Showing Progress in Fractions

One of the great things about teaching fractions to my Mathemateers group is that they knew pretty much nothing about them. This meant that whatever they learned would show oodles of progress – always good for impressing line managers.

(Not that it matters in this circumstance. I am the booster (remedial) teacher for the Year 6 group, therefore reporting to the Year 6 teacher who in turn reports to the Key Stage 2 Phase Leader. However I line manage both these people, so it’s less of a line and more of a circle…)

The assessment system we use showed that all the children in the group struggled with fractions. For example, Sarah‘s profile in ‘number’ looked like this:

Sarah's lowest 'ticks' were in Fractions
Sarah’s lowest ‘ticks’ were in Fractions. My school used the Incerts assessment system.

Of course when I asked Sarah some questions, it transpired that her prior assessment in fractions was, shall we say, over-ambitious, in that the assessment system said “she is developing the ability to use simple fractions that are several parts of a whole”, when actually she couldn’t do this question from ‘Recognizing Fractions 1‘ in the Khan Academy (which I have written about previously).

Most of the children couldn't do this question when we started.
Most of the children couldn’t do this question when we started.

 

Of course there’s the whole issue about performance and learning here. Sometimes children really do know something, but for whatever reason they don’t show it. This is performance. Performance variation is one of the main reasons for the difficulty in carrying out accurate assessment in education.

But for me as a teacher, this is great. I can now teach some stuff to the children and show great progress. And that’s what I did. Pretty soon the children had motored on to ‘Recognizing Fractions 2’ and even managed to do questions like this by the end of the first week.

By end of week 1 children could do this
By end of week 1 children could do this

No I’m not saying this is world-record teaching, but it does show progress. And what’s great is there’s an image, you can talk about it with the child and then the child has to write down the answer in fraction notation. It’s the perfect move from the Pictorial to the abstract. The downside, if you only use the Khan Academy is that children don’t write down what they did in their books and so their progress isn’t there for external visitors. And that’s not good if you’re a very book-scrutiny focused kind of school.

What would be great would be if we had already moved on to the New National Curriculum. However, as you well know, Year 6 are still working to the old curriculum. You see Incerts have just released their tracking system for the new curriculum and it looks fantastic. Here’s a picture of the ticks I could make about Sarah’s fraction learning:

What the new assessment for fractions looks like in Incerts.
What the new assessment for fractions looks like in Incerts.

However I can’t use that for my current group because they’re in Year 6. Nope. I’m going to have to cope with the learning that’s actually happened in the children’s brains and their SATs results in a few weeks time. Speaking of that, the final tool I’ve used to show progress is the Testbase tool that is a store of all the previous SATs questions. Sounds boring, but it’s really, really handy at the stage of the school year when teaching in Year 6.

 

What AfL is for

Rob Coe recently posted an interesting essay about how AfL might well be over-rated.

I broadly agree. And of course I’m in no position to argue against him – my experience only relates to the impact of AfL on 12 teachers in a small primary school of around 240 children. However, my experience of AfL has been really positive and I’ll explain why…

Everyone knows that there are only 4 things that improve teaching, and one of them is subject knowledge; the purpose of AfL is to increase subject knowledge.

Teachers have curriculum strengths and weaknesses – this is particularly apparent in the upper reaches of primary school, where the required qualification in English and maths for a teacher is a ‘C’ grade at GCSE. There are significant numbers of children at this level who may be working close to that level, hence the teacher’s subject knowledge may simply be not high enough to meet the needs of the students.

This is where AfL comes in. Assessing the children closely against rigorous banks of knowledge statements such as those found in the APP materials for English and maths, means the teacher discovers holes in their own subject knowledge – they find out what their students can do, they can see the next steps and they can determine whether they have the subject knowledge to teach those steps. At this point, if they don’t have the subject knowledge, it’s either time to panic, or seek help from their senior colleagues.

It is exactly at this point that things go wrong – senior colleagues (in other schools, I might add) are often keen to tick the AfL box rather than address the underlying problem. Unfortunately it is far easier to make things look like AfL is happening than to actually increase the subject knowledge in your staff – this involves a level of skill and compassion that is beyond many senior leaders in our education system. In this culture, rather than seeking the improvement they need, teachers who need to develop their own subject knowledge will develop all sorts of strategies to conceal it. In fact one of those strategies is writing the letters WALT and WILF on your whiteboard – a point that Professer Coe alludes to.

It is the culture of the school that makes a difference here. In my school we are all learners and my headteacher repeatedly reinforces a ‘no blame’ culture. Only yesterday, my year 6 teacher (whom I line manage) was teaching me what modal verbs are. Similarly we are all happy to educate each other so that we increase each other’s subject knowledge. We have found systems such as APP and Incerts (an online assessment system based on the old National Curriculum) really useful because they have helped us identify what we are good at teaching and which areas we still don’t know much about. We use them as assessment for learning, but really that means increasing our own subject knowledge so we can teach better.

What is Number Ninja?

The ultimate 'Number Ninja' badge. Nobody has achieved this level yet.
The ultimate ‘Number Ninja’ badge. Nobody has achieved this level yet.

Number Ninja is essentially an assessment system for maths that uses badges to reward children for making progress. It’s for children in the Primary age range from 5-11 years of age.

I had become frustrated with some of the maths assessment we were using at my school. I felt they were either too slow or too lenient and they didn’t reflect what I consider to be the golden triangle of maths achievement – understanding, pace and accuracy. For example we were using a ‘99 club’ – several iterations of this exist. It was a good system, demanding recall of multiplication facts and division facts. Each class would do the test once a term and the children would be rewarded with a certificate in an end-of-term assembly, with a class prize going to the class that had obtained the most certificates. However the one we were using allowed 10 minutes for each test, which was just too long for my liking.

We also use a system called Incerts which calculates a national curriculum level for each child based on the number of statements ticked. I find this system both convenient and accurate, but in my opinion the current National Curriculum under-rewards children for mental mathematics skills.

A second problem was inconsistency across the school. While we had two main whole school systems, teachers were using a range of assessment systems within their own classes that didn’t continue beyond that year group. For example some people were using the excellent mental maths assessment developed by Wigan LEA some years ago (get it while you can – this website is no longer supported). Other people used their own times table systems that they had borrowed from other places or created themselves.

What I wanted to do was create a wider system that demanded more from the children in terms of pace but still maintained a whole school rewards system in a big termly assembly – this is useful to keep a high profile for mathematics.

So I did 4 things:

  1. I kept Incerts and 99 Club – there’s no point throwing away good stuff if it’s already working.
  2. I developed a new mental maths assessment system called ‘Grid Club’. This is much more pacey than 99 Club.
  3. I introduced Khan Academy. While I’m not overly impressed with the instructional videos on Khan Academy, I do really like the assessment system that goes alongside it.
  4. I created a spreadsheet to collect all the scores from the different systems and calculate an overall Number Ninja score – this is what I use to award the badges.

Here’s an example of what the Number Ninja spreadsheet looks like. It’s from the Year 3 class. Teachers enter the numbers in the coloured columns and the number on the far right is what the spreadsheet generates. It is colour coded to tell you what ‘Number Ninja’ level the child is on.

Number Ninja spreadsheet
Here’s what the spreadsheet looks like

Any questions or suggestions about Number Ninja – I would be grateful to hear them!

Good Data: the inspection clincher

Wednesday 14th May was a particularly stunning day for myself. Not only did I finally teach a lesson good enough to be judged ‘outstanding’ by Ofsted, but the data that I produced also helped us do well in the inspection overall.

First, some context. Ofsted are the National body in the UK that inspects state-funded education. Recently (January 2012) a new inspection framework was produced that streamlined some 22 categories into only 4. Consequently, we had begun hearing some horror stories of many schools in our area moving down a category – it seemed it was harder to average out at the same grade you had previously been on. Ofsted judges schools in one of 4 ways: 1 – Outstanding, 2 – Good, 3 – Satisfactory and 4 – Inadequate.

Of course, our fears were that we would move down a category, losing our good status to take on that dreadful label – ‘satisfactory’. It was not to be. We came out as a ‘Good’ school and the report reads particularly well (I think).

So what of the data?

Well, we knew in our hearts that we do a good job for our children. The school is set in a part of Birmingham within the highest 20% of deprivation in the country. The children enter the school well below average and leave the school broadly in-line with national expectations, but how could we prove that in numbers?

It was a function and 3 Google Spreadsheets that came to the rescue.

I keep tracking sheets for reading, writing and mathematics for all students and looking at them, I could see that the children who we’ve taught for a while achieve better than those who’ve just joined us. In other words the children we teach, do well; we have a small but significant group of children who join us late and don’t make as much progress.

One of the data sheets that impressed the Ofsted inspectors

So I used my Google Spreadsheets to calculate a range of measures from current attainment in each subject, to the progress being made. The function that helped me the most was the ‘countif’ function  – I’d recommend finding out how it works if you don’t already – there’s guidance within both Excel and Google Docs.

I used the countif function to help me calculate 12 important numbers for each group – overall, boys, girls, SEND (special educational needs or disabled), FSM (free school meals) and higher achievers. This data showed that all groups who had been taught by us through the Key Stage 2 department (ages 7 to 11) were achieving at or above national expectations

In addition, a second sheet showed that in each year group, progress in reading, writing and maths was good or outstanding.

Sample of the progress data for each year group (if you’re a UK education data guru, you’ll understand what those numbers mean.

In all, I used the spreadsheets to calculate 363 separate numbers to demonstrate to Ofsted that we are still a good school.

I was helped in this process because we use an assessment system called Incerts, which fills up my spreadsheets with meaningful numbers from teacher’s assessments. Once we demonstrated that our monitoring of this assessment was effective by analysing current samples of teacher assessments in books, the inspection team were content to believe that our data did indeed demonstrate that we are doing a good job for our children.

And next time we’ll be ready to argue for ‘outstanding’.