Thursday, October 14, 2021

Autumn Math Walk

 “I'm so glad I live in a world where there are Octobers.”
L. M. Montgomery, Anne of Green Gables 

What a beautiful time of year it is in Southern Ontario! We have been spending much time outside each school day exploring the changes in our school yard. The children are curious about the world around them and ask many questions about their surroundings and the autumn treasures they find. Many of their wonderings have been mathematical in nature - Why is there a pattern on the sunflower's seed head? What are those holes in the stump and where did it come from? Why is a Daddy Long Legs an arachnid and not a spider?  How do leaves change colours? Why are the clouds moving so fast in the sky?

There is math everywhere. If one looks deeply enough, there is always a mathematical connection in nature. The sunflower seeds follow the Fibonacci Sequence - a numerical pattern meant to help maximize space and fit as many seeds into the head as possible. The perfect little circles in the stump might have been caused by a wood boring insect or bird looking deep into the bark for food. Daddy Long Legs have a different body than spiders even though they have eight legs. Leaves change colour because the amount of sunlight they need to create their own food lessens in cold weather (as the Earth's axis tilts us away from the sun), resulting in a chemical change in the leaves. 

I've been motivated to continue to look for rich mathematical wonderings and opportunities for inquiry each time I'm outside - even on the weekend with my own children. I find it fascinating to see math applied in an authentic, interesting, real world connection. The math in nature is beautiful! Inspired by this mathematical beauty I have written a book called Autumn Math Walk that includes photos and narrative to help readers delve deeply into exploring math in the outside world. I've appreciated the interest in this book and loved seeing the ways educators have used the text in their classrooms. Learning from one another is so inspiring!

I'm so very excited to partner with Pembroke Publishers and offer a free teaching resource to complement my book Autumn Math Walk!

Autumn Math Walk Teacher's Guide is a free resource that can help educators understand the math that exists in the natural world, and use this information to provoke conversation and understand with children as they explore nature. Perhaps children will be inspired to author and illustrate their own Autumn Math Walk book unique to their specific surroundings!

Saturday, October 2, 2021

Pumpkin Math

Autumn is such a wonderful time of year! The colours and textures can inspire such rich math conversation! This past weekend we visited a few farm stands in the area and all I saw was math around me! I'm hoping that these photos will be useful as math prompts for 'math talk' conversations with children.

Show children a photo and ask them to share what they 'see, think and wonder' about each photo. The 'see, think, wonder' thinking routine can be used to help children delve more deeply into exploring and articulating what they notice in a specific situation. As children notice and name what they see, they can make connections to their own experiences and ideas, and form questions for further exploration and math research. 

Educators can also ask children specific math questions to guide their thinking. This can be especially helpful if the math concepts in the photos are geared towards an existing exploration the children are having, or if specific curriculum and assessment investigations are needed by the children. Sample math questions are provided below!

How many bumps are on this pumpkin?
 How big around is the stem?
What patterns do you notice?

How are these gourds organized?
What other ways can you sort the objects?
How many do you think are in each bushel? How do you know? 

What patterns do you see?
Why is the pumpkin more narrow at the top?
How big around might this be in the largest part?  

How many pumpkins do you estimate are in this box?
How many pumpkins might fit in the box if it was filled to the top?
How much money do you think the farmer should charge for the entire box of pumpkins? Why?

If these pumpkins are $3.50 each, how much would all of these cost? 
Should bigger pumpkins cost more than smaller ones? Why?
Which do you think is the biggest? How do you know?

Which pumpkin would you pick if you only had $2? Why? 
If you had X dollars, how many pumpkins could you buy?
How much money do all these pumpkins cost altogether?
What symmetry do you notice?
What patterns do you see?
How many pumpkins would a full crate hold?
Which gourd does not belong? Why?
How could you sort these? What's your sorting rule?
How many gourds do you think are in this bushel?
Halloween Math uses the 'see, think, wonder' thinking routine to explore seasonal objects and experiences in a mathematical context and is now available from Amazon!

Friday, August 27, 2021

Joyful Math Trailer!

In Deanna Pecaski McLennan’s kindergarten classroom, math isn’t limited to a specific block of time. It’s built into the environment and inseparable from everything her young students do. All of the math is infused with a sense of exploration, wonder, and joy.

Deanna’s book, Joyful Math, is about creating invitations for young children to engage with math ideas through art, literacy, and outdoor play. She focuses on building spaces in early childhood classrooms where children see themselves as mathematical thinkers with valuable ideas from the very start.

Joyful Math is filled with a range of tools and models, including:

  • stories, vignettes, and photos illustrating how to develop a classroom environment that fosters curiosity and wonder for mathematics
  • practical tips for inviting students to engage in mathematical play throughout the day
  • examples of ways to document children’s experiences to make math learning visible to parents and the greater community

Supported by her experiences exploring math with young children, Deanna’s methods will inspire educators to be curious about math, take risks, try different approaches, observe carefully, and collaborate with children as co-learners.

Get a copy here!

Stenhouse Publishers (United States)

Barnes & Noble (United States)

Pembroke Publishers (Canada)

Amazon (United States and Canada)

Thursday, August 26, 2021

15 Easy Autumn Invitations for Learning

Autumn is a beautiful time of year! There is so much potential for encouraging rich, playful exploration with natural objects that children find fascinating to explore. In this post I will share 15 easy to create autumn invitations for learning that can be presented in the classroom as table top activities, or investigated during outdoor play. These sparks for learning integrate math, literacy and science while offering potential for additional inquiries depending on how children explore and manipulate the materials. 

Educators can observe each activity and provoke further discovery using a 'see, think, and wonder' learning routine. After watching the children play with the materials, ask them to share what they are noticing while playing by stating "I see...". They can then be asked to reflect upon their observations and begin to build their theories about the play by making connections in an "I think..." statement. Finally a question for further exploration can be crafted in an "I wonder..." open-ended query. As children pose questions and share their curiosities about the materials and the world around them, the educator can record observations, reflect upon how to support children in additional work, and gather materials to enhance and evolve the play. 

For example - "I see many different kinds of leaves. I think they might be different sizes. I wonder if I can order them from smallest to biggest."

Natural Objects Colour Matching - recycle paint chip strips by providing them to children and encouraging them to find objects in the yard or placed on a table that match each shade as closely as possible. Encourage children to explore the different shades of each colour.

Roll and Fill the Web - create a spider web by wrapping a shallow basket with thick yarn. Encourage children to roll a die (or multiple dice), add or subitize the pips, and add that many spiders to their web.

Spider Game - create mini catapults by securing a wooden clothespin to a solid block or piece of wood with an elastic. Children can manipulate the catapult and fire a plastic spider into the web. Every spider that lands on the web earns them a point! Children can record their points using tallies, and compare their scores to others.
Measuring Circumference - present a variety of interesting pumpkins and gourds to children. Ask them to suggest ways to measure the circumference of each object. Order the objects from smallest to largest circumference.
Counting Seeds - encourage children to use fine motor skills to remove the inside contents of a squash, gourd, or pumpkin. Provide a variety of tools (e.g., hundreds charts, ten frames) for the to use when calculating the total number of seeds they have removed.
Gourd Runs - present a variety of gourds and recycled floor boards to children. Encourage them to create a variety of ramps and runs to experiment with rolling the gourds down.
Geo-Pumpkins - encourage children to create their own shapes and designs on pumpkins by using pushpins and elastics. Children can push the pins into different places on the pumpkins and then stretch an elastic around them.
Gourd Catapults - present a variety of recycled tubes, wooden boards and mini pumpkins to children. Model how the tubes and boards can be used to make a catapult. Children can be encouraged to stomp on the catapult and launch the pumpkin as far as they can. Brainstorm with children how to record how far the pumpkin travels. Discussing safety rules beforehand is recommended (e.g., ensuring no one is standing in front of the catapult before launching a pumpkin).
Creepy Crawly Pick Up - provide a variety of seasonal trinkets to children in trays. Encourage children to pick up and move the materials using a variety of fine motor tools (e.g., chopsticks, tweezers). Children can sort the materials in the trays in different ways (e.g., by colour, size).
Roll and Fill - provide a template for children to use (grid paper also works). As children roll the dice and add the pips, they then colour the corresponding number of objects or squares on their paper. First to fill a line, section or the entire page wins. 
Big Body Spider Webs - encourage children to wind yarn or twine around natural materials outdoors (e.g., stumps, tree trunks, branches), creating a large spider web. If the web is large enough, children can move their bodies in and out of the web, avoiding the yarn as an obstacle course. Large plastic spiders can also be added and the web transformed into a dramatic playscape.
Pumpkin Weigh In - provide a variety of measuring tools (e.g., balance scales, digital scales) for children along with a collection of pumpkins and gourds. Encourage children to measure and record the weight of the objects. Provide challenges like asking children to find the lightest/heaviest pumpkin or ordering them from lightest to heaviest.
Hanging Leaves - attach yarn or twine between to objects (e.g., tree trunks, posts). Provide a variety of real or fabric leaves and clothespins. Encourage children to attach the leaves to the twine in a variety of ways (e.g., sorted by shade, in a pattern, smallest to largest). Children can explore the play yard for other interesting objects to hang on the line.
Natural Materials Sensory Table - fill a sensory table with autumn items found in the play yard or provided by families. Add tools including magnifying glasses, tweezers, scissors and sorting trays to enhance the play.
Which One Doesn't Belong - present a variety of different pumpkins to children. Ask them to explain which one they feel doesn't belong and articulate their thinking using math ideas and terminology.

Saturday, August 21, 2021

Cultivating a Classroom Space for Math Learning

“Do not wait until the conditions are perfect to begin. 

Beginning makes the conditions perfect.” 

Alan Cohen 

As we head back into the school year many educators are working thoughtfully to create environments that are rich with math possibility. In Reggio Emilia the environment exists as the 'third teacher' inspiring, supporting, and extending children's learning in rich and complex ways. I have been contacted by many educators asking for advice on how to best set up their classroom and routines in order to create as many opportunities for authentic math as possible. This has inspired today's blog post - how to cultivate a math rich learning space for children at the beginning of another school year. (I recognize that many areas will have Covid restrictions and following the advice of your local health unit will be important as you plan for your programming.)

When I reflect upon my own math pedagogy and practice these are what I think stand out as mathematically meaningful for the educators, children and families that share our space. Although this check list isn't all inclusive, I thought it might spark some ideas to support and inspire as we enjoy the final weeks of summer and start back in our classroom with open eyes, minds and hearts this year.


1. Make math a part of every space in the classroom and child's school world. In the classroom are there math tools and materials available for use beyond a 'math center or math shelf'? Do children see how math relates to every subject in the space (e.g., how materials are sorted and stored on the toy shelf, how measurement is used when children decide on a size of paper to use for their project)? Can they translate math tools and ideas into other spaces in their immediate school world (e.g., see how math relates to their walks in the hallway or work in the gym)?

2. Ground and build math concepts into known objects for children. When introducing, extending or innovating a math idea is it organic and natural to the child's explorations and world? For example, it is more natural to engage children in an exploration of measurement if they measure things in their immediate world using the stick they are playing with, instead of using a standardized ruler (e.g., "Can you find something the same length as your stick in the yard?", "What is taller than your body?").

3. Use available math moments with children. In our classroom we have a large block of uninterrupted play each day. It's sometimes challenging to manage children, materials and activities during center time. However I try to engage with children as much as possible in the activities, and take on the role of 'play partner' together with them. When I am actively playing I am able to closely observe what they are saying and doing, helping me to identify and extend the rich math learning that is organically occurring (e.g., helping children to recognize why their tower keeps falling, using math terms when they equally share the play dough, introducing math terms as they discuss how many cars are in their parking lot).

4. Become a math role-model for children, families, and colleagues. Even if math isn't your favourite subject, how do you discuss it within your school and classroom? Are you excited by new activities and resources? Do you demonstrate a growth mindset? When mathematical situations arise with children that you aren't sure of, can you use these opportunities to showcase positive thinking and problem-solving? Share your new math learning with others - suggest articles and books you're reading and post these throughout your classroom to enhance documentation displays.

5. Find the math in everything. Many educators plan forward by choosing curriculum and programming expectations and then building activities to fulfill these. Try back-mapping activities from time to time; embrace child-centered, organic experiences and then deconstruct them in order to identify the rich math concepts and curriculum expectations that they utilize. You'll be surprised to find that math happens in almost every experience children have in the classroom.

6. Try looking at life through a mathematical lens. When planning invitations for learning in your classroom, see what math you can sneak in as well. Changing one or two elements of the experience might be enough to engage children in rich math. It reminds me of how I used to sneak veggies into my children's meals - a little can go a long way!

7. Collaborate mathematically with colleagues. Share new ideas and resources informally. It's easy and effective to create math invitations and activities and share these within your school or division. If every educator plans one or two activities and these are shared, children will benefit from many rich and interesting games and activities without the burden of planning and preparation it would take one educator to accomplish the same.

8. Record and celebrate your math moments. Help children, families, and colleagues recognize that math happens everywhere in the classroom by creating a documentation display with photos, anecdotal observations and connections to curriculum. This bulletin board can be built over the course of the school year as artifacts of learning are continually added by staff and students. Keep sticky notes nearby and invite observers to record their own ideas and share them by posting the notes within the documentation.

9. Engage families in joyful math with children outside of school. Consider ways that you can promote and extend math for children after school. Encouraging families to play math games and activities together with their children will not only provide children with additional meaningful math moments, but it may help older family members reconcile their fear or dislike of math. In our classroom we send home family math bags once a week. These are filled with math invitations and materials so that children and their families can play games inspired by our classroom work.

10. Build your collection of math stories, songs and games. Children love to sing, dance and play games. Ask colleagues to share their favourite games and activities, and use these to help with transitions and other 'math moments' throughout the day. Quite often the words in songs can easily be improvised to match something happening in your classroom, and many rich storybooks have mathematical elements and problems embedded within them that can inspire children.

Wednesday, August 18, 2021

Joyful Math Preview, Webinar and Review

Curious about my book Joyful Math? Click here for a preview!

"Deanna shows us that math can bring joy! Written to support play-based math learning for young children in clear and concise language, this colorfully illustrated text is all you need to give the gift of math to children. When math is connected to children's play it becomes real, meaningful, authentic, and joyful for children and their teachers."
--Dr. Diane Kashin, RECE, retired early childhood education professor, co-author of Play and Learning in Early Childhood Education

"Deanna's book provides a window into an early childhood classroom, sharing stories of young children's mathematics learning. The mathematics is embedded in a place of wonder, joy, and collaboration, full of playful learning with materials. The classroom stories share a joyful approach to the teaching and learning of mathematics which is sure to both inspire and provide a wealth of ideas for educators."
--Janice Novakowski, District Teacher Consultant (Mathematics) in Richmond, BC, Canada and coordinator of the BC Reggio-Inspired Mathematics Project

"In this beautiful book, Deanna McLennan shows us how teachers can create an environment for children to engage in mathematical play and learning with joy, curiosity, and discovery. Teachers will welcome these wonderfully authentic invitations to bring joyful playful math into their classrooms throughout the day."
--Katie Keier, kindergarten teacher and co-author of Catching Readers Before They Fall: Supporting Readers Who Struggle, K-4

"This is so much more than a math book. It's about a kindergarten teacher who is confident in her teaching, passing on sensible suggestions and practical advice to others who are looking to create interesting, engaging learning environments for their children, outside and in. It contains nuggets of commentary that are an inspiration and a joy to read. It's a reflective narrative of how Deanna integrates math into her everyday life of the class in meaningful and respectful ways based upon the principles and practice of the Reggio Emilia approach."
--Juliet Robertson, author of Messy Maths: A Playful, Outdoor Approach for Early Years

"What if all children had joyful math experiences in their earliest years? You may be wondering what would that look like and where do I start. Read Joyful Math and step inside Deanna McLennan's masterful, joy-filled kindergarten classroom. Here the natural curiosity, inventiveness, and exuberance of children is harnessed for deep mathematical learning through exploration and play. Deanna respectfully shares with teachers the methods she has developed over the years to surpass mathematical standards without leaving joy to chance. Rich with stories, conversations with children, and awe-inspiring photographs, Joyful Math is a game-changer for the early childhood math landscape."
--Katie Egan Cunningham, author of Start with Joy: Designing Literacy Learning for Student Happiness

Interested in learning more about how to bring Joyful Math to your classroom? I am pleased to share a webinar here that I have presented in the past for Pembroke Publishers.

"Join author/educator Deanna Pecaski McLennan as she discusses building a kindergarten classroom in which math is inseparable from everything students do. She encourages you to create invitations to engage with math through art, literacy, and outdoor play. With stories from her own classroom, Deanna inspires you to be curious about math, take risks, try new approaches, and collaborate with children as co-learners."
Read the review for Joyful Math in the June 2021 issue of Professionally Speaking. 
Eager to learn more? Consider joining the Facebook 'Joyful Math' book talk happening September to November 2021 on Facebook!  
Have you read and enjoyed Joyful Math? I'd appreciate a review on Goodreads or Amazon! Thank you!

Monday, August 16, 2021

Embracing Math Talks Outdoors


“The book of nature is written in the language of Mathematics.” 

The children were gathered around a zinnia in the garden. Right in the middle was a fuzzy bee covered in pollen. I stood back and listened to their conversation. 

"Wow! Look at those cool wings! They are as big as his body!"

"I like his hairy little legs. He holds onto the flower when he walks."

"Look at all the pollen on him. It covers his entire body!"

"I wonder how much food he all day."

Spending time outdoors in nature is vital for children's mental and physical health and well-being. In our kindergarten program we are usually outside for one or two hours each day. We engage children in a variety of play-based, inquiry-based experiences. Each day we also encourage children to freely explore the yard. I love to step back and observe their play. The observations they make, and the questions that they ask, are filled with rich math potential. Many times we have had a deep math exploration as a result of their observations and wonderings about the natural world.

Many educators are familiar with Sherry Parrish's Number Talks - a strategy where children participate in daily math explorations designed to help them play with numbers. Children are introduced to a problem and asked to visualize what is happening, while using previous math knowledge and experiences to perform a quick calculation. Children are encouraged to share their ideas with one another. As the math conversation occurs children learn from their peers as they explore different ways the math was solved. This daily practice helps build confidence and fluency in math as students reflect upon their ideas, gather feedback from others, and acquire new ways of interpreting and solving math problems.

In the July 2021 issue of Mathematics Teacher: Learning and Teaching PK to 12 Jo Boaler writes about how educators can leverage 'data talks' to help students delve into analyzing and understanding data more fully. Similar to a number talk, data talks encourage children to notice and wonder about different representations they see (e.g., bar graphs, line graphs, collections of objects). Boaler posits that data talks will help children visualize and make sense of the information they notice emerging in different data, helping them to grow as critical consumers of information.

http:// Like number and data talks, educators can embrace the power of math talks outdoors to help children recognize, understand and appreciate the authentic and integrated ways that math exists in nature. 

Math talks outdoors can happen in two ways: 

Preplanned - educators who wish to engage children in an exploration of a specific math concept (e.g., patterning, symmetry) can guide children to an object or experience outside that demonstrates this in real life. Perhaps an educator is hoping to spark an interest in symmetry, or needs additional assessment opportunities for this topic. S/he can guide the class to the garden where they can observe symmetrical flowers and engage in a conversation about what they see, think and wonder. 

Spontaneous - educators carefully observe children's conversations and interactions outdoors. As children notice and wonder about a specific phenomena (e.g., how fast the wind is blowing, the shadow a leaf is creating on the ground), educators scaffold and support the mathematical inquiry. Educators listen to the questions children ask, and help them conduct research into finding an answer. The research into the question or wondering can happen briefly, or extend over time, as additional resources and information are used to deepen the mathematical exploration and understanding. As math ideas emerge, educators can 'notice and name' these in the context for children (e.g., "The distance around a tree stump is called the circumference. We can measure it in many different ways. Let's find the stump with the biggest circumference in our yard.").

Math talks outdoors will inspire children to look at their world through a mathematical lens. Seeing math concepts in authentic contexts will help children understand the relevance math has to their lives and the world around them. Abstract mathematical ideas can become more concrete and easily understood and internalized by children. Some of our richest math inquiries have sparked as a result of the children's curiosity about the world around them. 

Some tips for getting started:
  • Uses the see/think/wonder routine where children are asked to state what they see in a particular situation or object, share what they think about this situation or object, and share a question or wonder they might have. (I see circles forming when the rain drips into the puddle. I think these are happening because the rain is falling from the sky quickly. I wonder why some circles are bigger than others.)
  • Record children's conversations and take photos of their explorations for future reference. These can be brought to a whole group meetings for further discussion, or reviewed at a later date for assessment purposes. 
  • Look for interesting objects and events in your school yard in which to draw children's attention. Use a 'notice and name' strategy where you share your observations and connections with children in order to pique their curiosity and spark an investigation.
  • Connect math concepts and vocabulary when exploring outdoors. Help children see the math in the natural world, and practice using the proper terminology (e.g., The way the tree branches are positioned  is called a fractal pattern.")
  • Bring outdoor math talks inside by using artifacts and photos with children during whole group discussions. Similar to outside experiences, ask children to observe an object (e.g., feather, shell) or photo (e.g., of a child jumping off a stump) and make mathematical observations and connections.
Like number and data talks, the possibilities for learning by regularly incorporating math talks outdoors are limitless. Invite children to share their ideas, connections, and questions with one another, as they appreciate the beauty and joy that math outdoors has to offer.

Saturday, August 14, 2021

Small World Play and Math

 "Old things are better than new things, because they've got stories in them."

Kami Garcia

What is hiding in your cupboards and closets? For 20 years now I have kept an old, beautiful china set from my grandmother high up on my shelves. I can honestly say that I haven't used it once; life with busy children doesn't lend itself to tea parties and fancy dinners. Each time I opened the particular cupboard in which these beautiful objects were stored, I'd feel a sense of guilt. They were treasured by my Nana and used for special gatherings. Now they collected dust.

As I look ahead to the next school year, I am eager to bring beautiful, inspiring materials back into our classroom. Covid has meant that many children have been home with their families, isolated from the world. I anticipate a higher than normal level of anxiety and stress as we return to school, even if we are eager and ready for this new chapter. Having beautiful, interesting materials in the classroom space can often welcome children and pique their curiosity, helping them transition into the space and overcome their feelings of anxiety.

Last week I cleaned the kitchen and as I handled the china, I wondered if it could be integrated into the classroom as play props. Not only would that give the bowls and cups a sense purpose, they would beautify our space. I liked the idea of being able to enjoy them on a regular basis; each time I look at them they remind me of my grandmother and I love feeling her presence in my life.

I had been eager to use a small teacup set (found at Value Village) in some way. I knew that the children loved small world play, and that imaginative mini playscapes held potential for rich math learning. I decided to turn my china into a tea garden. In each piece I placed small stones at the bottom for drainage. I planted succulents in the potting soil because of their hardiness and ease of care. 

I anticipate placing these materials on a low shelf in the classroom. They will be a semi-permanent fixture there. They will beautify our space when not in use, and be accessible enough that children can access them without needing to move them around the classroom. I have always felt comfortable integrating fragile materials into our space. My experience has been that when children feel empowered as learners, they care deeply for the materials and handle them gently. I'm also prepared for the possibility of accidents. The children are capable and careful when something breaks and I am willing to trade this risk with the reward of using these materials.

I am purposely not adding character props to this learning invitation. I would rather see how children integrate other materials we have into their play (e.g., mini animals, wooden clothespin dolls), or create their own fairies and other figures at the art center. I also see potential for creating a similar invitation outdoors in some way (e.g., fairy door in a stump). As I observe the children I will take note of their ideas and interests, and help to scaffold and support the math learning as it emerges. Some math ideas I think might present include:

  • a discussion of proportional reasoning as children explore the size of the small world and create additional play props
  • an observation of pattern as children see, think and wonder about what they find on the china
  • practice with one to one correspondence as children set the table for a tea party and create additional props to support their storytelling (e.g., plates, forks, food)
  • STEAM as children create their own figures to integrate in this play (e.g., dolls, fairies) or create their own mini worlds (e.g., dollhouses from boxes)
  • observations of shape and size as teacups are compared to one another
  • connections with capacity as children consider how much liquid might fit into the cups, or create their own tea parties while playing in the mud kitchen or water table

I'm sure as children explore the materials additional ideas will emerge. I can't wait to see what they discover! I'm eager to search my closets for other materials to upcycle and bring into our learning space!

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