was a success, but it was a terrifying ordeal.

Being able to adapt on the fly is key, and it’s something we need to prepare new and trainee teachers for. I’ve had thoughts about how to do this, but nothing concrete. One idea is to have them “wing it” occasionally- ie show up to a lesson every so often unprepared. Do you have any ideas on how we can help prepare for the times when we need to act on the fly.

Future Education Policy?

April 2, 2015 5 comments

So it’s that time again and we’re well and truly into Election season. Paxman has given Dave and Ed a good going over on C4, we’ve had the election debate and the nation is (I hope) deep in thought about which way they want to go. I’m waiting with baited breath for the manifestos so I can really get to grips with their policies. So far, we haven’t got manifestos, but the labour party have released a pamphlet entitled “Changing Britain Together“, which sets out some key themes which came out of the national policy forum last autumn and which will be in the manifesto.

These are what they believe to be the key facts on education:

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And here are some of the things they want to change:

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So what do you think?

Well let’s take a look, first up we have:

Guarantee all teachers in state schools are qualified

This is something I’ve argued for before. I can understand the argument that someone who is an expert in their field and wants to teach it should be allowed, but teaching isn’t that easy. You need strategies to deal with the classroom climate, you need pedagogical ideas on how to pass on your knowledge and you need to know what’s on the curriculum in your subject. These are (or should be) dealt with within teacher training. I don’t necessarily mean experts should have to go away and complete a qualification, the could do it on the job such as salaried schools direct or teach first etc.

Require teachers to continue building skills and subject knowledge with more high quality training and new career paths

This is a great priority to have. We all need to continually develop our practice. We need to reflect on what we’re doing and improve upon it. Subject knowledge is key, the Sutton Trust Report “What makes great teaching?” told us that the most important thing you improve outcomes for students was teachers having a strong pedagogical subject knowledge. This is particularly important at the moment as we are moving to new curricula across the board, new GCSEs, A levels, all subjects, all key stages. We need to ensure we are sharp on all the content to ensure the best outcomes for our learners.

Ensure schools are locally accountable with new local Director of School Standards responsible for intervening in underperfoming schools.

I’m not too sure about this one. On the face of it it looks good. It looks like there will be a safeguard to ensure all children are receiving a good education, but what will trigger the intervention? And what will that intervention be? These are two massive questions that I don’t know the answer to, so I can’t really comment further. I guess we’ll need to wait for the manifesto.

End the flawed free schools programme and instead prioritise new schools in areas with a shortage of places

This one makes me laugh a little at the ridiculousness of the free schools programme. Money is being spent on mew schools in areas where the existing schools are not fully subscribed, yet areas which are oversubscribed are still in need of new schools. Surely it’s common sense to ensure that schools are being built where they are needed?!

4 promises, the first two would, if done well, make great strides towards improving education for all. The final one is so common sense it seems daft it even needs mentioning, but unfortunately it does, and the third is one I need to know more about. What are your views on these 4 promises? I’d love to hear them.

This is based on the bit specifically on schools policy, the leaflet is 52 pages long and covers all policy areas so do have a read, and make sure you read the manifestos when they come out. And for goodness sake, don’t forget to exercise your democratic right on may 7th and vote, apathy and disenfranchisement are what breaks democracy.

Trying to be a better maths teacher

January 17, 2015 1 comment

Recently the excellent Mark Miller (@GoldfishBowlMM) has written a couple of posts around trying to improve as a teacher. In the first one he spoke about the importance of subject specific pedagogy, and how departments an see excellent results if they give over time to developing together. In the second he wrote about how he’s developed his teaching by striving to become a better English teacher and the subject specific ideas that have helped him.

Ironically, I read the post and saw many links to mathematics teaching and how these ideas can help us all improve in our own subjects! But the idea that focused, subject specific CPD is the future is one I’m totally on board with. I remember as an ITE trainee sitting through a lecture on Bloom’s Taxonomy where all the examples were history and English. I saw the examples and how they might make a difference in those subjects, but I couldn’t see at all how they would relate to maths. It wasn’t until a long time later and a discussion with my NQT mentor that I finally realised.

Subject specific pedagogy

Robin Alexander wrote in 2010 that he feels the key to improving teaching is to get teachers talking about pedagogy, and I’d certainly agree with that. I feel that there is plenty to discuss in general, but that subject specific pedagogy discussion is even more important. So get involved! Get involved online, read blogs, comment, write your own (use WordPress!) and engage with Twitter. There are thousands of maths teachers all over the world waiting to exchange ideas. But also get involved within your department. Share your ideas with your colleagues and ask them what they think, ask how they approach those subjects and try to get the discussions started.

Engage with the subject

I keep my mathematical abilities sharp, I engage with puzzles, I read around my subject and I discussed maths with others. I do these things because I enjoy them, but I feel that they have made me better as a maths teacher.

There are many books you can read, apps and websites you can get involved with and puzzles you can try. They are fun and helpful.

Try things out, within reason

I often try new approaches in lessons, whether it be a new activity I’ve seen or heard about, or another method or a new pedagogical approach. I think when trying these things it’s important to remember that things aren’t always importable. Something that works for me in my setting may not work for you in yours, but it’s worth trying out and then refining if necessary. I’d also say if something fails once, that doesn’t mean it isn’t worth trying again, with a different class.

I put within reason as it can be tempting to try everything, and if you try too much all at once it all gets lost within each other and you can’t pick out the impact for anything you’ve tried.

Mark with a notebook and/or A camera

Whether you’re marking books, homeworks or exam papers, have something with you to make notes with. If there’s a misconception that keeps cropping up, make a note or take a snap. You need to address it in the next lesson. I also like to show examples of great work too.

These are a few of the things I do, on a regular basis, that I feel help me improve. I hope they have given you some ideas. If you have other points to add, please use the comments.

Time, Collaboration and CPD

January 8, 2015 4 comments

Collaboration, it’s been on my mind a lot recently. Partly because it’s the focus of my current masters assignment, and partly because it keeps coming up in conversation with various people. It’s a complex word, with many degrees of meaning attached, and something we all do, but possibly not enough.

I’ve read a lot of literature for my assignment, and there are some key themes that keep cropping up.

Talking pedagogy

Many of the articles I read, not least West (1998), expressed views on the importance of getting teachers talking about pedagogy. Discussing approaches to lessons, discussing questioning styles and discussing resources. Alexander (2008) even went as far as saying that it was, in his view, the most important thing we can do to improve teaching.

I often engage in these discussions with colleagues, both within school, those in other schools and now with the explosion of teacher social networking teachers from across the world. I feel this has been a great part of my improvement as a classroom teacher, and hope to continue.

TIME

The Sutton Trust Report (Coe et all 2014) spoke about lesson study in Japan and the impact it had on driving improvements in Teaching and learning, picking out the collaborative aspects of it, and the time built on for shared reflection, as being a major part of it. This ties into the ideas from West and Alexander I mentioned earlier.

This seems particular relevant to me at the moment as I keep seeing letters from MPs in response to the recent NUT lobbying programme about workload. The stock response seems to be that Nicky Morgan and her department are working to reduce bureaucracy and free up time for “what really matters in the classroom: teaching and learning.” on the face of it this seems a good thing, but I worry that it might be missing the point. Teachers in the most high performing countries (according to PISA) have considerable less time teaching and learning, and significantly more time for planning, marking and professional development. And I feel this is they key. Often in the UK teachers are supported through their NQT year and then that’s it, no CPD to speak of except the odd death by PowerPoint, unless they go on a weekend of course! Workload can be high and they can then shy away from the sort if collaboration and pedagogical discussion that may actually improve their teaching and save them time in the long run. I recently re-read this from John Tomsett who mentioned this nice quote from Dylan Wiliam:

“Every teacher needs to improve, not because they are not good enough, but because they can be even better.”

We all do strive to improve, but sometimes it is hard to find the time. I recently spoke to a teacher who expressed irritation that he’d not been able to observe others to help improve his practice for a long time, and another who hasn’t been offered the opportunity to go on any subject specific CPD for a long time.

Worldwide collaboration

There was a recent issue of Forum entitled “Teachers reclaiming teaching”. This issue had many articles written by bloggers, some I was familiar with and some I wasn’t. The main focus of the issue was the benefits of this new world staffroom that we all have access to. I personally find it fascinating and helpful, but I know a lot of teachers have neither the time, nor inclination, to really get involved with that. I think it’s a shame, but it wouldn’t matter too much if we were all having these discussions anyway, as it would only take one person to bring in an idea. The ideas you gain from elsewhere may not work in your context, but thru may. Being able to have discussions about pedagogy with your colleagues is means you can share opinions on things from outside and whether they can work in your context. If you’ve tried and it doesn’t, then you can discuss why.

As Bob Hoskins used to say, “It’s good to talk.” but in the words of Paul Heaton we “need a little time.”

References

Forum (2014) Volume 56 number 2 Teachers Reclaiming Teaching

Alexander. R. (2008) Education for All, The quality imperative and the problem of pedagogy IOE London

Coe, R. Aliosi, C. Higgins, S. And Major L. (2014) What makes great teaching? Review of the underpinning research. Sutton Trust.

West, M. (1998) Quality in schools: developing a model for school improvement. International handbook of educational change. Kluwer: Dordrecht

Northern Rocks

June 7, 2014 4 comments

Today was the “Northern Rocks: Reclaiming Pedagogy” event at Leeds Met Headingley Campus, #Nrocks.

The event was organised by Emma Ann Hardy (@emmaannhardy) and Debra Kidd (@debrakidd), and like Nten-researched-york,  had a mass of fantastic speakers running workshops. So much so I had terrible trouble selecting some of the workshops, and I cannot wait to catch some of those I missed online! (I believe they were all taped and will be available).

The event started with a panel discussion, chaired by event host Debra Dimbleby. The panel was: Mick Waters, a professor and former Chief Education Officer; Ian Mearns MP for Gateshead (@IanMearnsMP); Dominic Cummings, former policy advisor for Gove; Kevin Courtney (@cyclingkev) of the NUT; Richard Gardner of the Independent and Dot Lepkowska another journalist. The discussion was at times really interesting and focused around Ofsted, Policy and Performance Related Pay.

Some of my favourite soundbites:

“We need to stop dancing to Ofsteds tune”- Mick Waters

“Hey ministers, leave them teachers alone”- Richard Garner

Then the surprising: “This WILL be the last national curriculum” – Dominic Cummings

Professor Robert Coe (@Profcoe)

For the first workshop I chose to see Prof Coe, the theme was research and he looked at various strands of research and it’s findings. He also loomed at the impact in schools, and the impact he’d like to see. He covered a lot in the time and I left the session with a long list of further reading I’m looking forward to getting into when I find some time.

Tom Sherrington (@headguruteacher)

The second session I attended was by Tom Sherrington and was in the CPD strand of the programme. I am a regular reader of Tom’s blog, and I often finish reading them wondering if Chelmsford (now Highbury) are commutable! (they aren’t.)

This session was no different, and left me firm in the knowledge that Tom would be an amazing person to work for. He spoke of his distain at lesson grading and performance related pay, “PRP is a legal requirement, so we pretend to have it!” and his commitment to staff development and research informed CPD. If Tait Coles if the king of “Punk Learning” then Tom is the king of “Punk Headteaching”, with his attitude to PRP and the fact he has extra INSET days “because we felt they’d be beneficial, and no one has said we can’t.”

Tom’s presentation included some fantastic examples of the research based initiatives going on at KEGS and how they shared them. He’s written previously on the subject here.

He spoke of creating a professional culture in the school where staff are striving to develop and are thoroughly engaged in driving their own CPD.

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He also spoke of getting the basics right. Talking about the progressive vs traditionalist debate he quipped that there’s no point arguing about the benefits, or not, of thinking hats if the behaviour is stopping the class from learning.

On the traditional progressive debate, he referred to it as a symbiotic relationship, like a tree, believing parts from both to be important.

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You can see Tom’s presentation, complete with links to relevant blog posts, here.

Tait Coles (@totallywired77)

Next up was the Punk Learner himself, who welcomed us into the room with The Fall’s “Hit the north”.

When browsing the programme I saw that Tait’s session was around inequality in education, and as this is something extremely close to my heart I opted for this session over a few others in the timeslot I would also have liked to see.

Tait’s presentation was almost like a call to arms. Setting out his feelings around the inequality in the system and why he feels the system is broken. A lot of the things he mentioned are things I’m currently investigating for a masters assignment and I picked up some good references.

The session itself was enjoyable and thought provoking l, and I intend to write more on it later. It included my favourite quote of the day: “I don’t want you to think like me, I just want you to think!”

The questions section at the end was also brilliant and included a lively debate on cultural capital and the role of schools. I have plenty to say on that too, but that’s another post for another day.

John Tomsett (@johntomsett)

For the final workshop I chose John Tomsett. There were many others I would have loved to see in this slot, but John is another of my favourite bloggers, having seen him do the keynote at Nten-researched-york I was worried it might be the sane talk, but the title was such that it seemed different, and it was.

John’s session was, in many ways, similar to Tom Sherrington’s. They both left me feeling that they would be great to work for, that their schools would be great to work in, that CPD and PM should be highly personalised, non-judgemental and intrinsically linked. They both mentioned they had more than average INSET days, and that they cared about creating a growth culture for staff and students alike.

John then spoke about his own teaching. He expressed his strong view that the headteacher in a school should be the HEAD teacher in that school. He then showed some videos he’d used to identify and improve his own teaching. Showing that even experienced heads can grow.

He spoke deeply, openly and honestly about his own journey, gave me a ton of books I now need to read and got me excited about his own book!

He shared this quote from Saracens Rfc:

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Sharing the Saracens philosophy, which is to get the best players, develop them and keep them happy. He applies this philosophy to Huntingdon and sees similar rewards.

Hywel Roberts (@HYWEL_ROBERTS) and Mike Waters

The final session was led by Hywel Roberts and Mike Waters. They spoke about the 4 key themes of the day: Policy, Pedagogy, Professional Development and Research. Their session was funny, thought provoking and entertaining, and included opportunities to discuss the day with others.

Mick left us with a final, poignant, thought for the day: “The only thing consistent about Ofsted Inspections is their inconsistency. The judgement will depend in the assertiveness of the headteacher and the lead inspector.”

All in all, the day was fantastic. I thoroughly enjoyed it and have gathered knew info and ideas which will help in the classroom, in my studies and in the future. This write up has been done without my notes, so apologies if I’ve confused anything. This is just my views as they stand. There are many strands of discussion from today I hope to discuss further in future blogs.

Engaging with research

May 20, 2014 3 comments

I’ve had a number of conversations today that have got me thinking about educational research, Ofsted guidance, and how they are, or worryingly often aren’t, linked to what’s actually going on in schools.

During one conversation with a PGCE student I was informed about certain practices which were heavily integrated into the CPD offer at her previous placement school which have now been totally debunked. This led the conversation down a windy path. We discussed lots of things but the crux of it was centered around how this could have happened.

The reasoning isn’t necessarily fully correct, but we hypothesised that this could happen when people leave their own learning behind once they qualify. The possibility is that people can be trained in whatever is deemed good practice at the time, but without continued learning and engagement with research and policy they don’t necessarily know when the world moves on.

In another conversation a colleague of mine seemed shocked that I was writing an essay, and when I told him that a few of the books were great and would be worth his investment he suggested that that takes one hell of a commitment to education. I took this as a compliment, and thinking about it later it struck me that it does take one hell of a commitment to education, and only a handful of staff at the school would have such a commitment.

Is it any wonder, then, that despite Ofsted changing tack in line with the most up to date research some schools are still working from an old playbook? Many schools are still grading lessons, I even know of some where grading and judgement are attached to a constant programme of learning walks. This is despite of the fact that all evidence points towards a developmental process of lesson observations being far more productive and beneficial to the teachers.

I feel lucky to be in a school that has stopped grading observations, and where learning walks are fed back to the entire school as a “we saw this good practice” style report. It would seem that this is not commonplace elsewhere.

In some schools, it would seem that management have little interest in the research and as such are working from massively outdated ideas. We need to work on ensuring the profession is moving forward, that we are developing new staff as best we can, that we are learning from our mistakes and learning from the research. This means engaging with it, and questioning it where appropriate, as David Weston (@informed_edu) and Tom Bennett (@tombennett71) suggested in York. When we have engaged and questioned, then we can apply it to our own context and each improve our own practice.

How can we do this?

At ResearchEd York John Tomsett (@johntomsett) mentioned that at his school he has appointed Alex Quigley (@huntingenglish) “Director of Research”, this sounds like a fantastic role, and shows how seriously this is taken at Huntingdon. Perhaps more schools would benefit from such a role.

Tom Sherrington (@headguruteacher) tells us in this post that he sees the development of a research based CPD programme as a major priority as he starts a new headship, which shows how committed he is to this vision.

Shaun Allinson (@shaun_allinson) runs a “blog of the week” for his school, to engage staff with the Blogosphere, this is a way into the research and could be beneficial for all.

These are a few excellent examples, but I fear they are in the minority. I think, though, that above all, the burning issue is time. 3 hours isn’t enough time to “Plan, Prepare and Assess” for up to 27 lessons. The majority of teachers work 55-60 hour weeks as it is and would baulk at any additional “work”. It’s not impossible to engage with it on a full timetable, I do it and I know others who do and benefit from it, but to get buy in from everyone on top of such vast workloads is unlikely.

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