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.