Steven White is the Nursery Manager at and an education consultant in Outdoor education, with 13 years of experience in childcare and early years education. In 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. Look out for part 3 coming soon for further discussion on the Language of Mathematics, and ideas on how practitioners can encourage children to engage with the maths all around them. You can also .
In I mentioned Problem Solving briefly, referring to (Carr et al, (1994)) 3 concepts. Now taking into consideration that when we are sharing thoughts on possibilities to further Children鈥檚 experiences (through extensions from our observation of Children鈥檚 interests) for problem solving and creating good problems, I am often asked during training with practitioners, "What does Problem Solving look like in practice?" and, "Why is it important to create problem solving opportunities in the first place?"
Within our staff team, we believe that problem solving is of huge importance. We believe that when creating Mathematical thinkers, we are also encouraging critical thinkers, confident reflectors of their own experiences, encouraging a development of a range of coping skills, and promoting mind over mood abilities to nurture themselves throughout their daily lives, at a developmentally appropriate stage that is unique to their own individual needs.
Before, during and after our project based approach to learning, we offer Children open ended resources (along with other resources) that are collated in a bag, box, hat or whatever we deem appropriate (and readily available) to store items within. These items are then offered to promote provocation for further discussion to occur. Philosophical, open-ended questioning engages our Children throughout the debate, and helps to explore the many opportunities to extend the Children鈥檚 fascinations. Sharing thoughts on the possibilities for progressive pathways further expands on the guidance of the , or , through a responsive, subtle, holistic and reflective approach.
(Above) Children aged 2,3 and 4 engaged in role play with their dinosaurs.
Project based learning, projects and creating the story
When we recently began the redeveloping process of our outdoor play space, Children were engaged in the development of the space from the start, staff and families also included in the entire process, as we are inviting all to use this space. Creating a sense of place, all should be invited to engage in the development and continued up keep of this motivational play scape, coming away from a Disneyfication of the outdoor space (meaning, a play-scape that is constructed almost over night with little to no input from the Children, or community as a whole). With the sketches complete, they remain merely as a rough guide, as we discussed that we wished to see the play scape take shape as it was constructed, and hoped that it would morph into something else over time due to its use and the weathering effect.
Children in our 3-5 group, designing our play-scape whilst engaged in discussion on 鈥淭hings you鈥檇 like to have in our garden鈥 and 鈥淲hat do you think of the current designs for our garden space?鈥
Through documentation of Children鈥檚 discussions, we sketched out the play scape. Further discussions on how happy the Children were with the potential new play scape place followed.
Finally, we are then seeing through to completion the design process - doing what we said we would do, with everyone on the journey. A process that took 5 months (Nov 2016-March 2017), to see the first of the physical changes from our 1st discussion, the play-scape being further (subtly) developed to this day.
Processes and Strategies (4 stages)
Stage 1: Starting
Our group of Children had started an investigation through the planting of their potatoes. It was too early in the process for them to harvest them. The group requested that soup would be cooked using our fire, oven and vegetables. We titled this experience 'Potato to Pot'. We discussed how we might acquire our ingredients, and one Child (aged 3) said, 鈥淲e go to the shops鈥, with this we gathered ourselves and off to the local shop we went. The Children estimated how many potatoes they needed to make enough soup for all the Children in their group 鈥淥ne potato might make enough soup for only 4 Children鈥 advised a boy (aged 4). Then discussing how many other ingredients we needed to complete our soup making experience, the Children estimated for the leeks and again for the Carrots. 鈥4 leeks only, they are long and that will make enough I think鈥 Girl (aged 4). 鈥4 carrots also, 4 leeks, 4 carrots and 4 potatoes, will be enough I know鈥 Boy (aged 4). The produce was acquired, handing over the money to the Children, as they would purchase their goods. Goods bagged up, we headed back to the Nursery.
Stage 2: Working on the problem
Upon arrival at the Nursery, the bag of vegetables was placed on the table in the 3-5 room, the Children went off to become engaged in play. Once they were ready to re-engage with the 'Potato to Pot' experience, they approached the practitioners and asked, 鈥淐an you do soup now?鈥 Boy (aged 2). One practitioner softly invited the Children to help make the soup. Using peelers to remove the skin, then knives to chop the veg, the group then set about preparing to make the soup. Discussions took place around what should be done with the peelings. 鈥淭he Chickens can have them鈥 Girl (aged 3), 鈥淵es, they will really like them and they can eat the soup too!鈥 Boy (aged 4). Now that the prep work was completed, some of the Children left the area. Another Child advised 鈥淲e need to cook it, it鈥檚 going to take lots of minutes, if you don鈥檛 help it will take hugest minutes to do, and if you do help, it won鈥檛 take that much!鈥 Boy (Aged 4). The practitioner asked, 鈥淗ow do we make the soup now?鈥 Girl (aged 4) 鈥淧ut it into a pot, some water also, then we boil it all up, so yummy!鈥
Stage 3: Getting deeper into the problem
Filling up the pot, the groups discussion began to form around the notion that they had purchased 鈥淭oo much vegetables in the pot鈥 Girl (aged 3), 鈥淢aybe when it boils it will shrink down and not be so much?鈥 Boy (aged 4). The Children added water to the pot, once happy enough with the amount of water poured into the pot, the pot and its contents were then transported (by the practitioner and some Children) to the fire pit and the boiling process commenced.
Stage 4: Reflecting and Concluding
Once the soup was cooked and enjoyed, the Children played for some time, in the garden. Gathering together, prior to then heading off home with their parents, staff reflected with those Children who wished to do so. Advising us that 鈥淚t was nice, but too much leeks and I don鈥檛 think I like Carrots so much!鈥 Boy (aged 3) 鈥淚t was nice, I liked buying all the 'vegebables' then cutted them all up鈥 Boy (aged 3), 鈥淚 think we had far too many leeks and carrots, next time maybe we don鈥檛 get so many?鈥 Girl (aged 4). 鈥淚t took a lot of time to wait for the fire to make it, we could use the inside cooker next time鈥 Boy (aged 4).
This was a great mathematical problem-solving experience for the Children, and a very simple one at that. Through the skilled practitioner鈥檚 observational skills and interpretation, then documenting of the story that unfolded - from firstly requesting to make soup, to the consuming of the soup - we followed the 4 stages as discussed. It was the skill of the practitioners that highlights the vital importance that such experiences offer, which can easily be overlooked if not recognised by the adult.
The full cycle - engagement, experiential learning, connection vs consumption, concluding and reflecting of the process - completed the experience for the Children. This experience, (which may or may not be repeated) may provide observations of Children choosing to purchase less ingredients, in turn costing less money to do so. Possibly Children with Practitioners will create the fire prior to preparing the soup, or, opt to use the cooker in the kitchen, these are only some of the many possibilities to further extend this Mathematical experience, which are not exhausted by any stretch of the imagination. We wait to see if the Children revisit this experience and will observe these possibilities unfolding, or, we may not.
Look out for part three of Steven's blog, which looks at successful problem solving and levels of sophistication in children's play, and how they can be used to help nuture maths skills, coming soon. Or.
Further Information
If you're interested in finding out more about engaging children with maths through play, you might like the Alliance publication, .