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Blog: I Like Solving Problems
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24th January 2019

“I like solving problems-it makes me feel like a superhero” Penny 5 years

Supporting children to develop key mathematical skills & attitudes in the Early Years.

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I have recently been lucky enough to deliver a session at the Alliance for Learning Teaching School Early Years conference. The day was a real celebration of Early Years with ideas, research & strategies being shared, debated & discussed.

This is an overview of my session which Alliance for Learning have kindly agreed for me to share with the Nexus Education community.

The aims of the session included:

  • How to develop a positive maths identity in the Early Years
  • Developing effective adult-child interactions to support & challenge early mathematicians
  • What do we mean by critical thinking in maths teaching & learning?

The session started with sharing quotes from children regarding their views on maths.

“I don’t like maths as I have to sit on the carpet for too long”

“I think it’s hard as all the numbers get jumbled up in my head.”

“Maths is too much answer time & not enough learning time”

“I think I would rather play with the cars or the dinosaurs”

Quite telling…children are very good at telling it like it is. Already these children are developing opinions and habits of mind about maths.]These habits of mind are already negative and potentially could be a barrier to them moving forward in their learning; especially if this is an engrained long lasting memory.

Quotes were then shared from grown ups about their feelings about maths.

“I have always been rubbish at maths”

“What’s the point of pi or knowing about isosceles triangles?”

“I just couldn’t make any sense of it. It didn’t seem relevant to me or when I grew up.”

“I think I decided that at an early age maths wasn’t for me. I have managed ok without an O level in it so far.”

 

Unpicking these quotes shows a sense of almost acceptance that maths isn’t for them and they had resigned themselves to this situation.

One of these quotes is actually from me- the 3rd-one-it is a true reflection of how maths lessons left me feeling. I needed to see the relevance in maths for me to buy into it, for me to be able to know how everything I was being taught fitted together. It all felt very separate; in distinctly individual compartments, with a clear focus on recall & barking out answers.

My question here at the conference was if this was the feeling shared at home & comments like this were part of the language of maths, what were the children brining in with them into your setting or school?

Influential in this area of maths identity is from Jo Boaler. In her book ‘The Elephant in the Classroom- Helping Children Learn to love maths’, Boaler has found that a poor maths identity can develop as early as 2 years of age with observations showing children moving away from activities where there is a right or wrong answer AND instead preferring to take part in much more creative, open ended activities which allow a sense of exploration, trail and error and creativity.

From 2! We all know how difficult it is that it is much harder to undo a learnt response.

Influential in Boaler’s work is the research of Carol Dweck; particularly about Dweck’s views on fixed and growth mindsets. The reason for including Dweck’s research within this session was to explore how a positive attitude to maths acts as a driver towards feeling that you CAN and whether this ultimately means that you WILL achieve.

Think of children you support- what are the ones like who are successful at maths. What are the ones who find maths a struggle like?

Do those who succeed at maths know how to apply their key maths skills in a range of experiences? Do they keep going, adapt and modify approaches when their first attempts didn’t satisfy? Do they understand the power of mathematical language in helping them shape their emerging understanding of maths content?

How does their positive attitude make a difference to their maths learning?

Do the children who find maths more difficult have a more narrow window of trial and error; relying on a limited number of strategies? Do they seek out a greater level of adult support to provide different strategies and ways of problem solving? Do they also have a sense of ‘I can’t do it’ when faced with a new problem?

Perhaps if we focus on these drives and attitudes rather than just providing them with more of the same (i.e. content), would this be a way in for children to improve their maths learning?

Consider what this means for us at out level-are you more inclined to be totally engaged in something if you have a glimmer of a slight chance of succeeding and the feelings which happen as a result of that achievement, rather than taking part in something where you haven’t felt those feelings before?

Jo Baler summed up this view perfectly ““Teachers need to offer mathematics as a learning subject not a performance subject.”

Jo Boaler ‘The Elephant in the Classroom’ (2017)

Just this slight shift in how maths is viewed and therefore communicate to the children may be the extra push for some children to see the enjoyment of being involved in maths learning.

Different suggestions of how can we create a positive maths identity for your youngest children were then shared.

 

Ideas included:

  • Be a positive role model ourselves: We all bring memories and experiences about our own subject knowledge and confidence. This may be positive which is great as your natural enthusiasm will shine through and enthuse your children about maths. But it may not be as positive-it may even be extremely negative- like mine. I can still remember the feeling of not keeping up with the rapid fire mental maths test at my primary school. This experience still leaves me with a feeling of panic, despondency & impending failing. If this is an engrained emotion, there is even more importance, I would argue, to make sure that others never feel like that. That they develop & maintain a positive view of maths exploration as an opportunity to learn. Enable children to see the magic in maths and by doing that you may also rediscover some of the magic for yourself.
  • Be conscious of making connections for children: Connectivity is vital as a motivator for children to not only learn the maths content you are sharing with them but also to helps children feel propelled into applying their knowledge. Relevance plays a key role here. Like most things, children need to appreciate ‘what’s in it for them’. Will this enrich their lives, deepen their sense of exploration & feel emotionally satisfied in what they are doing. That content, satisfied feeling in your tummy.
  • Acknowledge that for some children maths is a journey (with no sat nav!): the maths journey is full of roadside information, possible wrong turnings and occasional pit stops whilst children are immersed in new information, then come to terms with it , apply and modify. For some children this journey will be quite direct where they soak up the new information and then are able to use this alongside their secure dispositions & attitudes to learn deeper & move forward. For many children they will be times that they need to stop & revisit, maybe even take a different route to ensure learning is deeply assimilated. Having this close collaboration between the what they are learning and how they are learning ensures that all children reach their own destination, refreshed & ready for what meets them next.
  • Excite, enthuse & inspire: consider how you do this for your children. A lot of this will already be developed and communicated through the ethos that you nurture within your room but also consider the role of the environment in this ethos. When planning perhaps ask yourself, “Where’s the maths?” in my environment. Does it move pass the purely aesthetic which is important to initially engage children but des it also allow for possibility thinking, creativity, exploration and challenge? Are you using your key mathematical manipulatives with an understanding of the mathematical potential within them? Perhaps scan your environment for a pattern of maths enjoyment as well as maths content. Can you also see alongside the potential for maths content, the opportunity for children to use their maths characteristics also?
  • Be brave to go with the children: one of the most exciting parts of being in Early Years is the way children can completely surprise you! Children can come up with a million more times more imaginative, amazing maths ideas then adults can think of. Whilst planning has a place within teaching and learning (recording the thought process in a written form for example), consider all events within your daily routine as potential opportunities for maths content learning and maths skills learning. These could be the incidental and spontaneous times but may also include routine times such as snack time, welcome and goodbye time. Edit your planning, scribble on it, celebrate the bits which worked well and equally those which took an unexpected direction. Planning which looks like it is used to inform how support can best meet the needs of the children is a priceless document, regardless of its less than pristine appearance.
  • Keep learning & reflecting: have a thirst for knowledge yourself. Keep discovering, finding out form other professionals. Reflect on what you have read and listened to with the aim of using this information to redefine your own pedagogy. This may happen in a variety of ways: collaborative discussion, modelling opportunities, research into practice, team teaching, an extortionate online account, or social media. As well as developing your own pedagogy continue frequent professional discussions with your Early Years team to ensure that there is a level of consistency of beliefs and how these affect provision.
  • Question, challenge and ponder everyday.

 

Next, we considered what the role of the adult in supporting the mathematical journey of all children could look like……

The following points were presented as a mini audit; a framework to support reflective and professional discussions.

  1. Understanding of child development (specifically maths): discussed above but needs to be constantly revisited in order to refine ideas and thoughts.
  2. Implementing this understanding into the environment: discussed above but again needs to be part of a reflective on-going cycle of review.
  3. Supporting children through sensitive & authentic conversations: consider the kind of support & interaction you give to your children. Do you explain, for example, new key mathematical vocab so everyone has a clear understanding of what the words mean in order for children to attach them to the actions they are doing? Do you offer a variety of ways for children to communicate their mathematical thoughts & ideas? These could include verbal, non-verbal, early mathematical mark making, pictorial or using concrete materials. How do you move children at the brink of deep learning as well as those who need the additional support to make sense of the maths being shared? Possibility questions are really effective for this “I wonder what…” “How can we…” “Prove it” give children the opportunity to use their knowledge and dispositions in a much less intense way then a closed question which may demand very little thinking and adaptation of knowledge.
  4. Reflection & modification: This builds on the on-going development of your own pedagogy about Early Years maths & one of the ways this can be quite acutely refined is when you put children into the mix! What you may have read about literally comes to life when the principles of research are shared and experienced with your children. Crucial here, I believe is the consideration of how observation of your children happens. Is it interactive observation rather than passive observation. By that I mean, do all adults tune into what their children show, tell and feel about maths by being part of their learning rather than simply observing it? After interactive observation, next to consider is what can be put into place to move their learning forward, deepen their thinking and improve their attitude to maths exploration? Do I need to explicitly model maths learning and content? Do I need to manipulate the environment differently? Do I need to rephrase the language I am using? Do I need to support the child in the undoing of a misconception? Do I need to either plan an adult led activity, an adult initiated challenge activity or a well modelled child initiated activity?

Identify the barrier and consider a range if strategies which include the delivery of maths content trough a characteristics framework.

Next in the session, time was given to exploring critical thinking and it’s importance for securing the drive to learn maths.

Critical and creative thinking need to be embedded in every mathematics lesson. Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

……teaching through problem-solving rather than for problem-solving.”

Dr Catherine Attard 2017

Initial discussions on this characteristic highlighted critical thinking as a life skills and its place in maths? Critical thinking is an integral part of the EYFS and is part of the characteristics of effective teaching and learning.

Choosing ways to do things: this talks about supporting children to be able to use their developing and secure mathematical knowledge alongside their capacity to manipulative this knowledge in a range of mathematical problems with secure understanding. For example can they use their knowledge of number binds to 10 to help them understand part part whole representations? Essential here is the development of their drive….their oomph to enquire and find out. How do we do this? Explicitly sharing a range of problems and how they can be tackled may a way to show children what this skill involves. Alongside modelling and thinking aloud gives children the permission to know that this is a useful strategy to organise their thoughts and also enables them to make sense of the language, maths content and desire to keep finding out.

Making links: this element of critical thinking involves supporting children to be able to transfer knowledge into a range of other mathematical activities- adaptation leading to stronger more diverse patterns of connections. For example, can they use their understanding of the relationship between numbers when they are starting to find out about subtraction and addition? If we as adults don’t share these links with them then they may not ae able to make them for themselves and therefore risking a view which looks at maths as a disjointed set of facts or information. Deep secure learning is much more difficult to foster without connectivity.

Having their own ideas: here, we are asking children to solve problems based on prior knowledge. They understand what problem solving is as a tool for learning & are able to choose from their developed range of strategies & ideas to begin to tackle a new problem. This willingness to have a go is based on a level of prediction, connection & confidence. Here collaboration of adult and child ideas and thoughts are instrumental in helping the children build up a bank of strategies. Revisit these strategies frequently to offer reminders and also to modify, add and strengthen. Spend time on this discussion of possibilities, talk through the process of finding out and exploring. The more we do it, the more children will do it.

Revisit the characteristics framework and use this alongside the curriculum subject content when planning. The development of a holistic view of maths, with consideration given to all elements scaffolds all children’s learning potential and ensures that they experience a layered framework which supports, challenges and celebrates.

Final thought of the session:

“What will you do tomorrow to engage, excite & motivate your children?”

Thank you to everyone at Alliance for Learning for giving me this opportunity to share my thoughts. It was exciting to see so many dedicated Early Years practitioners and listen to their own inspiring ideas.

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