The language of Mathematics (part three)


Steven White is the Nursery Manager at Tiptoes Nursery and an education consultant in Outdoor education, with 13 years of experience in childcare and early years education. In the third and final part of this blog, he shares his insight with us into how problem solving and critical thinking can be nurtured to support the development of maths skills and confidence in maths. You can read part 1 again here, or catch up with part 2 here.  


In part 2 of The Language of Mathematics blog we looked at problem solving and project-based learning as tools to encourage Children's understanding of mathematics. Here, we examine problem solving further, looking at levels of sophistication in play, and traits of successful problem-solvers. 

Levels of Sophistication in play

Deloache and Brown (1987):

We are likely to recognise these levels of sophistication when we observe our Children at play. This study observed levels of sophistication in approaches to the Children playing with the train track:

  • Brute Force: hammering bits to fit
  • Local Correction: adjusting one part, often creating a different problem
  • Dismantling: starting all over again
  • Holistic review: e.g. repairing by inclusion or removal

Brute Force: hammering bits to fit

For the purposes of our story telling we observed our Children building a Den in the local forest space. Using these levels of sophistication we observed the variance across our group of Children in our 3-5 group. Some Children gathered up sticks and forced them into the ground to build the Den, in between gaps of the walls they then forced them in and at times, and damaged the Den’s structure. Becoming somewhat frustrated with this, they tended to give up and return to their free play. The experience of this could take place for the Child, as the practitioner recognised the Child’s developmental stage, where it wasn’t deemed to be a destructive process, as often might be the case.

Local Correction: adjusting one part, often creating a different problem, Dismantling: starting all over again and Holistic review: e.g. repairing by inclusion or removal

Two boys aged 3, attempted to cover the entire den with fern, that was found strewn all over the forest floor. In doing so, the added weight to some sections of the den became too great, resulting in sections of the den to collapse. Exploring this problem, with the appropriate amount of time to do so, they discovered that it would be a better option to remove the fern first, replace the sections of den with stronger and thicker pieces of wood vs that of the slender pieces that were there previously. They took greater care in placing the fern on the newly acquired wood and tested its durability several times, before attempting to place more fern on top of each other, overlapping each fern, to provide greater shelter from the elements. Once convinced of their creation, they invited their friends to test it out. The feedback was great “I could sleep here all night, what a good Den you have built!” Girl (aged 4).

As practitioners, we also reflect on the Children’s experiences through the research of Askew and Williams (1995), during which a list of traits was produced, which would highlight what is required when creating successful problem solvers. 


Successful problem solvers traits 

(Askew and Williams (1995))

  • Get a feel for the problem e.g. talk it through, asking questions
  • Plan, prepare and predict outcomes e.g. gather bigger sticks before building
  • Monitor progress e.g. check that the fern will not destroy the Den
  • Systematic in possibilities e.g. separate slender sticks previously tried from those not tried
  • Alternative approaches/evaluating strategies e.g. try different positions for sticks
  • Refining and improving solutions e.g. solving a puzzle again in fewer moves i.e. the completion of the Den

Routine activity

  • Preparing, getting the right number e.g. scissors, paper for creativity
  • Sharing equal amounts e.g. snack or lunch time
  • Tidying up, making sure nothing is lost
  • Gardening e.g. working out how many bulbs to plant where
  • Cooking e.g. measuring amounts in a recipe using scales or jugs

Routine activity is a vital part of the Children’s learning experiences at our setting and we document them accordingly, for they provide an endless amount of quality engagement. These observations help to reduce the anxiety that the practitioner might be feeling, where they feel that they must provide activity after activity to offer a quality experience for the Child, or, provide enough evidence to document the learning. Routine activity has provided our team with observations where the Child is often found to be in their deepest experience of their learning (zone of proximal development). This is observed when the Child’s focus on their task is unchallenged by their surrounding environment, the goings on of others or the possible distractions surrounding them. Tending to the garden further promotes mindfulness in our Children, as they care for the garden and enjoy the fruits of their labour during harvest time.  

Snack or lunch time can be often over-looked to provide meaningful observations, and can be seen as a means to an end rather than the enjoyable experience that it can be. This is true for Practitioners and Children alike, when in fact this time provides us with some of the best opportunities for the curriculum to come to life. I often think of the best plans that I have made for future endeavours tend to occur when sharing bread with family and friends.


Discussion Sessions are of high importance in our setting, for sharing ideas and to gather knowledge and understanding at any stage throughout the Children’s time with us. This is not group time, nor is it a planned session set at any specific time, as it is a fallacy to believe that all Children share best at 10am in the morning, or just after lunch time. For example, we as adults do not operate in this way, so therefore we do not expect it of our Children either. What methods do we use? We trial new approaches, continuing our research to improve Children’s (and Practitioners) experiences. We enjoy engaging in the more traditional approaches - practitioners enjoy the full circle experience where they enjoyed this as a Child and are now sharing this as an Adult. The hope is that we do so to motivate Children, for them to feel safe to share their thinking and their thoughts. To feel accomplished problem solvers, and champion critical thinking through an avenue of Mathematical experiences. The biggest aim, is to keep things simple. Why would we want to over complicate things anyway?

Methods to promote discussion

  • Reflection circles
  • Decision making
  • Picnics, trips off site e.g. how much water do we take for us to drink
  • Design projects e.g. indoor setting or garden project
  • Hiding experience e.g. what’s in the discussion box today?
  • Story problems e.g. unfair sharing, remainders and fractions, making things for fairies or giants


Further Information

If you're interested in finding out more about engaging children with maths through play, you might like the Alliance publication, Discovering Maths through Play.

Find out more about Steven's setting Tiptoes Nursery here

Visit the Tiptoes Nursery Facebook page here

Read more from Steven on his blog here