Which One Doesn't Belong? Using Autumn Treasures to Inspire Math Talk

 The children were gathered for whole group. I displayed a collection of pumpkins and asked them a question - which one does not belong?

"I think this one doesn't belong. It's got the thickest stem. If you look at the others their stems are thinner. One pumpkin doesn't even have a stem."

 

"No, that one is green. All the other colours are normal pumpkin colours but that one isn't. Green is a dark colour and I don't even think pumpkins are supposed to be green."

 

"What if we make two piles - green and non-green?"

 

"What about this one? It's got the longest stem. That's different from the others. The stem is even longer than my hand if I put them next to each other."

 

"Yeah, but this one doesn't even have stem. That makes it different from the others. I wonder how it grew without a stem!"

 

"I know! This little one is different. It's the smallest. If I put the pumpkins in order by size this one would be on the end. It's teeny-tiny!"

 

"No. This is the one that is different. It's the only one with bumps."

 

Math talks can be incredible powerful experiences for young children; as they engage in interesting and meaningful conversations they uncover problems of importance (e.g., which pumpkin does not belong), engage in a problem-solving approach (e.g., using their senses to explore the pumpkins in depth and making connections between previous experiences and current explorations), and discover a variety of solutions (e.g., justifying why their chosen pumpkin does not belong using descriptive language). This builds confidence and agency in their work as mathematicians. They build theories about the world around them as they support their ideas with observations, draw upon previous experiences, listen to and consider the opinions of their peers, and revise their thinking as needed. Open ended math talks give children time and space to notice and wonder about something they find interesting and meaningful about the world around them. I purposely chose pumpkins for this math talk because the children have been quite excited about Halloween, and curious about the autumn artifacts we have placed around our classroom and outdoor space (e.g., leaves, gourds, decorative corn).

According to Antonia Cameron (2020) in addition to helping educators fulfill curriculum and assessment obligations, thinking routines included in regular math talks can be used to:

• develop specific content ideas
• meet different standards
• develop playful mindsets in children
• practice problem-solving models
• facilitate communication skills  

Children are natural researchers who engage playfully with the world around them. They are driven to answer questions that promote a curious and wondrous mindset. They test their theories and revise their understandings through conversation and experience. Math talks can become powerful learning routines that empower children and build community over time. Children can share their ideas, justify their thinking, consider the ideas of their peers and whether or not they agree with them, and use this information to advance their mathematical understandings.

 

West and Cameron (2013) suggest a number of reflective points for educators to consider when designing mathematical thinking routines including:

• 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. 

Giving children freedom to play with problems empowers them as mathematical learners. They grow their individual and collective mindset as they trust their abilities and engage in productive struggle. They question the world around them and delve deeply into complex wonderings and questions. This provides educators with rich opportunities to infuse complex math ideas into authentic moments of learning; building the big math ideas and spiralling curriculum as needed. Making time for regular math talk in the classroom celebrates children's thinking and empowers them as the amazing mathematicians they are! 

 

Cameron, A. (2020). Early childhood math routines: Empowering young minds to think. 

    Portsmouth, NH: Stenhouse Publishers.

 

West, L., & Cameron, A. (2013). Agents of change: How content coaching transforms 

    teaching and learning. Portsmouth, NH: Heinemann.

New Podcast!

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

A Playground for Mr. Big Legs - STEM in the Outdoor Classroom

"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.)

 

The more the children learned about spiders, the more determined they were in their quest to create a playground for Mr. Big Legs. They designed spaces for him - a garden, house, slide, swing, and bridge - by drawing blueprints on their clipboards. They considered the size, shape, and materials needed for each creation.

     

 

During the next outdoor play time, the children brought their drawings outside and referred to them as they worked in the garden. Some children enhanced their drawings and others started anew. They looked to the materials available outdoors, and planned for how to build using only natural materials found in our space. 

 

                           

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."

An obstacle course - notice how Mr. Big Legs will have to climb through the structure, along the stick, hop on top of each of the stones and land on the leaf. The child who build this sequenced the steps in her course and articulated exactly what the spider would need to accomplish along the way while playing here. "This would be so much fun to play on - do you think he will know where to start and where to finish?"

 

A bedroom - this child created a circular structure so that Mr. Big Legs could weave a web near his playground using the rocks as anchors. She knew that many spiders used webs as a home and place to catch prey, and wanted to be sure he had this in his new area. "Spider webs are circles, so I put the rocks in a circle."

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.