Marking is Planning

We are about to start the next cycle of Teaching and Learning Communities at my school. Each community or group is looking at a different aspect of teaching and will help inform the future policy and practice around that area by carrying out small scale action research projects. They are mostly based around what we believe are the non-negotiables of a lesson (learning intentions, differentiation, questioning, AFL for in lesson intervention and plenaries), alongside two broader topics, namely Progress over Time and Marking is Planning. It is this last one that I’m facilitating and that I want to explore a bit.

I first came across the phrase in a post from David Didau – I think he coined it – and it hangs on the premise that marking to which students respond not only informs you and the student but also plans a chunk or entirety of a lesson. David talks about Dedicated Improvement and Reflection (DIRT) wherein students work on individually assigned and focussed questions and tasks. This helps reduce the problem of feedback that is never acted on by students, gives meaningful differentiation for every student in our classes and reduces the time involved in the feedback loop.

Most of the bloggers that have explored this are teachers of written subjects and for them the individually assigned task can be about redrafting based on feedback. I’m not sure that works in the same way in Maths – redo this problem based on my feedback? Maybe sometimes. Mostly though, I think it is about giving a directed, probing question that helps push my students thinking further and that begins a dialogue over time. There must be time built into lessons for students to respond to this feedback otherwise I have wasted time for no meaningful reason.

Possible ideas to support marking

Over the past few years, we have tried various methods to make our marking more effective. Some of these are great for certain topics and some don’t work as well for others. The marking needs to be speedy and, a concept I read about on this blog, needs to follow the x10 rule – it needs to produce a task for students that should take at least 10 times the amount of time I took to mark it.

Highlighter

I love my highlighter, almost as much as I love my post-its. Graphs, calculations, constructions … highlight errors and have students identify and correct them. This could be the scales on an axis or a sign error in a calculation. If it is repeated error then you could do one worked example and highlight the other occasions this error crops up. Having students to write what the error was and how they can avoid doing it in future has been really powerful for my students.

Probing Questions

While my department never really bought into APP as a way to continually assess our students – at least in so far as the A3 grids and tracking was concerned – the collections of probing questions are invaluable in my marking. I collect the ones on the unit we’ve been working on at the start of the unit and then when I’m marking use these as prompts to set a probing question for the student. I want a probing question to explore the thinking behind a concept, to address a misconception or to drill down to an issue that needs to be addressed. I want a student to have to think about it – it shouldn’t be something they can answer off pat – and it should be something that helps them move their understanding forward.

Screen cast

If there is an issue that I’m seeing appearing in several books then I start to think about other ways to help support these students. One method I have found working well is a screen cast. I simply use my iPad to talk and write my way through a problem, explaining my thinking and reasoning, asking questions and pausing. I aim to make the videos 2 minutes or less. The students then watch these as homework and then error spot some sample work or try some examples themselves.

I’m always searching for feedback and marking strategies that minimize on my workload while maximising on student engagement and progress.

Are there any corkers I’m missing?

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What-if-not – how to extend any problem, no matter how closed

download

I’ve been continuing my summer holiday reading in between, you know, having a holiday. The Art of Problem Posing is a book I’ve been dipping in and out off since it was recommended to me by Andrew Blair over at http://www.inquirymaths.co.uk and I finally got round to finishing it. The first edition was published in 1983 (the year I was born!) and it is still relevant and useful to my classroom today. This is a really readable book that presents a good model for posing problems both for teachers and students. It has lots of places to stop and engage meaningful with the content and, even though I probably skipped over those bits too much, these really helped to make the points more meaningful.

I was going to summarise and review the book but instead I thought I’d focus on the big take-away that I am going to be using a lot. I think I was already doing this but it is definitely going to feature more and more in my practise – namely, what-if-not.

What if hoax

When we solve problems, our first stage is to accept the problem as given – find the area of the triangle, discover the connection between Pythagorean’ triples, etc – and solve it. We can use the habits of mind and toolkit that we have developed (will blog on this but I think John has done a much better job than I will over here). But, what happens then? Or what if we can’t get started?

Well, we could think about what made that problem up (it was about the geometry of a triangle or it was a list of numbers where a connection seemed to exist) and start to play with it. We can extend any problem by asking the what-if-not question. What if it wasn’t a triangle but a square? What if one of the sides was curved? What if we were interested in perimeter instead of area? What if there wasn’t an obvious perpendicular height? How many other triangles will have the same area? What if the numbers were surds? Immediately, a whole vista of Mathematics opens up and any problem that was quite closed can become open and rich. We can either make the problem smaller and more manageable or larger and more all encompassing.

The book then looks at a couple of examples in detail and details some action of problem-solvers at work.

I’m going to make a poster of what-if-not (that I’ll share here) and encourage students to think about ways we could alter a problem – adding it to the toolkit. This could work really well as a plenary or extension with students of all abilities as we encourage Mathematical thinking. I think it could also help broaden the depth of questions I get from Inquiry lessons – what if something from the prompt wasn’t true or was different? If we are thinking about students having agency and ownership of the Mathematics being taught, I like helping them recognise that any problem that I present to them is one I have found to be interesting and useful but it is not sacrosanct. This could be another way to encourage students to engage Mathematically.

But then again, what if I didn’t do that?

 

Image from http://www.transitionnetwork.org/stories/mandy-meikle/2012-09/if-not-transition-then-wat

Annual observations – good or bad?

So, last Friday I had my annual senior management observation.  I’m due to pass into UPS2 in September and my current Head feels that she should observe all people at threshold points.  I think that is a pretty good policy and I  think I’d want to do the same if the positions were reversed.

I hadn’t been observed for 14 months and as it got closer to the date of the observation I started to have a real crisis of confidence.  I have been observed regularly by student teachers, teaching assistants, prospective teachers, trainee social workers and the students I teach – but none of them were there to give me feedback on what I was doing.  I don’t know where it came from but as the observation got closer I started to panic and decided there was nothing I wanted to do more than leave teaching and train to be a farmer.

I put in the hours of planning, thought and rethought ideas, came up with lesson sequences and developed enough material for a unit of work, never mind an hour long lesson.  Finally, I committed to a lesson plan and sent it to the Head.  Then I thought I started to calm down but my body seemed to have a different idea because I kept waking up in the middle of the night.

The observation went well and the Head was very complementary but given how much time and energy I spent thinking about it, I’d have been disappointed if it hadn’t gone so well!  And that’s the point … how useful are these annual observations?

My school is currently thinking about informal and more regular observations.  Will this decrease the stress?  Or will it make it last all year?  I know I’m not doing it for the people who come to watch but for the kids who are in my care day in and day out.  At the same time, I want to show the best of what I can do, that’s what is being judged after all.  It’s often said it is a game but it is one I find myself playing even when I don’t fully agree with it.

Please don’t get me wrong, I like being observed, I like feedback, I like the process of growing and developing as a teacher – I don’t like the feeling of insecurity and lack of confidence when it comes to a ‘big’ observation.

We are due to have a visit from our friends at Ofsted – somehow that feels similar, though the no notice inspections are supposed to help that I guess.  I’m not sure it does.

I think supportive and regular observations of teaching is good.  I don’t think I’d have been nearly as worried if it had been less than 14 months than I’d had a member of the senior team in my classroom.  I like the idea of more regular observations as long as it comes with feedback.

What do you think?  Regular informal observations or irregular formal observations?  Is this a game we have to play?  Am I just being an idiot?  Should I get more feedback from the students I teach?

Overwhelmed but optimistic

INSET day today – weird to go back on a Friday and then have a weekend before anything meaningful happens.  Today was a lot of meetings and a little bit of preparation.  I really thought I was on top of things but the nature of the beast changes when you are actually in your classroom, I find.  Suddenly I’m being distracted by the 101 things I need to do and I find it hard to focus on the important.  Overwhelmed was how I felt but with an underlying sense of optimism!

The school updated the website and is relaunching it.  It doesn’t seem that much different to what was there before but they have installed Moodle alongside it.  This is great – noone else is really using it but I’m setting it up for all of my classes.  I’ve used Moodle before but forgotten lots, so looking for ways for it to help with the learning and assessment of my classes.

For now, I’m going to enjoy the weekend and look forward to teaching some students on Monday.  Normality, here we come!

What role does a teacher have now ideas are dead?

In his NY Times Op-Ed piece yesterday, Neal Gabler asserted that ideas are dead.  He believes that we don’t care as much about ideas as we used to.

In effect, we are living in an increasingly post-idea world — a world in which big, thought-provoking ideas that can’t instantly be monetized are of so little intrinsic value that fewer people are generating them and fewer outlets are disseminating them, the Internet notwithstanding.

I think I mostly agree with the tone of this piece.  There does seem to be a decline in thinking deeply, reason and logic seem to be falling on hard times.  Gabler reckons that science

is typically regarded in the media as mystifying at best, incomprehensible at worst.

This made me think about the role of the teacher in this.  Is it our job to provide contact with these big ideas?  To help our students see the value of thinking about information rather than just collecting it.  It is not a popular tune, not something that is seen valuable by many people at all, but that doesn’t make it unimportant.

Which brings me to show-and-tell.  Dan Meyer made me think about the value of showing students media which exists beyond my content area.  Of letting them see a Rube Goldberg machine and dealing with the comments like, ‘they have no life’ or ‘too much time on their hands’.  Of seeing that putting effort into a project just because it is cool isn’t time lost – that there will be benefits that mightn’t be obvious.  Dan says:

It’s so obvious to me that the kind of person who would create a cocktail-mixer from balsa wood and twine is simply blowing off steam that life will eventually focus in a direction that will be extremely a) constructive, b) profitable, or c) both. I can’t make this obvious to my students.

So, in this wasteland of ideas, I think we need to excite our students with ideas – big and small – and encourage them to think.  Encourage them to use their time well – following, developing, nurturing their interests.  While teachers are still excited by ideas this might be possible.  There exists a scarier possible future, one in which teachers get bored by ideas.

Let’s hope we don’t get to that point and help our new teachers see the value of ideas, even as we show our students.  I’m going to be using a show-to-tell model in my classroom – how about you?

It wasn’t like this in my day …

Sometimes it is embarrassing admitting that I teach Maths.  I’ll be at a party, my job will come up in conversation and then people will tell me about how much they hated/loved Maths – how they are terrible/great at it.  Sometimes, that is where the conversation will move on to more interesting things and I’ll sigh with relieve.  But, every once in a while, I’ll be treated to the erudite insights that my new friend has to share on the nature of the educational system and the failings of kids these days.

What I always find uncomfortable about these conversations is the subject of expertise.  After all, everyone has been a student for at least 13 years, surely everyone has a valid opinion about what makes a good school, a good teacher and a good set of qualifications.  Well, I’m not sure I agree.  I’ve trained to do this job, I’m studying for my MA and I work on engaging and enthusing 200 students a week – maybe my opinion should carry a bit more weight in this conversation?

I’m still digesting Carol Vorderman’s report and I’ll likely be posting about it for a while.  I was really interested to see that some things never change:

Employers and their organisations also complain about the low level of mathematical competence of their new employees and now many hold numeracy courses in mathematics to allow them to ‘catch up’. p4

This is the same reasoning that was given for the commissioning of Cockcroft in 1983.  Maybe things were better some mystical day in the past or maybe, just maybe, the raising of the leaving age of compulsory education is of importance here.

We have had four different qualification systems since the Second World War:

1) School Certificate

2) O Level

3) O Level and CSE

4) GCSE

The report talks about each of these and points out that none of the systems worked for every student or every employer.

Major problems have been associated with all of them.

There never was a Golden Age. There have been times when we have met the needs of our more able children at the age of 16, but we have never had a satisfactory provision for the whole cohort. p51

I think this is really sad.  We do need to be designing curricula and qualifications that are engaging and relevant to all of our students.  I agree we can’t continue to watch 300,000 students a year be classed as ‘failures’ when they don’t achieve a C grade at GCSE.  We need appropriate and worthwhile qualifications that allow for success and progress in a meaningful way that employers will respect and take on board.  Why should the foundation curriculum be a cut down version of the higher?

nor is it good enough for the system to gear itself to them [the top 15%] and for everyone else to receive a trickled down version of their requirements. p3

We need a better system.  I want to be part of that.

In the past, end-users [students] and teachers had much greater influence over school mathematics and we advocate a return to that situation. p5

Bring it on!

Maths Curriculum Design in the UK (England in particular)

When the National Curriculum was published there was much furor the impact this might have the individual classrooms around England.  Teachers were furious to be forced to teach a given set of topics, in a given order and to be have to use the level descriptors imposed from outside.

[Update: Adam points out I made a mistake here.  While the NC set out things that needed to be taught, it wasn’t until the introduction of the National Numeracy Strategy that order was felt to be imposed.  Of course, this was non-statutory but often wasn’t treated as such.]

That was long before I joined the teaching profession.  I’m about to start my 7th year as a qualified Maths teacher.  All my career I have worked in the state sector, working in different roles in 4 different schools.  All of those have used the Sample Medium Term plans from the National Numeracy Strategy as the basis of their schemes of work.  There was some tweaking and developing, but the underlying structure was the same.

With the ongoing curriculum review and the assurances from Whitehall that teachers are going to have more autonomy, I’m worried – are we ready for it?

In the recent report, “A world class mathematics education for all our young people”, this comment is made:

In this country we have a long tradition of successful innovation in curriculum and pedagogy, particularly in mathematics, science and technology. This has come almost entirely from the grass roots, from individual teachers, small groups or charitable organisations, and has often been done on a shoestring. By contrast, many large government initiatives have not been particularly successful but have cost a lot of money. p24

In my experience, this long tradition was largely suspended with the advent of the National Strategies.  There is still work going on (Bowland and Nuffield come to mind) but this is only brought into most classrooms when it fits neatly into the pre-existing schema.  I agree with the report when it says:

There has been a culture of policies which are non-statutory being almost universally viewed as obligatory by teachers and schools, due to the government agencies’ reliance on them for their tick-box style of assessment. This has not helped the mathematical education of children. p8

With the dismantling of the strategies and the support that has provided for years being removed, I’m concerned we aren’t ready to take on the challenges of developing innovative curricula in our own departments.  I’m not convinced that the spiral delivery of the Sample Medium Term (SMT) plans has been effective but equally I don’t know how many teachers of my generation have been equipped to be able to design something better.  While I welcome the opportunity to unfurl our wings and allow innovation back into the development and design of the mathematics curricula on a local and institutional level, I fear the supports are being removed too soon and that rather than innovating we are at risk of stagnating.

Am I wrong?  Is your department already using an innovative curricula that bears little resemblance to the SMT plans? Is the spiral curriculum a keeper?

Blog archives – catching up with conversations past

Have you ever moved to a new city, started a new job, joined a new club or class and found you were the new person in a friendship group.  I’m part of a small church in Brighton and, being such a transient city, people come and go all the time.  For those of us who have been around for years, conversations often contain references to people who others have never met.  It is hard to remember and often cumbersome to fill in the gaps, watching the moment or joke slip away.

I’ve felt a bit like that as I approach the “edu blogosphere”.  It seems not many educators in the UK blog about education, so it has been awesome for me to find some inspiration on other parts of the globe.  Blogs like dy/dan, Think Thank Thunk, Point of Inflection, f(t), etc. are all really inspiring but for each of these I’ve come late to the game.  The conversation started a long time ago and I feel like I’m missing the in-jokes.

Strangely, this isn’t the end of the story though.  The wonders of archives mean that I can go right back to the start and follow the conversation up to the present.  I can follow the development of a blogger in terms of thought processes, pedagogical philosophy, etc.  I can watch as more people comment and take part in the conversation, itching to join in but knowing for most people the moment has passed.  I can see people come and go, competitions be set and the winners be declared.

I’m currently working my way through the dy/dan archives – having read everything up to April 2009.  I’m enjoying it lots but am confident I’ll enjoy it more when I can join and engage with a present conversation.  It is strange to be thinking about the current events that are reflected, thinking about where I was and what I was doing while this conversation was happening the first time round.  I don’t want to live in the past but I do want to inform my present with lessons from the past.  I’ve come across loads of conversations that have helped develop my thinking that probably will not come up again on this forum because it has been dealt with.  So, I read on.

Has anyone else ever done this?  Am I more of a freak than I think I am?

Brain Rules – John Medina

I’ve really enjoyed reading Medina’s book. I bought it three years ago, started a difficult job and put it down having only read a few pages. Picking it back up to engage with and think about has been really helpful.

Summer is that time in which lots of teachers move into dry-dock and tweak those obviously failings, reflect on what worked and what didn’t. Other colleagues forget entirely about the classroom and don’t think about school again until Sept 1st. What has been interesting this summer for me, is that I have been excited to keep the learning going, supported by Twitter, my Google reader, my to-do list and my notepad.  Another sign that the bailing of water has stopped, the storm has stopped and the refit of the teaching boat can continue unabated.

In his book, Medina sets out 12 rules that he derives from recent advances in neuroscience and fully supports all of his claims with peer-reviewed research.

The links this makes with everything I’m thinking about – assessment, the importance of the visual, the resetting of the ‘ten minute’ attention window – is great.  A real sense of everything being connected.  When I think about my learning as a teacher I see lots of important parallels.  I don’t learn well when under continual social stress, I don’t learn well when I don’t sleep or exercise enough and so on.  Medina gives some suggestions for further research and ways his findings might be implemented in the workplace and school.  As I think about how these findings might change my living and working, reflecting on how I can use this information to help my students then I feel the book I’ve read has been worthwhile.

Highly recommended.

Interesting New York Times Article

Interesting article about whether training teachers or paying them more is the best way to go.

Some interesting points about MKT (Mathematical Knowledge for Teaching) – evidently teachers who score higher on this knowledge achieve better results [see Deborah Ball]. Evidently, no closet to knowing how to ‘teach’ this knowledge though, so just another measure to see whether the teachers you already have are able to do their jobs effectively.