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.