Mother Nature as Mathematician: Learning Outdoors without Commercial Materials

“In every walk with nature, one receives far more than he seeks.”

John Muir

    

In our program we spend at least one hour outside each day exploring our play yard and interacting with nature rain or shine (excluding dangerous weather). Although we are fortunate to have an ample collection of materials to use, there are many days that we bring nothing extra outdoors with us. We ask children to interact with the world around them and spend time immersed in nature. Challenged to create play opportunities using only natural elements encourages children to pay close attention to what the world offers and they often wonder about objects and phenomena that they might not otherwise have noticed (e.g., the strength of the wind, an interesting insect, the size of leaves). It's also a great way to encourage children to become resourceful and use their imaginations. In land-based learning knowledge is shared and a respect for nature is encouraged.

 

Curious about the size and colours of leaves, the children were encouraged to gather a leaf collection on a stick. This helped them practice fine motor skills and they were eager to quantify the leaves they collected.

 

Much of what the children discover is mathematical. Mother Nature tends to be a beautiful mathematician offering a variety of sizes, shapes and patterns in natural objects. Children are curious as they describe, classify and sort what they find into collections. How many times have you found an assortment of rocks in a child's pocket? Being outdoors without toys also facilitates amazing risky play and children are eager to quantify their achievements (e.g., how fast/high/far can my body move compared to my friend's?). Risky play is an amazing way to encourage math learning in kids (see this post for more information). 

 

I'm often asked by others how children become so attuned with their surroundings and invested in their work in the natural world. I believe that it is because we spend so much time outdoors that children are so immersed and excited. As educators we act as play partners with the children and explore together. We use a 'notice and wonder' thinking routine where we think aloud about something we are curious about (e.g., "I see the leaves swirling in a circle on the pavement. I wonder what is causing them to move that way.") and model for children how we might go about exploring this further (e.g., "I think I'm going to record what I see using my device so I can watch the leaves moving again and think about why this is happening."). I also really enjoy standing away from children and just listening to their observations and theories about the world around them. The things they notice, and the questions they ask, provoke some of the deepest math learning experienced in our program. Children are deeply invested in their work. 

 

Since children become so aware of their surroundings, they are often quick to notice changes. The landscape evolves as the weather and seasons shift and these patterns offer many mathematical learning opportunities. Knowing the land so well also means that children become invested in caring for it and understanding how and why we need to be sustainable learners. 

The children were proud of their abilities to balance on a wiggly log. They decided to count as they stood on it, and see if they could beat their 'time' with each subsequent try.

 After finding a pair of ladybugs in the grass the children created a 'home' for them using natural loose parts. Interesting discussion occurred regarding what the ladybugs would need in their home, and what size would be best for each feature (e.g., bed, kitchen).

 The children enjoyed picking dandelions one spring day. We challenged them to see who could find the longest and shortest stems. Without measuring tools the children had to figure out how to fairly measure each stem. 

Although we are lucky to have a lovely, large play yard to use, exploring nature can happen anywhere. Even a puddle has the potential to spark children's imaginations and facilitate rich discovery and discussion. If your space is limited, consider going on nature walks around the community in which your school is located. Perhaps a trail or garden can be visited nearby. Field trips are also a fun option (e.g., orchard, farm). Bringing natural objects into the classroom is another way to help children connect with nature (e.g., pumpkins, sticks, acorns) and continue their explorations after outdoor time has ended.

 The children marvelled at the circumference of the large trees located near our school. We asked them how they might measure and compare the trunks in order to find the largest one.

 After making snowballs on a winter day the children thought it would be fun to see how many they could stack inside angled branches of a tree.

 

Prints in the snow always spark rich conversation about who (or what) might have visited the yard. 

 

Dew drops on a web discovered early one morning led to fascinating theories about how strong a web must be. 

 

Finding fossilized rocks and identifying shapes and patterns leads to some great imaginative thinking about what might have lived within the rock long ago.

 

Some tips for getting started:

• Learn more about your local habitat so that you can facilitate discussions with children regarding interesting objects and events that occur in your area (e.g., native plants, migration patterns).
• Go on guided walks to help children practice using their senses to observe the world around them. Scavenger hunts focused on the senses can be fun and spark inquiries (e.g., listening walks, bird hunts).
• Start collections of objects found outdoors that can be displayed in classroom (e.g., feathers, seeds, dried flowers).
• Provide challenges for children that will help them interact with natural materials (e.g., Can you build a house for the ladybug? Can you find and order ten sticks from largest to smallest?).
• Use tech to support your work outdoors. There are many great apps that can help you identify leaves and insects. Posting ideas and questions on social media can facilitate discussions with others from different areas.
  
• Take photos and videos of children's work outdoors and share this for reflection during a consolidation circle. Use the discussion to help spark future work outdoors (e.g., Today we found many flower patterns in the garden. I wonder if there are patterns on other living things in our yard.).  

It's rare that we don't visit the outdoor space. On the days when it is too stormy or cold to head out, we often find children watching the outside world through the windows. In a time when children may suffer from a Vitamin N(ature) deficit, spending unstructured time outdoors without the distraction of toys or teacher-prepared materials may spark a deep love of nature and facilitate rich math learning that would not be possible otherwise.

Patterns in Nature

"Go down deep enough into anything and you will find mathematics."

Dean Schlicter

It's amazing what you can see when you look at everything through a mathematical lens. 

On Friday one our of children came to school clutching a tiny snail in his hands. He was so excited to share it. "Look! It's so small and slimy!" he giggled as he opened his fingers and revealed it to his peers.  The children asked if we could put it in a clear glass aquarium so they could observe it for the day. 

In kindergarten this is not an uncommon request; children find many treasures in the outdoor world and bring them inside in order to explore them further. We are always finding natural artifacts in our classroom - rocks kept in the children's coat pockets, wild flowers stored in cubbies, pinecones and leaves strewn about the room. The old me - the teacher who I was before I fell in love with math - would have smiled at the children as they observed the snail and complimented the experience with literacy materials such as nonfiction books and drawing tools.

But on Friday this was not the case. Ever since my own mathematical mindset grew over the last few years, I saw this as the perfect opportunity to ask the children what math they noticed in the snail.

"Shapes...it's a circle! I see circles!"

"There are swirls on it, like when we made swirly lines with the gems."

"It's little and other snails are big."

"We can see how far it goes with it's slimy trail."

"I see a pattern...the shell has colours on it."

Although there was interest in all ideas, the children focused mostly on the patterns on the snail's shell. I wondered if it was because we had recently explored patterning with loose parts.  

The children helped me create a 'Patterns in Nature' exploration area where the snail could be observed and other natural patterns could be investigated further.

I added close up photos of other animals so that the children could notice many interesting and different patterns...

It was fun guessing what animal owned the pattern and seeing the different ways we could describe what we saw, since many patterns were not neat and linear and had to be investigated further in order to be uncovered.

We also added some nonfiction books about shells and other patterns in nature. Photos of patterns from a recent trip to Fighting Island were also added to the centre so our SK children could reflect upon their experience on that trip and make connections to the current activity.

Some children spent time observing and drawing what they noticed while others just enjoyed watching the snail.

Later in the day we went outside for some play and the children began noticing some of the patterns occurring in the garden. I encouraged them to document what they saw using the class iPad.

Here are some of their findings. Can you guess what where these patterns might be found?

Many people wonder how children can engage in rich mathematics in an inquiry-based, child centred classroom. Although I also introduce ideas to children through interesting provocations and whole/small group lessons and activities, it's easy to see from the small act of a child bringing a snail to school how educators can cultivate a genuine interest in and appreciation of math in daily events. When one looks at the world through math-coloured glasses, you never know what you might discover! Math is everywhere!

What's Inside?

Last week the children were very interested in seeing what they had each brought for snack. There were some great conversations happening at the snack centre about what the food looked like, smelled like, and tasted like.

 

Today I brought in some different kinds of squash. I wanted to extend the children's interests and thought this would be an engaging way to do so.

 

First we passed the different squash around the carpet. The children were encouraged to use many senses to explore; what did the squash feel like (exploring textures), how heavy was it (exploring measurement), how did it look (noting similarities and differences). This was also a good activity to reinforce turn taking.

During playtime the children were invited to explore the inside of the squash. This lead to many interesting math discussions - equality (2 halves of a squash are the same as 1 whole), estimation and counting (how many seeds are inside), measurement (which squash is biggest? which has the biggest seeds?) and shape (some squash are round and some are not). The children also practiced their fine motor skills as they used the tweezers to pick the seeds out. This took a lot of patience and perseverance because the seeds were slippery and stuck in the squash guts!

 

 

Families we are hoping to cook some squash for the children to taste. If you have any you are able to donate to our room, we would appreciate it! Also, if you are interested in volunteering to help with this activity, please let us know! Thank you!

Our Garden

Our children were so excited to plant their own seeds today. Thank you to those families who sent in donations. 

Children took total responsibility for this experience today - filling their pots with dirt, choosing their own seeds, planting the seeds, writing the name of their seeds on a stick and watering the seeds. 

We included art and literacy in our planting area to help showcase what we planted and share our ideas with others.