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.
Last week’s #mathscpdchat focused on what we could do to support less mathematically able children. It’s an important issue for teachers. Poor numeracy skills put children at a definite disadvantage in life as outlined by National Numeracy here.
In my experience of teaching less able children, I have often found that one of the main problems is that they have been moved onto abstract methods and thinking too quickly, before they have really got a strong sense of number and good mental images to support their understanding. Pressure to prepare children for assessments contributes to this, but we need to be aware that if we move children on too quickly, we are often trying to build understanding on very shaky foundations and sooner or later the cracks will show.
In last Tuesday’s discussion, we agreed that building up basic number sense was essential. Ideally, this starts to happen in Early Years Settings and KS1 with lots of use of concrete apparatus and representation, but in KS2 and beyond, the use of manipulatives and images remains an important tool in building up understanding. The CRA approach to building understanding is a good one to bear in mind. We start with Concrete apparatus, move to Representation when children are more confident and finally to Abstract when children have a firm grasp of what is happening, linking each step to the previous one.
I’ve found ten frames and Numicon particularly useful for helping children to build their number sense, but Cuisenaire, multilink and Base ten equipment can all be helpful too. Another way of building this is by regular use of dot talks in the lower years of primary and number talks at higher levels. In dot talks, children are presented with a pattern of dots and asked to work on their own to calculate how many dots there are in all. Then the class or group discuss the different ways they worked this out. This helps children to see different ways of breaking up numbers. Number talks work similarly. Children are given a calculation and initially work on their own to solve it. Then the class discusses the different approaches. Again this helps children see that there can be multiple approaches to the same problem and that no one way is the ‘right’ way. They may also start to see connections between the different approaches.
@School-LN reminded us of the importance of making connections, and suggested an interesting way of helping children to do this. Children are given sets of numbers, shapes or bar charts, for instance, and asked to sort them into groups and then explain their choices. For less able children, maths can seem to be a lot of disconnected facts and procedures that they have to learn, but if we can help them to make connections, they start to realise that there is much less to learn than they feared. @PGCE_Maths suggested the report ‘Deep Learning in Mathematics’ which is well worth reading and argues the case for focusing on connections and relationships in maths rather than technical procedures.
@Janettww had some experience of using 3 act maths lessons, where students devise their own questions before attempting the maths and has found it very motivating for students at all levels of ability. This seems to be something that could really promote mathematical thinking.
@bm332 also raised the important issue of classroom climate. Many students really lack confidence and it’s important that they feel able to speak up when they don’t know or don’t understand something; @Maths4ukplc also pointed out that mistakes need to be valued as learning opportunities.
So altogether, lots of food for thought and lots of good ideas. The complete record of the discussion can be found on the NCETM site here and I’ve also put together a pinterest board which includes some of the resources mentioned together with some other ideas.
At the start of the school year, teachers tend to give a lot of thought to how they will make a positive start to the year with their classes: establishing new routines, setting up an attractive and supportive classroom environment, building relationships with children. All of these help to set the tone for the year ahead.
In each new maths lesson, we have the opportunity right at the start of the lesson to set the tone for the whole lesson by the way we start it. There was a very useful and interesting discussion about lesson starters on twitter yesterday evening on the NCETM initiated #mathscpdchat. Lots of different ideas and resources were shared but all agreed that making a positive start to the lesson was crucial. I’m a great believer in having something ready for the children to do as soon as the lesson starts. That way, children get the message that we’re here to work and make the most of every second of lesson time. The actual content of the starter will very much depend on what we are using it for.
Why have a starter activity?
In the discussion yesterday, someone made the very good point that we don’t have to have a starter at all. Sometimes it might be appropriate to move straight into the content of the lesson – finishing off work from the last lesson or starting to explore an open ended challenge that will last for the whole lesson time, for instance. However, I’d guess that mostly teachers will want to have a starter for most lessons and so, before we reach for our tried and tested bank of staple activities, we need to ask ourselves just what the starter is for. There are a number of very valid reasons for using a starter activity and we need to choose an activity that is appropriate to our aim. Here are a number of possible reasons for using starters and some suggestions of activities that might be used for each.
Hooking students in
Our starter can be a way of engaging children’s interest. Puzzles and challenges can be good for this. The 7puzzle site provides a new number challenge every day and it’s worth looking through the archives as some puzzles are much more challenging for others and could be aimed at different age groups or ability levels. The Chris Moyles quiz show used maths challenges which I’ve found have been popular with KS2 children and there is a bank of them here, although I’d recommend watching them beforehand to check the content is entirely suitable for the age group. Sometimes, just an image on the board which gives something to think about can excite interest. I particularly like the examples of bad maths here. In the twitter discussion yesterday, @PGCEmartin suggested using short video clips or web pages of news and sports items and asking mathematical questions about them.
Connecting with previous learning
This might be by recapping a skill learned in the last lesson, giving time to respond to feedback in books or getting children to explain a concept or skill recently taught. Building up a learning wall which is kept current can help with making these connections too.
A mental ‘warm-up’
All kinds of activities can be used for this. There are lots of sources of interactive games that can be used on the IWB, including those at mathsframe or Crickweb. Number chains can draw on a range of mental maths skills. As I think I’ve mentioned before, I’m also a big fan of having a structured programme of daily counting.
Skills practise or skills building
This very much overlaps with the mental ‘warm up’ idea and similar activities can be used but it’s worth thinking about which particular skills need building up by your group. I’ve used tables practice sheets, for instance with children working on the times table that they’re currently learning, and a similar idea could be used for number bonds and all sorts of calculation skills. I’ve used maths minutes which are available for different primary age groups and found that children respond well to them. Target boards like these can be used in lots of different ways and it’s worth building up a bank of them. Another idea is to have a number of the day which can be done either by using a permanent display or by means of a worksheet. The number can be changed every day and the instructions varied to suit different ability levels.
Particularly as end of key stage tests or end of year assessments draw near, it can be good to choose activities that help children revise previously learned concepts and skills. Sites like the BBC Revisewise or Education City (if your school has a subscription) can be good for this. Games like ‘Who wants to be a mathionaire’ can also be used.
Introduction to the lesson content
Sometimes, you might want to use the starter to introduce the main topic in some way. I love this video for introducing division, for instance. A simple idea suggested by @TheMathsMagpie yesterday was to have cards with key questions on one side and the answers on the other, which children could use to test each other.
Finding starters online
In the discussion yesterday, we agreed that it’s important to vary the kinds of starters we use. However, it’s always good to have a trusty source of starter activities which we can fall back on. I’ve already mentions 7puzzleblog, Crickweb and mathsframe. Nrich has some suggestions for starters on its excellent site. Other good sites are the Transum Starter of the day site and the Flash Maths site, which is aimed at secondary but has several activities which would be suitable for KS2. Another site mentioned in yesterday’s discussion which I hadn’t come across before was A+click which looks very useful.
As a quick reference, I’ve put together a pinterest board of starter ideas which contains links to most of the sites I’ve mentioned and some others too.