Thoughts on maths
Like many people the word maths is not one of my favourite words and I tend to shy away from the subject. I think that this goes back to my school days when groups were set and I didn't thrive in the fast paced, complicated classroom formula loaded didactoc teaching from the front. So I went down a group and lost my confidence and peers but gained a slower paced, softer learning environment which got me through.
Funny how our childhood experiences stay with us.
Teaching maths in early years
Obviously, leading and teaching an EYFS curriculum means that maths can not be avoided. A likeable way of teaching maths must be found so that I have the confidence to inspire that in young children and not put them off and through experience, observation, EYFS training and having a child of my own who loves anything mathematical, I have found it!
Does this mean that I have maths mastery? Well, I have certainly mastered a love of maths.
On this page I explore what maths looks like and means for the early years, hopefully giving you some encouragement and impetus to exlplore more and discover a new love of maths teaching if you have not had that before. Please let me know your thoughts.
I heard this term for the first time during the Early Education Annual Conference 2017 (#EEANC17) from Elizabeth Carruthers. She is a headteacher doing PhD research in this area and shared her findings in a presentation at the conference. She explains that how we teach maths to children is about our pedagogy and how we view children as learners. If we understand children to be full of experiences and knowledge, then we can respect it and build on it. How we regard maths is also important. If we are open and view maths not as rigidly having right or wrong answers then we can teaech it in a different way.
Elizabeth explains that the term open maths came from discussions with "real teachers in real classrooms". She encourages us to look at maths from the whole. To see it as infinite and huge rather than narrow and limiting. So for example, as well as breaking down counting into parts 1-5 and 5-10, help children to see maths in context and let them ask and answer big questions like "what is the biggest number?" In her blog, Elizabeth states
Open Mathematics considers children’s own emerging mathematics, which has no right or wrong answers. Children analyse, hypothesise and experiment and their own thinking is supported, nurtured and developed. This open culture supports a spirit of freedom where children feel free to cross out (for example) their mathematical notation, change their minds and develop their own strategies. Play is recognised as a vehicle for children to express their imaginations, and this is crucial to children’s development of abstract concepts like mathematics. Open Mathematics is not neat and tidy but it involves deep-level learning and sometimes the chaos of thinking, refining and finding new mathematical ideas.
Further on in Elizabeth's blog she shares her research about the use of resources and how an open mathermatics method enables children to have freedom to explore and develop their mathermatical thinking. For example, children might be encouraged to experiment graphical representation in maths using writing, drawing and tallies. She promotes enabling children to "put down their thinking on paper in any way they find useful". She states
It is this freedom to invent and think through their own mathematics that is vital to learning and understanding. The Williams Mathematics Review (2008) was clear in their recommendations that to secure effective pedagogy there needs to be “a culture with a significant focus on mathematical mark making, in line with early writing; that encourages children to choose their own mathematical graphics to support their mathematical thinking and processes” (DCSF, 2008:26).
Elizabeth's blog Open mathematics, open minds is very informative and full of research findings and pedagogical theory. It can be found on our conference page along with content from the other brilliant presenters on the day. She concludes by saying
Open Mathematics is underpinned by a democratic pedagogy where children and adults co-construct learning. Teachers and practitioners actively seek knowledge about children’s learning both from the children they teach and their engagement with a professional learning community.
Open maths in practice
I wanted to explore graphical representation using an open maths concept so I tried it out during a day teaching nursery children. We had some polished stones in a tray and I modelled drawing some gridlines with a large marker pen on large paper. Some children wanted to draw their own grids with large pens and big paper. Others asked me to draw the grid. I was interested to see what the children did around representing the stones, or arranging them. It was open ended. I had no end product. My aim was to see where they took this infinite maths and how they built it upon their knowledge. There were many surprises. By not limiting and keeping it open, children wrote numbers: 200, 500, 10000.... One child wrote numbers 1-51 and could have continued further I think (something to follow up). Some children placed stones in each grid box in a pattern arrangement and others drew representations of the stones.
I was fascinated by the children's graphical representation, their knowledge of number, their excitement and ability and their interest. This is just a snapshot of the session and not a full write up of what the children achieved. I share this because I was encouraged and inspired by the children's love of maths and their confidence in working with it. Their confidence in big numbers and infinite maths makes me want to explore it more at home and in school.
If you are less confident in maths and need inspiration, I encourage you to try it yourself.
A very helpful paper from the National centre for excellence in the teaching of maths entitled Mastery approaches to mathematics and the new national curriculum (Oct 2014) helps us to understand the conecpt and theory behind maths mastery. It states
Though there are many differences between the education systems of England and those of east and south-east Asia, we can learn from the ‘mastery’ approach to teaching commonly followed in these countries. Certain principles and features characterise this approach:
- Teachers reinforce an expectation that all pupils are capable of achieving high standards in mathematics.
- The large majority of pupils progress through the curriculum content at the same pace. Differentiation is achieved by emphasising deep knowledge and through individual support and intervention.
- Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons and resources to foster deep conceptual and procedural knowledge.
- Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts in tandem.
- Teachers use precise questioning in class to test conceptual and procedural knowledge, and assess pupils regularly to identify those requiring intervention so that all pupils keep up.
The intention of these approaches is to provide all children with full access to the curriculum, enabling them to achieve confidence and competence – ‘mastery’ – in mathematics, rather than many failing to develop the maths skills they need for the future.
The Association for the teaching of maths
Maths in the EYFS
The Statutory framework for the early years foundation stage explains that mathematics is a specific area of learning and thus is not a prime area like personal, social and emotional development, physical development or communication and language. The prime areas take priority and are the focus for under 5s because from these "foundation" subjects, all else flows. Children can not learn with confidence unless they have their primary needs met through dispositions and attitudes and all aspects of personal, social and emotional development. If they do not have the language and communication skills to explore concepts and play confidently and happily then the foundation will not hold up. Without the physical skills of gross and fine motor devleopment a child will not have the physical control and spatial awareness and bodily confidence that is needed to play and apply learning. Everything comes back to these 3 prime areas of learning.
Maths, as a specific area uses and applies all the prime learning area skills to extend learning. For example, the activity I wrote about required a child to be happy to be in nursery, able to be interested, approach me with confidence, understand my actions, be interested and motivated, be engaged, understand my instructions, follow my lead or initiative, use their body to sit, stand, make marks and representations, apply their thinking, notice patterns and much more. All these skills are acquired and practised through an effective EYFS from 0-5, applying the characterisitcs of effective learning
- playing and exploring
- active learning
- creating and thinking critically
which crucially run all the way through each learning area and learning environment.
The framework states for maths that experiences and activities must
involve(s) providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measure (page 8)
It specifies the early learning goals (for the end of the EYFS)
Numbers: children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.
Shape, space and measures: children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them. (page 12)
Development matters is non statutory guidance for the EYFS. It sets out useful suggestions in every learning area for observing what a child is learning, what adults could do and what adults could provide in an enabling environment. The Mathematics learning area is on pages 22 to 36 in two sections: numbers and shape, space and measures. Practitioners must be aware that the suggestions are not checklists as the document itself specifies
Children develop at their own rates, and in their own ways. The development statements and their order should not be taken as necessary steps for individual children. They should not be used as checklists. The age/stage bands overlap because these are not xed age boundaries but suggest a typical range of development.
Infinity and beyond!
Maths is a great learning area with so much potential and scope for play and learning. When practitioners feel encouraged and confident, mathematics can be part of everyday thought and lagnuage just as every other learning area. If we have fears and assocaitions from our past and how we were taught, let's make it different and help our learners of the future engage with a love for numbers, measures and tallies that come naturally to them because we have been open and unrestricting. As Carol Dweck puts it in an article about fixed and growth mindsets
A growth mindset – ours and theirs – helps students to seek learning, to love learning, and to learn effectively. (From "Boosting achievement with messages that motivate" - see link below)
Maths can be such a huge open and exciting subject. Let us teach it, apply it and practice it with an open pedagogy and a breadth of coverage that inspires children to reach to "infinity and beyond" as a certain popular Buzz Lightyear from Toy Story declares!
Further reading, links and learning
- Children's mathematical graphics: understanding the key concepts article by Elizabeth Carruthers and Maulfry Worthington (Feb 2010 / Feb 2011)
- Recognising mathematical mastery in child-led play, Di Chilvers in Early Years Educator (July 2017)
- Mastery in maths: what it is and why we should be doing it National centre for excellence in the teaching of maths
- Mastery approaches to mathematics and the new national curriculum National centre for excellence in the teaching of maths (Oct 2014)
- We need a revolution in how we think about maths, Jo Boaler in the TES (Dec 2015)
- How complex instruction led to high and equitable achievement: the case of railside school (USA) Jo Boaler
- Women and maths, Woman's hour (Feb 2010)
- University of Sussex research page for Jo Boaler's papers
- Maths resources for parents, Welsh government (Dec 2016)
- Annual national conference 2017 summary and inspirations from the speakers
- Primary school mathematics - to what extent is symbolic representation a key factor in the development of recording skills? paper by Jeanette Mills
- The Children's mathematics network website set up by Elizabeth Carruthers and Maulfry Worthington is a rich resource containing much research and pedagogical information.
- Mathematical problem solving in the early years, Mathematical problem solving in the early years: developing opportunities, strategies and confidence and Young children's mathematical recording on the NRICH website
- Mathematics teaching blog linked to the Association of the teaching of maths (ATM)
- Boosting achievement with messages that motivate by Carol S. Dweck