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.