Wednesday, November 25, 2020

Different Number Fonts

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.

Observing before interjecting allowed me to notice the amazing math repertoire children brought to their experiences as they manipulated the dice, examined the paper, made connections between the different representations of the numbers, and created their own games.

Click here for a copy of the number pages to use in your classroom! 

Sunday, November 8, 2020

Risky Play Inspired Math

"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." 

"I'm a little nervous to step on it. I'm not sure if it will tip, but I want to try and see if I can do it."
"Watch me! This stump is so tall that it helps me go super high when I jump off."
"I'm the tallest in our class when I stand on the big stump. I'm even taller than Mrs. McLennan!" 

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

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.

Thursday, October 22, 2020

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:

Friday, October 9, 2020

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.

Friday, August 28, 2020

In Conversation With TVO Teach Ontario

 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

Inspiring Math Learning Outdoors using Moments and Photos

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... 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

Interview with CBC Afternoon Drive


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:

One LaSalle-area kindergarten teacher took her math class outside


Sunday, March 15, 2020

Spring Math

The last week has been interesting for those of us adjusting to a new kind of normal here in North America. Like many of you, my family and I had a whirlwind of a week - cancellation of a trip two years in the planning, notice of school closure for weeks after our March Break, no time visiting family and friends, and limits to how often we are travelling in our local community.

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

Here are some fun ways to get outside and see/think/wonder about the math you discover:

1.  Natural and Man Made Patterns
Go on a hunt and see what patterns you can see or hear (e.g., bird calls, veins on leaves, fence posts, brick designs, tile mosaics). Bring a clipboard and crayons and ask children to copy and extend the patterns they see. Ask children to classify the patterns as natural or man made.

2.  Same and Different
Choose two or more random objects from the outdoors (e.g., a rock and stick, a leaf and bird). Ask children to describe the characteristics of each and see how many similarities and differences they can find between the two objects (e.g., a rock and stick are both hard and nonliving; a stick is longer than a rock).

3.  Number Hunt
Choose a range of numbers appropriate for the age of the child (e.g., 0 to 10, 0 to 20, 0 - 100). Create an easy template for children to use that help them track the numbers they see. Go on a walk with your child and encourage him or her to record how many of each number they can spot by placing a check mark next to the corresponding number on their sheet. At the end of the walk calculate how many of each numbers were spotted and analyze your data (e.g., which number was spotted the most, least, the same).

4.  Estimate and Count
Before venturing out with a specific destination in mind (e.g., biking around the block, walking to the mailbox) ask your child how long it will take to get there (e.g., five minutes to bike one block, twenty steps to the mailbox). Decide how you will conduct an accurate measure (e.g., use a stopwatch to time your bike ride, count steps as you walk). Once you have reached your destination compare your estimate to the actual measurement. What do you notice?

5.  Shape Hunt
Take a sketch pad and pencil with you on your next walk. Encourage your child to spot shapes in the world around them. Ask you child to consider if these are natural or man made shapes (e.g., a round flower, a triangle in the climber). Encourage your child to sketch a picture of the shapes they find or take digital pictures that can be reviewed at a later date.

6. Shadow Play
Experiment with how your shadow reflects your exact movements by playing in the sun. Ask your child to consider whether or not the shadow is a reflection? Ask them to explain their thinking and justify their reasoning. Play with shadows at different times of the day. Digital photos can be taken and the lengths compared.

7. Wiggly Worms
Worms are a treat for many children to find on wet, spring days. Ask the child to closely examine how the worm moves, and hypothesize how it travels so easily without arms or legs. Worms move by constricting their body muscles in a pattern. Ask the child to closely examine the stretching and pulling motion that it makes while wriggling about.

8. Puddles
Children love to jump and splash in puddles. Puddles offer children many rich math opportunities too! Ask a child to determine how deep a puddle might be (e.g., looking at how high it is on their boot, using a stick). Ask the child to hypothesize how s/he might go about measuring just how much water is in the puddle. Watch the puddle over time and record how long it takes to evaporate. Note how much smaller it is each day by drawing the outline with sidewalk chalk each passing day and comparing the different rings to one another. 

9. I Spy
Encourage children to pay careful attention to their surroundings. While walking outdoors look for interesting designs. Play a math "I Spy" game with children using only math clues (e.g., "I spy something with a circular pattern." "I spy something that has a growing pattern.").

10. Bubbles
Blowing bubbles provides an opportunity to engage your child in rich discussions about open ended math questions: What is the biggest/smallest bubble you can blow? Why is the size of the bubble different depending on the force of your breath? How high/far do you think your bubble might travel? 

11. Unusual Numbers
Encourage your child to look for numbers in unusual places (like the 185 on this hydrant). Ask your child to identify the number, and hypothesize the purpose for the number. See if you can find other similiar objects with numbers too (e.g., find other hydrants and keep track of what numbers are listed on each).

12. Foil Textures
Look for interesting textures outdoors (e.g., tree bark, bricks, paving stones). Give your child a small piece of foil and encourage him/her to smooth the foil on top of the object, carefully revealing the texture as the foil is pressed and molds against the object.

13. Number Challenge
Keep track of the different numbers you find. Challenge your child to find specific numbers (e.g., the highest number, the lowest number, their age, an even number, an odd number).

14. Sorting Rule
Find an interesting collection of objects (e.g., pile of rocks, sticks, flowers in a garden). Ask you child to list as many different ways that she/he could sort the objects as possible (e.g., sort by size, colour, shape, function). If possible ask your child to physically sort the objects.

15. Different Number of Groupings
Challenge your child to find groupings of objects. Can you spot 2s, 3s, 4s, & 5s? Here we spotted 3 groupings of 3 grasses for a total of 9 similar plants in the yard. Encourage multiplicative thinking when asking your child for the total number of objects (e.g., Three groups of three equals 9.).

16. Tape Resist Art
You (or your child) can create an interesting geometric design with tape on a flat, outdoor surface. Fill each section of the tape with sidewalk chalk or paint. When each section is filled, remove the tape to reveal a beautiful piece of mathematical art!

17. How Many Steps?
Find a challenging walking surface, like the wooden beam at the edge of a garden. Encourage your child to walk one step after the other along the length of the beam. Count each step. See how many steps your child can walk before she/he steps off the beam. Challenge your child to reach the highest number she or he can!

18. Leaf Patterns
Look for leaves on your walks - new leaves are emerging with the warmer weather and many older leaves are preserved in piles gathered in landscaping. Turn the leaf over and examine the vein pattern you discover. Use crayons and paper to create rubbings of all the different patterns you find.

19. Measuring Stick
Create a 'measuring stick' by finding a sturdy branch outside and wrapping it in equal segments using a heavy duty duct or masking tape. This is a nonstandard measuring tool so as long as the segments are equal, it will work. Encourage your child to explore the outdoor space and look for different things to measure (e.g., the depth of a puddle, the height of a plant).

20. Outdoor Easel
Create an easy 'easel' for painting or drawing still life observations outdoors by using a recycled plastic hanger to attach a paper to the fence. The hanger prevents the paper from blowing in the breeze, and can be used to hang the painting until it is dry. Encourage your child to paint or draw patterns that are visible in the outdoor space.  

21. Real Life Arrays
Encourage your child to look for real life arrays while exploring the neighbourhood, Help your child reframe the array as a multiplication sentence (e.g., "Three rows of three is the same as three multiplied by three.") and ask you child to calculate the product.

Spring Math Walk

To help inspire children and provide background information regarding the math that is accessible in the natural world around us, I am making the Kindle version of my newest book Spring Math Walk free on March 19. This offer is only valid on the site. I will add additional dates in the future. I'm hoping that this free resource will be of interest for families looking for additional math information for their children - helping them venture outdoors and becoming inspired by the amazing math nature has to offer!

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