It's always interesting to see how children innovate math materials. This week we provided pages with the numbers 1 to 10 written in interesting fonts. We offered each child a dabber and two dice and encouraged them to create their own games.
Wednesday, November 25, 2020
Sunday, November 8, 2020
"This stump is kind of wobbly. The first two are strong but when I step on the last one it wiggles when I stand on it."
The children were playing outside. I was fascinated as I watched them bravely climb onto different sizes of stumps lined in a row. The first two were solid and level but the last was visibly uneven. As children stepped onto it, it teetered and moved under their weight. Because it was much taller than the other two stumps, it was difficult for children to step onto, making it a challenging physical feat. Children lined up and attempted to balance on the uneven stump, jumping higher and farther from it with each subsequent attempt. By the end of our outdoor play time there was a line up of children waiting patiently for their turn - each eager to see if they could outperform their last big jump.
Risky play, like climbing and jumping off stumps, is incredibly important for children. They feel empowered as they engage in difficult tasks, building their physical and mental endurance. Children persevere through difficulties, building their grit and stamina and feeling untouchable in their moments of triumph. When children are successful in risky tasks, they take pride in their achievements and feel unstoppable. They feel inspired to tackle new opportunities and go further in their explorations. This helps build their confidence and sense of self. They feel like they can do anything!
As a big believer in risky play I recognize the many personal and social opportunities for learning that exist in challenging activities. However watching the children explore the stumps, I recognized that risky play also provides multiple opportunities for authentic and engaging math learning. Children are often eager to mathematize their achievements by calculating how fast, how far, or how high they have moved. As the children climbed and jumped, they were discussing balance, height, length, and time. They counted how many children were in line for a turn and discussed their place within it. They created a system for measuring the height and distance of each person's jump, and tracked these to compare growth. They strategized for how to improve their performance and planned for creating a more difficult obstacle course using additional stumps for future outdoor play times. A simple natural object like the stump created opportunities for rich STEM learning that were highly motivating and meaningful for the children. The math they explored was child-centred and authentic, and deeply connected to their immediate world.
It's easy to understand why educators (and families) shy away from risky play. We worry about children getting hurt and the consequences of these actions, especially in a playground or school setting. But depriving children of risky play sends the message to children that they might not be capable of achieving a goal. They may misinterpret our fear of the experience as a mistrust of their abilities. These hidden messages may result in children wondering about their own interests, strengths and needs, and fearful of taking other risks in their lives at school and beyond.
Encouraging and supporting risky play sends the message to children that as adults we trust and support them in difficult tasks. We acknowledge that they might be nervous or apprehensive to try something new, but let them know we are here to help them through the experience. Children develop a growth mindset and embrace mistakes and missteps as learning opportunities when they overcome an obstacle.
Co-creating shared understandings and expectations for children regarding the play is a great way to get started. Have an honest conversation with children about the benefits and risks of the activities, and brainstorm how to keep everyone safe throughout the explorations. As children gain experience in the activity they can add ideas to the overall expectations for play. Encouraging sharing afterwards can help children articulate how the risky play went - what worked well, what needs to be improved, and what can be done differently in the future.
Over the course of several days the children continued to play with the stumps. As I observed them I continued to notice math emerge in their work. Joining as a play partner helped me notice and name the math I saw, and scaffold and support their inquiries. I'm curious to see how their obstacle courses continue to evolve as we enjoy the lovely fall weather and spend more time together outside.
Wednesday, October 28, 2020
The children were gathered for whole group. I displayed a collection of pumpkins and asked them a question - which one does not belong?
- develop specific content ideas
- meet different standards
- develop playful mindsets in children
- practice problem-solving models
- facilitate communication skills
- what is the purpose of the math talk?
- what big mathematical ideas are you hoping to embed within the conversation?
- what are the needs of children and is the talk differentiated enough to include all?
- what directions do you anticipate the conversation taking?
- what assessment opportunities will the math talk provide?
A starting point for any math conversation is to provide a tangible artifact for children to explore (e.g., a pumpkin, piece of artwork, collection of loose parts) and ask them to notice and name what they see. Once they articulate their observations about characteristics of the object (e.g., shape, size, colour, texture, smell) they can make connections between these and the world around them (e.g., other objects, experiences, texts). Perhaps questions emerge in the conversation and children can wonder about some element of the object or conversation. This can lead to a research query to explore further.
Thursday, October 22, 2020
PODCAST: Building a Curious and Playful Early Childhood Math Community
In this episode of Teacher's Corner, I talk about my new book, Joyful Math. I also discuss how to nurture a curious and joyful early childhood math community with the author of Early Childhood Math Routines, Antonia Cameron.
Click here to listen: https://blog.stenhouse.com/podcast-building-a-curious-and-playful-early-childhood-math-community
Friday, October 9, 2020
"Look! Look at this spider! His legs are so long! Let's call him Mr. Big Legs!"
The children found an interesting spider in the garden one day. Curious, they gently picked it up and let it climb up and down their arms. It was so graceful in its movements that even reluctant children came for a closer look.
"He's so cute! Why was he in the garden?"
"Maybe that's where he lives."
"How do you know he's a boy?"
"The garden is so boring for him - nothing is growing right now."
"I know! Let's build him a playground!"
Curious about the children's ideas and how I could use their interest in spiders to enrich our outdoor space, I took photos and mentally planned for how we might proceed next. I considered what curriculum expectations might be met, and anticipated the math that might emerge. Such a simple and quick interaction with nature sparked a rich mathematical inquiry in our outdoor classroom that lasted for several days.
Our first step was to conduct some research. What did children already know about spiders? What did they wonder about Mr. Big Legs specifically? How might they design a playground that he would like? What could they use to help them acquire more information?
We read a number of texts together to gather information that might help enrich their understandings of what exactly a spider was and needed in order to survive. We organized our ideas on a large chart paper and referenced this over the course of our inquiry.
While exploring our school yard for more spiders, we noticed a really interesting tunnelled web just outside our window. The location was the perfect place to set up a 'spider observation window' where children could safely check on the spider during play time and carefully watch it in its habitat. Not only did this give children an additional opportunity to research, it provided children who weren't comfortable holding a spider a safe way to observe one up close without needing to handle it. (We wondered if the spider had eaten two others, or if this particular one shed its skin.)
Their work was stunning; the level of thought put into creating the tiny structures was incredible. Children considered measurement and proportional reasoning as they built to scale. Here are some of their creations:
A bed - notice how the sticks point upwards in a circular direction and there are leaves to cushion the center. "The leaves will be so comfortable for him! It will be a soft place to sleep, and the sticks will keep other bugs away."
A swing - notice how this child has balanced the top section of the swing onto two sticks. Later on he would add a long, slender leaf in the middle for Mr. Big Legs to swing on. "I hope that he can balance because this isn't very stable right now."
A garden - this child dragged his fingers in the dirt to make rows for Mr. Big Legs to use when planting rows of vegetables. "They need to be evenly spaced, because they need room to grow. That's what my dad does in our garden."
A slide - this child placed two sticks together on a slope resting in the corner of the garden. "I wonder if he will know to lift his legs. If he doesn't then he won't go down as fast because they are long and will bump against the slide."
A bridge - this child broke twigs so that they were approximately the right fit to be placed in the narrow hole in the garden. "I couldn't find any sticks that fit, so I broke them. I think Mr. Big Legs needs a bridge in case this hole is too deep for him. If it rains maybe he can pretend it's his pool.
Towards the end of the week the children found another Mr. Big Legs climbing on the brick wall. They eagerly picked him up and placed him in the garden so he could explore everything they had created. Proud of their work, they pointed out each structure and explained to him how he could use the equipment.
"This is your slide and here's your swing. You can play on those!"
"I made you a garden in case you don't catch any bugs in your web."
"And when you get tired, here's a bed for you to sleep on!"
I couldn't help but smile at their enthusiasm. I was amazed that something as simple as finding a spider in our yard could inspire such authentic STEM learning.
Friday, August 28, 2020
I was very excited to share some of my math ideas with the 'In Conversation With' feature of TVO Teach Ontario. You can read our interview here: In Conversation with Deanna Pecaski McLennan.
Friday, August 21, 2020
The world outdoors is filled with amazing math moments. Almost anything you find - whether it is natural or man made - contains an element of math.
From the symmetry we find in flowers or garden wheels...
...the interesting shapes we can spot in structures and found objects...
...the uniquely formed angles hiding in unexpected places...
...to the potential for discovering and playing with numbers.
The world around us uses math in the most interesting of ways.
Many educators are looking ahead to this school year, wondering how to engage children in authentic math moments while decreasing the risks associated with the current pandemic. Many experts recommend holding classes outside. This option is appealing, but some wonder how to take the math learning they traditionally offer in the classroom to the world beyond. How might one fulfill curriculum expectations and assess student learning while being outside?
I suggest looking to the world around you for math inspiration!
Whether you are a teacher who will be holding your classes outside, or planning to engage children in online learning, using the outdoors to inspire math talks can be an authentic and exciting way for children to delve more deeply into math concepts while seeing their application to real life.
Teachers can chose specific photos or places in the yard to introduce curriculum concepts needed to be covered (e.g., showing a photo of rain drops in a puddle to introduce the concept of radial symmetry) or ask children to see/think/wonder about a phenomena they notice and planning a mathematical inquiry centred around this (e.g., estimating and then problem solving for how to calculate the number of daisies that have grown in the garden).
There is math potential everywhere!
To help get you started, I have compiled a collection of 75 photos featuring natural and man made objects from the outdoors. You can access these here: Photos to Inspire Math Conversations
Feel free to use them to inspire math conversations in your physical classroom, or during an online math talk. Download them, print them, use them however you'd like to facilitate math learning with your students. Heading outside to explore math might seem daunting at first, but listening to the observations and questions that children have can be a wonderful start to a rich, mathematical inquiry.
I'd love to see the math learning you experience as we head back to school. Don't forget to tweet me @McLennan1977 and share the amazing #foundmath you discover in your explorations outdoors!
Thursday, August 20, 2020
It was a pleasure to chat with Chris dela Torre about my award winning paper 'The Beautiful Tree Project" on CBC's Afternoon Drive! To listen to our interview check out the link:
Sunday, March 15, 2020
The first few days were surreal; I had a difficult time saying goodbye to my students on Friday, wondering how long it would be until I saw them again. As my teaching partner and I prepped our centers and morning message, we worried about when the next time we would see each other might be. I walked out of school bringing home my plants, teaching materials, and personal belongings, not knowing when I would return.
In times of uncertainty, helping one another is one of the best ways to get through the stress and worry of what awaits. I know that many educators and families right now are wondering how to help support children even when we can't be together physically.
I love math. I also love to help educators, families and children love math. I have decided to create this blog post in order to continually provide ideas for how children can explore math in their natural world. The CDC is asking us to engage in social distancing and being aware of what is recommended is important. Right now being outdoors in our yards, on trails, and in gardens is still safe and encouraged. I realize that some of us are limited by our personal circumstances and not everyone has access to a yard or natural trail. I will try my best to vary activities in order to meet as many circumstances as possible. I will also tweet ideas for math learning on a regular basis @McLennan1977.
My hope is that the website will give ideas to educators who might be providing virtual support to the children and families in their care (e.g., if you are providing home schooling ideas, if you are engaging children in virtual classrooms), or ideas for families who are trying to engage their children in a sense of normalcy by playing and exploring math together in the outdoors. Check here regularly for new ideas as I will add more every few days, and feel free to email me questions or suggestions email@example.com.
Here are some fun ways to get outside and see/think/wonder about the math you discover:
1. Natural and Man Made Patterns
2. Same and Different
3. Number Hunt
4. Estimate and Count
5. Shape Hunt
14. Sorting Rule