Sunday, June 4, 2023

Eight Way to Encourage Math Learning During Risky Outdoor Play

This month I have a blog post featured on the National Association for the Education of Young Children's (NAEYC) website regarding how to engage children in math learning during risky, outdoor play. You can read the article here: Eight Ways to Encourage Math Learning During Risky Outdoor Play.


Sunday, May 28, 2023

STEAM in the Garden: Constructing Insect Houses from Natural Loose Parts

"Look deep into nature and then you will understand everything better."

Albert Einstein

The children were gathered around a large landscaping rock, working together to arrange twigs and stones they had picked from the ground nearby.
"I think that this side should be the living room and the bedroom can be over here," Jack gestured as he spoke. "The living room will be next to the bedroom and the ladybug can crawl across by using this little bridge."
"So what are these little sticks here for?" Mary pointed to a little row of twigs placed next to each other.
"Oh, those are going to be the bed." Olive answered.
"But that's way too big to be a ladybug's bed," Mary responded.
"Oh," Olive pondered. "I didn't think about that."
"That's okay," Mary smiled. "We'll just find more than one ladybug and then the bed will be the perfect size." 
Spring was in the air and the children were excited to discover that many little creatures were venturing out into the warm sun. Ladybugs, rolly pollies, and worms were abundant and this sparked the children's imaginations. Eager to 'help' the insects the children set to work building little houses for them. They searched the yard to gather materials they felt would be best suited to this task. I resisted the urge to bring out materials from the classroom because I wanted the children to be resourceful and use their imaginations by only having access to natural loose parts. 

Children first started by capturing an insect from the yard. The insect caught would determine the size and type of house built. Creatures that had wings and flew required a different style of house than those that were slow moving. 

Next the children sketched and planned the appearance of the house. They considered the available materials (e.g., sticks, stones, leaves, flowers, landscaping rocks) and used clipboards, paper and pencils to draw their designs. Once satisfied with their blueprints they began the building process. This occurred over the course of several days as children revisited, reflected and refined their houses. Sometimes new insects would be found and this would cause the process to be restarted. It was interested to sit back and observe the children as they worked and discussed their creations. I was available to offer support and encouragement as needed but left the children to their own ideas and explorations.  
For many educators a barrier to spending significant amounts of time outside is a lack of human made resources. This experience demonstrates that when children are invited to follow their ideas and only use materials that Mother Nature provides, the potential for math learning is as endless as their imaginations. 

Where's the math?

  • considering and comparing the characteristics (e.g., size, shape, colour, texture) of different loose parts including stones, sticks, acorns, leaves and flowers
  • spatial awareness as loose parts were pieced together to form the house
  • spatial reasoning as children considered how an insect might move through and manipulate elements in the structure
  • proportional reasoning as the house and its characteristics needed to be constructed to an appropriate size for the insect
  • process of design as houses were planned, built and refined to best suit the interests and needs of the children (and insects)
  • counting the number of loose parts needed
  • sorting as the loose parts were collected and placed into groups
  • calculating area and perimeter as the outside of the structure was made (e.g., rocks as the walls) and the inside decorated (e.g., sticks for the floor) 
  • growth mindset, flexibility and perseverance revising the plan when it didn't work as anticipated
  • articulation of math ideas as children explored one another's designs and asked questions for clarification and made observations about one another's work
  • the sharing of math thinking as photos were taken of each structure and children presented their work during the end of the day consolidation circle.

Tuesday, April 25, 2023

Calendar Math: Daily Date-Inspired Prompts to Inspire Math Talk

Math talks are regular, short conversations about purposeful math problems with children. These are intentionally crafted to invite children into specific math situations, helping them to improve their mathematical confidence and abilities. Math talks are meant to be open-ended opportunities that have multiple entry points and approaches for interpreting and solving the problem. To learn more please read my article Joyful Number Talks in Kindergarten available here:


The Journal of Teaching and Learning

Vol. 13, No. 2 (2019) pp.43–54


In my classroom I engage children in daily math talks during our first whole group time together. I often use the date as a focus for the number talk. For example, if the date is December 10, I use the number ten as the focal point of our math exploration. 

Over the years I have shared my math talks on social media and have been asked repeatedly to create a guide to support educators who wish to engage their students in math talks. This served as the inspiration my book Calendar Math. This book provides photo prompts and accompanying questions is that educators can use these to engage children in regular conversations in the classroom. In the book each calendar date (numbers 1 through 31) has four different pages with accompanying prompts. Use them for different months and also as sparks for creating your own daily number talks with children. 


To help educators get started here is a collection of photos representing the numbers 1 to 31 available as a PDF file. They can be digitally projected or printed and used as part of your morning math talk. Feel free to use them to support and supplement math discussions with your students!

Saturday, April 22, 2023

Creating Geometric Art Outdoors

 “Colour is a power which directly influences the soul.” 

Wassily Kandinsky 

We spend at least an hour outside each day, rain or shine. Often explorations in the yard are child directed but occasionally I like to offer invitations for learning - especially those that integrate math and art. A popular activity this week was creating geometric chalk art. It is a very easy and effective way to explore spatial awareness. 
Step 1 is to create a shape on a flat surface using masking tape. Divide the inside into smaller shapes.

Step 2 is to invite children to colour the inside of each shape using a different shade of sidewalk chalk.

Step 3 is to remove the tape once the shape is completely coloured and admire the artwork!

It's fun to create different sizes and shapes of chalk art...

...and incorporate it into dancing and jumping games!

Sunday, April 16, 2023

Using Outdoor Discoveries to Inspire Rich Math Talks

"It's the little details that are vital. Little things make big things happen."
John Wooden

Now that spring is emerging muddy conditions are common in our school yard. Although some educators shy away from messy spots, I find they are often one of the best places to notice and name rich, authentic math.

One morning the children were exploring the yard and noticed interesting tracks on the path. They took their time observing the different prints they found. They wondered who had been visiting the space and how the markings were made. They noticed that the prints appeared to be dried in the dirt and preserved in the thick mud. 

The tracks that fascinated us the most were those made by animals. Our school is located near a wooded trail and our yard is frequented after hours by coyotes, deer, geese, wild turkeys and dogs. The children compared the different tracks and used their prior knowledge to try and identify the animals. We also used a handy animal tracks identifier to help us as the difference between some tracks is minimal.
The children were also very curious about the shoe/boot tracks that they found alongside the animal tracks. Within each we noticed intricate shape and line details that differentiated them from one another. We identified many shapes including circles, diamonds, hexagons and squares. There were also many different lines in each - straight, wavy, and zigzag.


We wondered if our footwear matched any of the tracks. The children examined each other's feet to see if they could find a match between their shoes and any of the tracks. This inspired rich observation and discussion as small details were noted and comparisons were made. 
In order to capitalize on this interest I printed large photos of a shoe and animal print and brought them to our whole group discussion. I asked the children to consider what was the same and different about each print. I also used the thinking routine 'see, think, and wonder' to facilitate math talk and help the children mathematize the photos. 
We also brought this interest in prints to our art center where children were invited to paint our spare classroom boots and stamp them to see what kinds of prints they made. 
Once the tread prints were dry the children brought them to our whole group gathering time and we continued to observe and discuss the shapes and lines we saw in each. The children grouped the prints according to similarities and also compared the size of the marking to their feet in order to see which was the bigger foot. 
As spring weather continues to bring rain, the children's interest in tracks endures. The children are now curious about how long an entire track path is, how deep the prints are in the mud and how much space is in between each print. They wonder about how far and fast the person or animal might have been travelling and use these clues to help them hypothesize the speed and distance. Each time a discovery is made in the yard I carefully document the findings using photos and videos so we can bring the information back to our whole group conversations and build our collective knowledge about tracks. 

Our next step will be to record ourselves making tracks in the mud using digital tools. We will use the different recording options on our smart device including time lapse photography and slow motion recording. These will be interesting to watch and will hopefully help us understand more clearly how the distance, pressure and speed of movement will affect the way a print is made in mud. Stay tuned! 

Looking for a resource to support mud play? Check out my book Muddy Math available on Amazon!

Thursday, January 5, 2023

Daily Math Talks with Young Children


  “Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making, and interpretation of methods; it is a set of ideas that helps illuminate the world; and it is constantly changing.”
Jo Boaler

Math talks are a great way to engage children in open-ended explorations that invite them to think critically and creatively about a concept. An effective math prompt to facilitate a rich math discussion will be layered; it should be open-ended with multiple entry points for engagement. Even children as young as kindergarten are capable of participating in complex math conversations. In our classroom I aim to invite children into a math talk at least once a day; I sometimes use the numerical date on our morning message as the spark for exploration. Other times an interesting photo or collection of loose parts will be engaging and incite children into further exploration. I try to vary the invitations I provide in order to diversify the math we discuss and to reach as many learning interests as possible.

Recently I posted two Instagram Reels regarding our daily math talks that has generated many questions regarding how we engage young children in robust discussions about math each morning. There was much interest in these math prompts and many educators reached out with questions regarding how I create these prompts.

In our program we have a morning circle time. This circle is our first whole group gathering time for the day and helps set a positive atmosphere in our classroom. It is also a time to celebrate being together, and share news from our homes. We often use it as an opportunity to read a story and discuss any new and exciting activities or additions to our classroom space about which the children should know in order to be successful for the day. 
When I first started teaching kindergarten many years ago it was expected that the morning circle would begin with 'calendar time' where children would put a sticky number on a large grid to depict the day and there would be an extensive discussion about the calendar (e.g., day of the week, month, year). However over the years I realized that this was a very teacher-directed task and not as meaningful a use of our time. After reading Sherry Parrish's work on number talks I was inspired to use our morning message as an anchor for math talks. Wanting to still introduce the date to students, the numerical representation of the date became the foundation for our number talks most days. Sometimes I would use other prompts depending on the events and interests emerging in our classroom. If you would like to read more about number talks in kindergarten, you can access an article I wrote for the Journal of Teaching and Learning here: Joyful Number Talks in Kindergarten
I enjoy participating in a professional learning community with educators on social media and often tweet or Instagram my number talk prompts. Many educators have reached out to me how I create these open ended math talks, and to ask if I would consider sharing some ideas to try. Here are some examples of number talks we have used in the classroom. Feel free to share your own ideas in the comment section or tweet/instagram me @McLennan1977. 

To help support educators who are interested in starting daily math talks with children, I have published a book called Calendar Math: Daily Prompts for Math Explorations with Children

To help give an idea of what this book is about, and to help educators create their own math prompts, here are the first few pages of the book!


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