Understanding numbers

In an earlier blog I mentioned maths anxiety. This can be crippling for some children. We don’t know quite what’s at the root of this, perhaps it is the perception that, in maths, things are either right or wrong. The very thing that makes maths a joy to some children, makes it seem inaccessible to others. Sometimes parents are at a loss to support their children, entirely perplexed by this apparent mental block where numbers are concerned. Other times, one parent will confess that they, too, are unhappy mathematicians.

Some children experience difficulties acquiring maths skills as part of a wider learning difference. For others it is a co-occurrence. For some, it is the one thing that makes school difficult. We might think that makes it easier, but speak to a mathematician and you will realise that maths is all around us. If we are able to communicate, then technology can help support literacy skills in many ways. There is a tendency to suggest that in adulthood, we all use calculators, and that is true, but if a person has no feel for numerosity, the “numberness” of numbers, their difficulties will not be addressed by simply employing tech. Multisensory learning, employing physical props and manipulatives as well as a variety of visual prompts, catch phrases and memory boosters is as important for support in maths as it can be in literacy.

When children don’t automatically learn the alphabet, or take naturally to reading, there is usually support and understanding from school and parents. It may take time, and it’s not always perfect, but there are schemes aplenty promising to boost children’s literacy skills. So what should we do, if children don’t begin to display and record their mathematical knowledge in line with their peers?

Keep it light hearted

Songs, chants and rhymes are a great way to introduce children to number concepts. They are appropriate from a very early age, but can be adapted to suit children throughout the primary years. Use them to reinforce sequencing and concepts of time, number bonds and even times tables.

Make it relevant

If children can’t see the point of being able to do something, why would they put in the effort? Draw attention to numbers and quantities, talk about how many pencils you need on the table if all four children at the table need three colours each. How many people are here today? If there are 28 in our class and one person is missing, how many members of the class are in school? How many slices of cake/pizza do we need? How many chairs are there and how many people? Too many/not enough? (Adapt to suit the age and stage, but you get the idea)

Prompts and displays

Posters and displays can be really helpful, but children need to be taught to use them. Whether on a classroom wall or in the kitchen or bedroom at home, if the prompt isn’t pointed out, it may as well be just decoration. Start by showing them the poster, talk them through the concepts, teach them how to use the information on the poster to help them remember what to do, and make sure they know where the poster is in the room. If at all possible, place it where it will easily be seen by those who need it, without craning necks.

KNOW maths problems
More here

 Mathematical language

Teach this really explicitly. Talk about word origins and other related language. At the beginning of a new and unfamiliar unit of study, make a lesson out of this if necessary, so that children can be really comfortable and familiar with the terminology. This can be a real confidence booster. Have plenty of visual aids, including wall posters, desk prompts and pictorial mathematical dictionaries.

Physical props

See it, hear it, say it, do it. The transfer of knowledge for some will happen between hearing an explanation and seeing a demonstration, so that they are able to record what they have learnt. This will not be the same for every child. For many, being able to handle and count objects, or see and feel the difference in size, representing the difference in quantity, will unlock first counting, then comparison and simple addition and subtraction, and can be used very effectively to illustrate and practise multiplication and division. Look at Numicon, Cuisenaire rods and Mathlink cubes for ideas. There are all sorts of online resources using digital versions of these, but the physical props need to be truly familiar for these to make sense, if maths skills are not developing easily.

Manipulative
Recording ideas

Try to have a balance between developing and consolidating true understanding and recording things in writing. A written record is useful, but it is only meaningful to the learner if he or she is able to understand it and use it to model future calculations. Small hands lack the dexterity to write neatly, and so large books and whiteboards are more appropriate at the early stages of mathematical ‘literacy’. Later, the UK norm is for children to use books with 1cm square lined paper, progressing to 0.8cm. A wise dyslexia specialist recommended 0.7cm squares to me for my dyslexic learners when I was still a new teacher, and I have consistently found this helpful for them, where recording work more legibly is concerned.

Desk prompts and props

I have seen well-intentioned teachers design and provide double-sided A4 prompts containing every shape name, times tables, facts on the decimal system and many other reminders for Key Stage 2 learners. However, if a child needs a prompt, it needs to be clear and easy to use, not busy and confusing. One concept on one side of one sheet. If students are to keep them in their desk draws, include a picture of the prompt they need on your IWB presentation, so they can find it easily. The same goes for physical props: either supply the appropriate props when they are needed, or display them on the board, so that they can be accessed. Individual packs of resources in zip-lock bags/folders either in (TARDIS-like) desk drawers, or in a central classroom store.

These ideas can be adapted for whole class, small group, 1:1 and home use.

More maths-related posts can be found here

Downloadable resources related to maths are here

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When numbers don’t add up

Have you ever considered the proportion of nursery rhymes that include counting and numbers? There are plenty. For many children, these are their earliest encounters with number concepts. My son (and I) endured many hours of 10 green bottles as his poor, sleep-deprived father  attempted to croon something undemanding in the small hours to get us all back to sleep.

NumbersOnce his sister came along, they were facing away from me in the double buggy, but while he was an only child, he faced me, and I would chatter, chant and sing number rhymes at him. He used to love it when I would push the pram away (often uphill) and clap and count until I had my hands back on the handle. Before he even started at nursery, he had learnt to count to and write to 20, though he had not mastered signing his name. Looking back it probably shouldn’t come as a surprise that he has just begun to study maths at university, but he was my first child, and I did not train to teach until he had started school, so I had no idea that things do not come so easily to all children.

Maths anxiety

My memories of our maths sessions during teacher training are of a classroom where around 75% of the student teachers were very unsure of their maths skills. Our lecturer was a self-confessed survivor of maths anxiety. This puzzled me. I had clearly passed through school oblivious to others’ maths phobia. I had not studied maths post-16, choosing foreign languages and English. Undergraduate studies in applied modern foreign languages had involved some numeracy skills for the economics module, and I had had to deal with numbers great and small in my city career, but I had never considered myself a mathematician.

Number sense

When I was entrusted with my first class, I found eight year olds who routinely dotted their exercise books as they counted from one to complete each calculation. This was a mystery to me; I simply could not imagine that the students who did this were doing so because they did not have a way of visualising each number to hold it in their short term memory and perform calculations. But that is exactly what was happening.

Resources

Our text books (luckily) conformed with the government’s prescribed numeracy hour at the time, and I was able to adapt planning available online to suit my students. Occasionally, the textbook illustrations would include pictures of physical maths equipment such as cuisenaire rods, but our overstretched inner-city school did not have such luxuries. (The stationery cupboard was locked, and in a locked room. Our glue-stick supply was exhausted before Christmas)

more rods

Training

One of the first courses I asked to attend after completing my NQT year was run by BEAM (Be a Mathematician) and titled How to help dyslexics and dyscalculics who struggle with mathematics. It was eye-opening. I had sympathised with my students, and used everything I could find or make to try to ensure maths was accessible, but there was so much more I could do. That course transformed my maths planning, teaching, differentiation and resourcing in ways that I could not have imagined before.

Early Years

Later, when I worked in Early Years, first as a classroom teacher, then in learning support, the manipulatives, physical props and visuals came into their own. These, combined with the explicit teaching of mathematical language and concepts, can unlock numeracy for many children. I would like to see this kind of approach and equipment in use throughout the primary years.

more manipulatives

Over the next few weeks I’ll be sharing ideas to support children’s maths skills development. Do post any specific support needs in the comments, and I’ll try to address those in the blogs.

More maths-related posts can be found here

Downloadable resources related to maths are here

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Mathematics and Problem-Solving

Where learners’ EF (Executive Function) is underdeveloped and/or working memory is overloaded, mathematics can pose real challenges that go beyond understanding numbers or carrying our calculations. It’s common for EF to impact maths, not least because of the importance of sequencing, and EF difficulties can co-occur with dyscalculia as with dyslexia. Read more

Homework

Executive functions (Explained in more detail here: EF – an introduction) develop from early childhood and are seen as key predictors of academic outcome and life chances in the modern world. I discussed how EF difficulties might present or be supported in the classroom in EF and Learning – Classroom Survival.

Some students with underdeveloped EF find the demands of school overwhelming from the very start, whereas for others, classroom routines, resources and support can be a benefit. In both cases, homework is likely to pose a challenge, particularly as they grow older, since such independent tasks place significant burden on EF.

When a child or young person has underdeveloped EF they

Read more

Classroom Survival

Executive function (EF) difficulties commonly co-occur with other learning differences and specific learning difficulties, and they can pose life-long challenges. It’s important for those affected, their families, educators and employers to understand how EF impacts everyday functioning and what can be done to support this. For more on EF difficulties see EF – an Introduction.

Many of the challenges faced (and sometimes posed) in school and learning situations by students with EF difficulties are similar or identical to those experienced by their neurotypical peers. This is one of the reasons why teachers and parents can easily miss the signs that there is a support need. Unfortunately, all too often, the behaviours that actually signs of EF difficulties are labelled as immature, impulsive or even plain ‘naughty’.

So what might these behaviours be?

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Executive Function 

The chances are that unless you have (or a family member has) a diagnosis detailing executive function difficulties, or you are an experienced clinical practitioner, assessor or special needs educator, you may not have heard of executive function (EF) at all. As part of a research project in the summer of 2016, I conducted an online survey of teachers to gauge their knowledge and understanding of a range of learning needs: executive function difficulty was the least well known by the 170 respondents. Research shows that students with specific learning difficulties are likely to have executive function challenges. Based on published prevalence figures it is statistically very probable that every mainstream class will include a number of pupils with executive function difficulties.

Read more