I have mixed feelings about homework in primary school. As a teacher, setting, collecting, chasing up, marking and returning homework took up a lot of valuable time, and I wasn’t always sure it was entirely worth the time expended. However, most schools have a homework policy that stipulates setting at least one maths homework a week, so over the years I developed some ideas to make it as painless and productive as possible for me and the children.
Using online games
I’m always very keen for children to learn their number bonds and tables. The underlying conceptual understanding of these is vital, but at some stage sustained practice is needed. There are lots of online games that can help children to do this, not to mention apps that can be downloaded onto tablets and smart phones. Some schools buy into subscription sites like mathletics, but there are some very good free alternatives too like tutpup and sumdog. It’s possible to set up accounts on these sites as a teacher and track children’s progress so that if you set a homework of spending time on one of the sites, you can check it’s been done, or it may be sufficient to ask parents to sign a homework diary to confirm their child has done this. Of course, there will still be some children who don’t have ready access to the internet or access to tablets, but these days that’s often very few and it may be possible to accommodate these with a weekly homework club where they can use school devices, or give them an alternative homework.
Adopt a Shape
This was an idea I used when we were just about to embark on looking at 2D and 3D shapes. I gave each child a shape to ‘adopt’ – this gave me a chance to differentiate fairly easily by giving more familiar shapes to some of my less able children and challenging my higher ability children with less familiar shapes like icosahedrons. They were given the task of finding out as much as they could about the shape and presenting the information in any way they chose. I gave some suggested starting points, like finding the number of sides and corners etc. or finding the number of diagonals. The children really engaged with this idea and came up with some fantastic presentations, including 3D models in some cases. It made a fantastic starting point to our unit of work (not to mention filling up the working wall nicely!)
Write a worksheet
This was a task I used quite often when we’d spent some time looking at particular calculation methods. I would ask each child to write a worksheet for another child in their group. They had to include at least one worked example with an explanation of the ‘steps to success’. They also had to include some word problems and if possible give the worksheet a theme, possibly linked to our current class topic. Again, this was something the children usually responded well to. I would often give small prizes or stickers for the best ones and display these on the working wall and this appealed to the competitive streak in many children. Some would hand in beautifully illustrated sheets. Writing word problems to go with particular calculations really tests children’s understanding of that operation. A variation on this theme at the end of less calculation based units was to ask the children to make a poster to display their learning and be a learning resource for others. Again, this often produced some beautifully presented responses.
When beginning a unit of work on handling data, I would often start by recapping all the different ways the children already knew of presenting data. Depending on the age of the children, this might include tally charts, pictograms, bar charts, bar line graphs, line graphs, venn diagrams, carroll diagrams or pie charts. I might then ask them to collect as many examples as they could from newspapers, magazines or the internet and make a poster which they would annotate with explanations of what type of representation it was. For older children, I might also ask them to comment on whether that was a good representation and why that particular representation of the data had been used. This encouraged the children to notice how often data was presented in different ways in real life and start engaging with this.
Another data handling homework I would sometimes set in Years 5 or 6 was to give the children an opportunity to investigate something themselves. They were given a free choice of what to investigate and how they would collect the information. We spent some time discussing possibilities in class beforehand. They then had to collect the data and decide which was the best way of presenting the information. They also had to draw some conclusion from their data and lastly to reflect on their project and decide whether it was a true picture or whether their were factors which might have affected their results. This was a homework I set over 2 or 3 weeks, often over a half term holiday to give them time to plan and carry out their projects. I gave some helpful hints and prompt questions at the outset. This led to some really good work and some good discussion afterwards when the children shared their projects. One particularly memorable one was the boy who patiently recorded each visit to the toilet by each member of his family over a few days. Some definite trends emerged and the conclusions he drew were very entertaining!
Particularly when using measures, it can be good to set a homework which gets children using their newly learned skills in a practical context. So, for instance, homework could be to follow a recipe using metric units and record the result in some way (ideally be bringing in a sample of any particularly delicious results for the teacher to critique!) Or it might be to measure up a bedroom and plan an ideal lay out using furniture of given dimensions.
I hope this has given some new ideas to try. The beauty of many of these ideas is that they often take very little marking or can be used to stimulate discussion or as a learning resource in future lessons. They also tend to engage children much more than a traditional worksheet, and often get parents involved as well. Some can take a little planning to set – a bit more than photocopying a worksheet maybe, but I always make a point of keeping the prompt sheets etc and they can often be quickly adapted for a different age group or mathematical area.
As we move to the new primary maths curriculum, the old NC levels no longer apply but we are still waiting to find out what will replace them under the new assessment arrangements which have not yet been finalised.
I suspect many primary schools will continue to use the levels for the purposes of tracking children across the school or key stage. Whilst I agree that it’s important to track children’s progress in some way over time, over the last few years I have had increasing misgivings about the way the NC levels are used to do this. I feel there are several problems with this and I’d like to outline some of them here.
How we assess
QCA tests are commonly used to assess children at the end of a school year, and often at other points in the year as well. Others use other commercially published assessments. My problem with these is that in my experience, they are not reliable. As a maths leader, I got to know the year groups where we could expect rapid progress (according to the tests) and those where progress would be much slower and this often remained the same year on year, regardless of which teachers were in those year groups. As a class teacher, I got to know the tests that were likely to make my children look good and those that weren’t. I like to think that I bore this in mind in using my teacher judgement to moderate the results from the tests but see my later point about performance management.
To be fair, most schools don’t rely completely on test results and teacher judgement is used as well. The problem with this is that it takes a lot of experience to really know inside out what children ought to be able to do to achieve a particular level, let alone then knowing which sub-level to give. In theory, APP should have helped with this, but most systems are cumbersome to use and often wrongly used – just because I can find evidence in a child’s book that he or she has been adding 3 digit numbers, does not mean that they are secure in this.
Who does the assessment
In most cases, assessment is done by the class or group teacher. In theory, this is great. They are the person best placed to know what the child can really do, to be aware that a bad performance on a test is not typical, for example. They are in a position to see which aspects of maths children are secure on and which they need to revisit. However, in many cases, the progress of children in a teacher’s class or group contributes to their performance management targets, and now with performance related pay, the stakes are even higher. Added to this, in the current educational climate, is the ever present threat of capability procedures for those whose children’s progress dips. I do believe that most teachers try to act with integrity but the high stakes attached to progress but huge pressure on them to report optimistically. Unfortunately too, there are definitely teachers who knowingly play the system. In one school I worked in, a recently appointed class teacher discovered from his TA that the previous teacher had always gone over tests with the children just before they took them. The poor TA, herself fairly new, had assumed this was common practice!
The precision to which we track
When levels were first introduced, they were meant to give an overview of what should be expected of average children at certain stages. So the components of level 2 were those which an average 7 year old would be able to do. (Later these average expectations somehow became minimum expectations, but that’s a whole other blog!) However, this made tracking progress across key stages difficult because children would typically take 2 years to move up a whole level. So sub-levels were introduced and APS points. Many primary schools now use these APS points to track progress termly but levels were never intended to track progress at this level of precision. We simply can’t measure progress precisely in the way that we measure, say length precisely. There may be some justification for comparing the progress of different cohorts from the end of KS1 to the end of KS2 because at least here we are broadly speaking comparing progress with similar start and end points. But comparing how much progress one set of children have made in a single term of Year 2 against the progress another set of children have made in the same term in Year 3 is just not valid, in my opinion. When I was in Year 6, I knew that if children came up to me at the start of the year with a 3A, I had a fighting chance of getting them to level 5 by May, progress of at least 4 sub-levels. It would be very unusual for a Year 3 teacher to move a child at 1A at the start of the year to level 3 by the end of they year, and I would imagine it only happens very rarely. Yet, we make judgements about teachers based on comparing situations like this. From experience, I feel that level 2 is probably the level that takes the longest to move through. The jump from a 2C to a 3C in terms of conceptual understanding and skills is huge. Is it any wonder then that there is typically a dip in progress in Year 3 where the majority of children will be in the process of moving through level 2?
Life after Levels
I’m aware that I’m putting forward lots of problems about tracking progress using levels without really suggesting a solution. I’d suggest that any way of tracking progress term by term or even year by year is bound to be fraught with problems. Some have suggested that with the new curriculum we use a system similar to that currently used in Early Years, where children are judged to be Emerging, Expected or Exceeding the expected standards for each year group, but many of the problems outlined above would probably still apply. All I would urge is that any system of tracking progress using data is treated with great caution. The removal of the high stakes involved might also help teachers make more carefully considered judgements.
I’ve already blogged about some of my hopes and fears for the new curriculum here. In this blog, I want to think more particularly about introducing the curriculum to schools and suggest some useful resources.
It’s important to plan the change carefully and make sure teachers are well prepared. As the KS2 assessment arrangements don’t change until 2016, our current Years 3 and 4 will be the first to be assessed under the new curriculum at the end of KS2. The expectations for them in some areas will be higher and it may well be that schools choose to start teaching at least some of the new content this year so that there is less for these children to catch up in Years 5 and 6. This is particularly true in the areas of written calculations and fractions. Similarly in KS1, the tests and reporting arrangements will remain the same until 2016. This means that from September 2014, Years 2 and 6 should still continue to be taught using the current curriculum but all other year groups will need to move to the new curriculum.
Expectations for fluency with number facts and calculation methods will be raised and it may well be worth tackling this with some whole school initiatives. Some schools are choosing to give an extra 10-20 minutes each day to focus on this in particular, outside of the maths lesson, rather in the way that phonics is often taught discretely. For number bonds and tables, it would be well worth listing exactly which facts your school expects children to learn in each year group and sharing this with parents. It’s also worth tracking the facts that children know so that children who are falling behind in learning these can be given extra support. It would be good to discuss as a staff just what you all understand by ‘rapid recall’ of facts. You may find that some teachers feel children know their two times tables if they can chant the table, whereas others would expect them to be able to answer mixed 2 times tables questions, answering 20-30 or more in a minute. I have suggested some ideas and resources for teaching number facts and tables here.
The NCTM has a growing library of resources to support introducing the new curriculum. In particular, their Resource Tool could be a useful starting point. So far, only material for Years 5 and 6 have been added, but we are promised other year groups’ material before too long. For each year group, the content has been divided into several different strands. Selecting a particular strand and year group and choosing ‘Show Selection’ brings up the information below the tool. So for each of strand and year group, there is information on subject knowledge, connections (to content in other year groups, to other mathematical topics and to other subject areas), articles about good practice in teaching that strand, some suggested activities that could be used in teaching it, exemplification of the expectations and videos that support aspects of the strand.
The subject knowledge resources may be particularly useful for teachers in UKS2 where raised expectations may mean that they need a refresher in eg. calculating with fractions.
For more information about the new curriculum and some resources which might prove helpful when introducing it, my New Curriculum Pinterest board may be helpful. For subject leaders or senior leaders based in the Midlands, you may be interested in a course I am running next month on preparing for the new curriculum. I have lots of ideas and resources to share!
Like it or loathe it, the time is coming when it will be impossible to ignore the new curriculum (unless of course you teach in an academy). Year 6 will have another year to continue with the old curriculum but other year groups need to start teaching from it from next September.
I am currently taking the NCETM Professional Development Lead Support course (which I would so far highly recommend) and had my first residential training at the end of last week. In the main I found this somewhat reassuring. I am sure that Michael Gove had a heavy influence in determining much of the content and in particular the emphasis on the aim of fluency with recalling facts and using procedures, and generally higher expectations by the end of the primary years. Despite this, the three overarching aims are difficult to argue with, focusing on fluency, reasoning and problem solving. The NCETM approach is to emphasise that fluency can only be achieved, and should only be achieved by building on a foundation of good conceptual understanding. Their training and the training that we in turn will be passing onto schools explores the key role that representation and the use of concrete apparatus has in building up this conceptual understanding. They are also keen to encourage teachers to make connections between different mathematical ideas in their teaching.
My worry is about how well this message will be conveyed to schools. I have had two years of training as a Primary Maths Specialist, another year of work towards my masters in primary maths education, training as a Numbers Count teacher and have done lots of reading and research in addition to this. I understand the importance of representation and of making connections. I have seen the damage that can be done when children are moved too quickly to working with abstract mathematical procedures before they have been able to build up their conceptual understanding to support this. I have experienced those wonderful ‘light bulb’ moments with KS2 children who have fallen well behind and lost all confidence in their mathematical ability, but given the chance to step back a little and revisit concepts of place value or calculation using concrete apparatus, suddenly see how it works. Many of my colleagues however have not had these opportunities. I’ve learned so much from the high quality professional development I’ve received in the last few years and could probably fill at least a year’s worth of weekly staff meetings by sharing all of this.
In most schools, professional development time is very limited. Maths has to vie with many other subjects and priorities for staff meeting and Teacher day time. Courses can be expensive and require teachers to be covered which adds to the expense, and budgets are limited. In my opinion, however, it is good quality professional development which has the potential to make a huge difference to the quality of teaching and learning in schools. If even half the time and money which is currently spent on inspecting, monitoring, evaluating, tracking data and gathering evidence was spent instead on good quality CPD, I believe the impact would be incredible.
The introduction of the new curriculum could be a great opportunity for schools to revisit their teaching approaches, to ensure teachers are clear about progression and route ways, to explore the range of concrete apparatus and representations which will support conceptual understanding, to explore the links between different mathematical ideas and to share approaches and ideas. But this will require significant investment of time and money. I suspect, however that many schools will not find the resources to do this and instead the new curriculum will be presented as a list of requirements with the result that many teachers will feel under pressure to move children on too quickly, which could lead to even less conceptual understanding.
In his (always helpful) blog yesterday, Derek Haylock also made the very important point that the format of the new assessments (currently being developed) will have a great influence on what is actually taught in schools. Will these assess children’s understanding of underlying concepts, their ability to reason mathematically, their ability to apply their skills to problems? Or will they focus on assessing the children’s ability to use mathematical procedures fluently?
For more information about the new curriculum and some resources which might prove helpful when introducing it, my New Curriculum Pinterest board may be helpful.