Helping pupils work more neatly - Why is maths done on squared paper?

Update November 2013 - turns out that while students do appear to work more neatly on lined paper (purely a subjective view), they also seem to work much BIGGER. The result is them filling exercise books about 30% more quickly than they did with the squared paper (again a subjective generalisation, but noticeable across groups and the whole school). The neatness may improve but the basic quality of the work and hence the assumed quality of the learning is fairly similar. As a result we have just decided as a department to revert back to squared paper - mainly to slow down the consumption of books and the resulting growth in departmental spending! We'll just have to go back to policing the neatness...

Fairly short one this - bit of a work in progress actually, but showing good signs of positive effect...

Background
Standard practice in our school, and in every maths department I've ever seen in a UK school is to ask students to work in books with squared paper. this can be 5mm squared or 10mm squared, but it's always squared. We used 5mm squares.

However I often find that students struggle with this - the presence of the vertical lines seems to negate the horizontal ones in terms of organising their written work which can weave around all over the place. This is particularly true of weaker students or for students that struggle with presentation.

I thought about this for a while and it occurred to me that we only occasionally actually make use of the squares (drawing graphs, diagrams), otherwise the squares are a bit of a distraction for written work and note taking. We also have the issue that students often work more neatly when they draw a margin on the pages, but then we get into a battle of wills to insist that one is drawn (as it's impossible to buy a squared paper book with a printed margin).

On the other hand exam papers in the UK always give either completely blank space for working or a lined space. If a squared grid or graph paper is needed then it is explicitly printed into the papers. Similarly once you depart from the world of education it is very rare to come across squared paper unless you specifically need it.

So why do we persist with squared paper in classrooms?

I raised this in a department meeting and as a team we decided to stop with squared paper. As such our last delivery of exercise books was just lined, with a pre-printed margin (we've found they're also slightly cheaper than squared paper books - for those of you that are looking to shave down your departmental budgets!).

It's early days still - they're still rolling out across the department as students use up old books, however with about 30% of our students now on lined books the change does appear to be quite marked...

Students who used to scrawl all over the place on squared paper suddenly start writing on the lines (as they're trained to do in every other class where they need to write something down). This is purely a subjective thing, but the books with lined paper do look neater.

Speaking to students they much prefer to write on lined paper, and they say it's easier for them to organise their work.

What happens when they do need to draw a graph or need to use squared paper? the answer is obvious - We just give them a loose piece of squared or graph paper to stick into their lined book.

Is this purely about appearances?
Not really - it's about helping the students to make clear notes that they can understand, and can show their workings in a clear way.

Summary
1) The student's work is neater and more readable (so far this appears to apply across ability ranges and genders) - I've not got any pics to illustrate this but will try to grab some and update the post with them in due course.
2) The students say they prefer the lined books to work in
3) Lined paper matches the format given in exams and the likely paper available outside of the school environment
4) The lined books are cheaper

So why do so many maths classrooms persist with squares?

All thoughts welcome...

Giving summative tests formative impact

Not quite so directly related to managing variability this one, but it is a useful approach and it certainly does help if the whole department is doing it!

The problem
Summative tests such as the completion of mock exam papers just result in a grade. The grade is really useful for departmental level tracking, but the grade alone doesn't give the students an indication of what they need to do to improve.

This is the classic formative vs summative conflict that has been discussed at length in various forums - I'm certainly not the first to encounter this conflict. There is a wealth and breadth of work on this such as "Inside the black box" and other work of Dylan William, among many others.

So the challenge becomes to balance the need to do the summative tests to help predict grades and assess the performance of students, while at the same time making the result more meaningful than just a grade or level so that the students get something useful out of the tests as well.

The approach
I aimed to give the department and students a framework to help them diagnose where their performance  was strong or weak in a summative test so that it can be used in a formative way.

Perhaps it's due to my background but Excel came to the rescue again!

I created a sheet that allows student performance on each question or sub question on a test to be entered. (sheet is a bit clunky and may not be the most elegantly presented, but it works) This is a relatively coarse measure - full marks gets a green, some marks gets an amber, no marks gets a red - and it's subjectively assigned by the teacher (or possibly by the student). This can take a little time but data for a full class of 32 can normally be entered in less than 20 minutes once you get into the swing of it. Once filled in it looks like this... (I've chosen one with plenty of colour on it!)

Firstly this is quite a visual guide for the teacher. So in this example it is clear that Q5 & 16 were quite well completed but Q6, 11 and 13 were completely unsuccessful.

This can then be used to create summary graphs to help further analysis at a teacher level, like this...

However this still doesn't really give anything back to the students (useful for the teacher though). To make the leap to formative feedback the same sheet automatically creates a personalised feedback form for each student that looks like this:

The columns identifying "strong", "could improve" and "need to improve" correspond to the red, amber & green ratings on the first sheet.

Now this becomes more useful as it clarifies the topic, sub topic or specific skill that the student needs to work on. Note that the descriptions assigned to each question are teacher generated & editable to give whatever level of detail needed.

In follow up lessons the students can then be guided to tasks that will help them to fill in knowledge in their weaker areas. Additionally the teacher has a clear record of where skills lie or are missing both at class and pupil level, and therefore has guidance for future planning.

A further development of this general idea to give a greater emphasis on self assessment involves giving students time to review tests alongside a structure to help them to reflect and identify strengths and weaknesses. We use the following sheets as a template for the students to complete as a review, and then encourage them to identify 2 strengths and 2 weaknesses.

Depending on the group this sheet can be used alongside or instead of the red/amber/green one.

We've been using all of the above across Key Stages 3 and 4, and also in selected applications in Key Stage 5.

Other uses
I've also used the red/amber/green sheet to give feedback on written assignments and on presentations - the objectives & assessment criteria for the assignments can replace the question topics.

Nothing new
I'm fully aware that this isn't a massive innovation, many teachers review tests at a question by question level. What I'm not so sure of though is how many then use this information to form the basis of specific and personalised feedback to students.

I should also observe that I am aware that there are a great many schools where this type of thing isn't done at all for their summative testing, and as such they are missing an opportunity for some really useful feedback to both students and teachers.

The usefulness of these sheets and structures is in the fact that it is relatively easy to create good feedback that can be reflected and acted upon in follow up lessons.

Benefits - is it worthwhile?
This is one of many strategies we have been using in my department over the last 18 months.

At a basic level it has provoked useful and informed discussions with students about areas to improve. As well as being used for guidance in class, we have had students specifically take copies of these sheets home to use during independent study. Fundamentally the students like them and tell me and the department that they find them useful to shape their studies. If I saw no other benefit then this positive student message would be enough to encourage me that it was worthwhile. However we have a more tangible indication that the approach is working...

As part of a programme of regular mock exams with year 11 this feedback structure has allowed us to prepare almost the whole year group for early completion of their GCSEs in the March exams. Yes I know there are mixed views on early entry but our students were ready for these exams and the results they delivered prove this...

The results were published this week, and have already set a new school record for maths in terms of A*-C. Compared to other schools we scored 17% points higher than the average of similar schools with that exam board and 25%points higher than the average of all schools with them. With the remaining students completing exams in June, along with some students now looking to improve, we are likely to deliver in the region of a 5-10% improvement in headline results compared to last year.

I'll not claim that this feedback approach made all of the difference, but it was a contributing factor in amongst everything else.

Any thoughts?
I'd be keen to hear if anyone has another way to crack this nut, or if you have any comments or questions. Leave a comment or come and find me on twitter: @ListerKev.

Finding a common language - feedback and marking

My first post explained my aspiration for this blog but didn't really give an indication of how this managing variability thing can actually help in a classroom. Therefore I want to give a more clear example of what I'm talking about with this whole reducing variation thing...

The problem: Inconsistent Feedback and marking

Reviews of pupil's exercise books, "learning walks", and lesson observations highlighted that there was a wide range in the quality and quantity of written feedback and marking within the department. Some was little more than a tick and flick approach. Some had fairly detailed corrective work, but no other comments or targets. Some had extensive handwritten feedback.  It's fair to say we had the full range of practice, stretching from completely inadequate through to completely outstanding, and from clearly taking no time at all to a quantity of feedback so detailed that the time taken was significantly eating into the work/life balance of the teacher doing it.

A pupil voice

Critically as part of this - when pupils/students were asked, they basically didn't know what they needed to do to improve in mathematics. Vitally this included those with the really extensive comments that actually explicitly stated a recommendation or target for improvement. The written feedback even when it was there in quantity had simply not registered with them in a meaningful way. As a result they were also unable to converse about setting targets for themselves as they didn't have the vocabulary.

This would suggest that any time at all being spent on feedback was being wasted as the students weren't accessing it. Something had to change...

The goal: A common approach to feedback that captures the essence of the outstanding practice but maintains or reduced the overall workload of the department. In addition any changed process also has to improve the student's ability to recognise, access and act on the feedback - this isn't feedback for feedback's sake.

Obviously where next to no marking/feedback was being given then the workload for those involved needed to increase, since they were missing one of the basic requirements of being a decent teacher. However by giving a structure it gives this increase a clear focus and makes it easier to achieve. Those writing extensive feedback could actually afford to ease off a little if we provide a structure that captures all of their key points, and at the same time make the students more aware of it.

Establishing the essence of good feedback

Based on various models for feedback I came up with the following list of things that good feedback should include:

1. a strength that the student has shown in their recent work (acknowledge success)
2. an indication of the rate of the pupil's progress
3. an indication of whether the pupil is working at, above or below their target (we don't need to give them a grade or level, just whether they are on target)
4. an indication of how much effort we perceive that they are putting into their work
5. a clear target indicating how to improve

The bold in the last one is deliberate - as this then sets the scene for further use of this feedback. Critically we need to be able to come back to this target and review progress towards it over a reasonable period of time.

Lots of topics - how do we set meaningful targets?

A key issue with the way that maths tends to work, at least in the UK, is that we roll through topics fairly quickly, and as such a target set relating to the work just done could be meaningless if the next topic doesn't use that skill. For example setting a target for a student to work on knowledge of circle theorems is really hard to review and revisit if the next topic is related to histograms. Discussion with the department highlighted that this was a real blocker to setting good targets.

It became clear we needed some targets that work across mathematical topics (just as spelling, punctuation or sentence structure can be applied across all areas of English). What we aimed for were targets that help the students to become better mathematicians, not necessarily help them to master a specific aspect of maths.

In a department meeting we got together to come up with a list of targets by scribbling ideas on post-it notes and then filtering them down into a set of common themes, and trying to write them in a way that students can access. We now have a list of 15 numbered targets (note this is still a work in progress), all of which are intended to help the student to become a stronger mathematician. We're still working on these 15 but it's a great start.

Improving visibility to learners
With a good list of targets we needed to fix the visibility issue. Based on some initial trials students gave more attention to feedback when it was both clearly labelled as feedback and also when they knew there was a particular thing to look for. Having gone through some development we have created a sheet that can be filled in electronically from a set of drop down menus for each student. We then print this out on coloured paper to help it stand out in their books. (the electronic basis also gives us a clear and lasting record of the feedback given). Students are given the sheets and asked to stick them into the book, and then comment on them. An example of the output is shown below.

As you can see, by filling in this sheet the feedback instantly meets all 5 of the requirements I laid out for good feedback. Clearly we will always have the question of whether the teacher has selected beneficial targets or been accurate in assessments, however the structure makes it substantially easier to do this in a matter of seconds following a review of the students work. Vitally it is MUCH faster than hand writing all of this detail.

The aim is to do this for every student at least once per half term, with self assessment of progress towards these targets between times.

Pupil views
Having tried this across a range of classes and discussed it with students it is noticeable that those in receipt of these feedback slips are:

1. Substantially more aware that they have received feedback - they will rapidly flip to their most recent slip and are able to discuss it in terms of what they need to do to improve, and what they have done in recent lessons to help this.
2. The quality of discussion about feedback is substantially higher as the consistent targets is equipping them with a reliable vocabulary to use.
3. Through a common language students are better able to set targets for themselves and others as part of self and peer assessment. Groups have been setting their own targets from our list of 15 and then the teacher is just checking that they have chosen appropriate ones.

Staff views
I'll acknowledge not all were sold initially, however the whole department is now using this approach and we are seeing the benefits spread. It's not an overnight thing, but the clear benefits from pupil voice makes it worth it. The more embedded this gets the stronger it will become.

We are now much more able to remind students about the key thing they need to work on (e.g. "Brian, can you remind me what your target to improve is?" followed by "Can you show me where you've met this in your recent work?" is really powerful), and it is having a noticeable effect on the quality of learning conversations that are occurring in classes.

Departmental view
At a whole department level a recent book survey showed evidence in all books of good quality feedback, with meaningful targets set and referred to (a world away from where we were at the start of this process).  Many are starting to show evidence of early targets being met and new ones being set. It is clear that the students are responding more and more to these targets, both in written comments and also in the quality of the work done.

What's next?
This actually feels like the key to unlocking a whole range of improvements. By establishing a common language for teachers and students to use in terms of how to improve we are opening the door to more detailed and higher quality discussion with students about how they are learning.

Key next steps include final iterations of the targets and some work on developing the strengths to a similar level. We will keep reviewing the use of this and keep talking to the students about it. Simply having these little slips in student books is making a big difference to their perceptions of progress and how to improve - the future will look to build on this.

Thoughts welcome
So this is what I'm getting at with managing variability. We have put a system in place where it is substantially easier for the whole department to give good quality feedback, and thereby reduced the variability across the department.

Do you have any examples of similar initiatives? Could this help your department? Do you have any questions? - leave a comment as you need.

First post - getting started...

Please forgive the slightly tentative start on this - my first ever post on my first ever blog!
In this first post I'd like to set out the reasons for starting this blog and some initial thoughts - hence it's a bit wordier than I may have liked!

What's this all about?
My intention is that this blog will be aimed at exploring thoughts related to managing variability in teaching, due to my subject bias I will naturally focus on maths, but I would hope it is also relevant to other areas, and may also relate outside of teaching.

What's the agenda?
I have no hidden agenda, this is not party political and all thoughts expressed here are my own and not aligned to any particular organisation. For this reason I am not identifying the school I work at. I am undertaking this for my own personal interest, as part of reflecting on my day to day work, and in the hope that there may be others out there who may like to share their thoughts on these topics.

Who am I and why am I writing this?
As some background I initially trained and worked an engineer, and later as an engineering project manager in the car industry for at total of 10 years before re-training as a maths teacher. The car industry is one of the most closely scrutinised arenas for processes and quality improvements, with much of the modern understanding of Quality Management having originated in this sector. During my teacher training, and since qualifying as a teacher I have worked in a total of 4 schools, spanning a range of different intakes and levels of achievement. I am currently a head of maths at a large mixed comprehensive. As part of this I am involved in seeking to improve maths results for the school, increase uptake of maths and further maths at A-level and generally encourage a deep interest in the subject.

To date I have discovered a wide range of blogging and networking/twitter activity linked to the development and sharing of personal practice in maths and other subjects, which is excellent. I am also aware of activity at a senior leadership level, looking at whole school issues. However it strikes me that there is a relative lack of input from middle leadership/heads of department considering how to improve at a departmental level.

My personal view, shaped by my background, is that the key to departmental improvement is the reduction in variability of practice. Once practice becomes more consistent it is easier to ensure good performance.

So why do I think managing variability is so important?
In the UK we are in a bit of a state of flux with changes coming from the government and Ofsted, all with the central intention of "improving standards". Unfortunately what I personally feel is lacking is a good understanding of why "standards" are not at an acceptable level and exactly what an "improvement" would look like.

My suggestion is that standards themselves may not be the issue. Aspects of good and outstanding practice are happening every school day, in every school in the country. The issue we have is that in those same schools there are also examples of poor practice, possibly in the classroom next door with a very similar group and the same access to resources. Critically I don't subscribe to the view that this is simply because the outstanding practitioners are working harder or are more passionate about their classes; I've yet to meet a teacher that doesn't work as hard as they can to do the best they can.

So if factors like the teacher's work ethic, school setting, the type of student, the curriculum being followed and the range of resources available are all the same then how can we explain wide differences in the effectiveness of classroom practice within a school? Similarly how can you explain a wide variation in school "performance" across the country? We could follow a suggestion that outstanding practice is down to something less tangible like teacher personality, but the engineer in me would prefer to think of that as "noise" introduced into the system by the fact that humans work within it.

In other sectors where human factors have an influence on the end result there are actions taken to reduce this. For example on the best production lines the design is set up so that human error can't creep in, or in an aeroplane there are checklists for the pilots to follow.

Please don't think I'm proposing extra procedures or processes though! That's not what I'm about at all. In engineering the ideal way to reduce variation caused by human factors is to set things up to make doing the right process the easiest thing to do, so that it takes more effort and therefore a conscious decision to follow an incorrect or less effective process. Therefore my aspiration as a head of department is to first to identify best practice, and then to find ways of making that practice the easiest thing for the whole of my team to do, not just the exceptional practitioners.

I'm also keen to point out that I don't think that there is a one size fits all recipe for outstanding practice, however I do firmly believe that by having the right structures and guidance in place it is possible to open the door to good to outstanding teaching for the vast majority of teachers.

As I explore this in this blog I plan to consider various aspects of teaching & learning and how this can be developed to reduce variability and therefore improve performance. Much of this is work in progress for me and my department, sometimes it may be a matter of clear guidance, other times it needs some work to create structures to help. In many cases I've not yet found the solution but am working towards it.

Topics for future posts are evolving, but initial ones that spring to mind are:

• Marking & Feedback
• Structures for lesson planning
• Encouraging good standards of work from pupils
• Assessment & moderation
• Strategic uses of seating plans
• Departmental homework strategies
• Departmental communications

There will be more topics that raise their heads as time goes on, however in the mean time I'd be interested if you have any thoughts or suggestions relating to this post or the topics mentioned above...