Mathematics and problem-solving skills

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.


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


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.

A collection of infographics related to maths can be found here.

A collection of downloadable maths-based resources for printing can be found here.

More maths-related posts can be found here

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4 thoughts on “When numbers don’t add up

  1. Very interesting article. Also worth considering how other countries approach teaching Maths. Have just read a really interesting book about pedagogic approaches in top PISA performing countries which provides an insight into cultural and academic perspectives on pedagogy- Cleveland by Lucy Crehan. It’s worth taking a look.

    Liked by 1 person

  2. Enjoyed reading this blog, as you mention it is always fascinating trying to fathom how a student is processing Maths in their heads. I was not a natural at Maths at school but was always told that I was good at problem solving(I did not really know what they meant by this!). I still tell my students that I need a pencil & paper to do simple calculations & that there should be nothing embarrassing about that, if that is the way you need to process. So equally I say that cuisenaire rods are a great visual aid & you are never to old to get them out and show how 1/2 + 1/3 = 5/6 for example!( Love trying to make Maths fun for teenagers with visual aids, they seem to respond – just think that they leave Primary & all the visual aids are left behind. Check out my resource for A Level students was adapted from an A Level lesson on using Matrices but this Santa was designed for them, they loved it). Thank you for the inspiring blog. Jenny

    Liked by 1 person

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