I am a Reggio Emilia inspired Full Day Kindergarten teacher and mother to three young children. This blog is meant as a communication tool for the families of our children and as a learning tool for the many educators who follow us. Please feel free to comment on posts and participate in our collective understanding of emergent curriculum.
"Exploring trees outdoors is an enjoyable experience that children
love to do! Swinging from a branch, exploring leaves and bark, and
observing gnarled roots are all favourite activities that also integrate
rich learning. Heading outside to explore the yard uses children's
excitement and enthusiasm for sensory and nature experiences to inspire
rich mathematical and scientific inquiries about what they are seeing
and experiencing."
I was excited to see a review of my book Tree Math in the MAMT Spring Journal! You can access the review here!
As an educator helping children develop a love of and appreciation for math is one of my greatest professional interests. I strive each day to engage children in authentic math learning through play and inquiry. I was super honoured and excited this past spring to welcome ETFO into our kindergarten classroom and record a number of chats regarding how children explore math in our classroom.
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:
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!
“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.
“The book of nature is written in the language of Mathematics.”
Galileo
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.
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.
Our children are drawn to water. This past week we had a lot of rain and it created a giant puddle in the playground. The children were curious about how to cross the puddle. It was too big and deep to skip or jump over and they needed to cross it in order to get to the other side where their stumps and other favoured areas were.
One child decided to try using some of our loose building parts. He gathered many pieces of wood and laid them starting from one edge of the puddle. As he placed them side by side he observed the edges of the wood to see if the puddle was deep enough for the wood to sink into.
"I don't know if the wood is high enough. If the puddle is deeper than the wood, then this won't work."
I observed him as he placed the wood and then stepped on each piece, watching to see if the water rose higher then the wood. I noted the complex math and problem solving that had emerged in his work. He was considering the depth of the water and whether it was deeper than the wood was tall. After a few minutes some friends joined him.
As each piece was added the children continued to test their design to see if their feet stayed dry.
"We're making a bridge so we can cross!"
The children continued to lay the wood side by side. When it ran out, they were perplexed.
"We don't have enough to finish the bridge!"
They stood around for many minutes, stepping on their bridge, counting the pieces that were side by side, and then looking around the yard for any loose pieces of wood they might have missed.
"I know! Let's take half of the pieces and move them so that we can make the bridge longer! We'll just have to walk one at a time instead!"
The children realized that if they narrowed their bridge they could double the length by moving the pieces in different positions. The amount of wood they used hadn't changed but their problem solving allowed them to complete a workable way of crossing the water.
Success! The children children spent the majority of their outdoor time racing one by one across the big puddle. They even tried driving the tricycles across it - the process of experimentation in doing so led to some amazing conversations about the weight of the bike and if the wood would hold it, the position of the wood pieces and if they would stay in place while being driven on, and how fast the bike could be driven across without the pieces shifting and becoming ineffective.
The outdoors is full of possibilities for children to mathematize their play; this authentic experience of crossing the puddle motivated the children to engage in robust math that incorporated measurement and problem solving!
It's amazing the kinds of questions children can ask...
One of my favourite books to read in the winter in "The Mitten" by Jan Brett. The story is appealing to young children who love to retell the text and marvel at how big the mitten grows as each animal squeezes into it. This week I read the book again upon request by one of the children. At the end of the reading one child shared that she felt that the book wasn't really about "real things, because there was no way all those animals could fit into one small mitten".
Sensing an opportunity for something rich, I questioned the children. I asked them to consider whether a mitten could really stretch that large to accommodate all the animals, and if it couldn't, how big did they think it would have to be in order to do so.
The children engaged in a lively discussion and agreed that the mitten would have to be very large - much larger than the one portrayed in the book - and it would be very time consuming to knit. We agreed that one would have to know exactly how big it had to be because if it was too small the animals wouldn't fit, and if it was too big it would waste the knitter's yarn and time.
I challenged the children to create a mitten the exact size it would need to be in real life to fit all the animals in the text: a mole, rabbit, hedgehog, owl, badger, fox, bear and mouse. They readily accepted my challenge. The first thing we agreed upon was that we needed to know exactly how big each animal really was. The children weren't sure how to do this so I suggested researching their sizes on the internet. I helped them with this search.
Once we knew the size of the animals I helped the children measure out large butcher paper so that their drawings would be as realistic a size as possible. We discovered that the bear was the largest!
Here are the animals (excluding the bear) after the children researched, drew, and cut them out.
The next thing we needed to do was calculate how big the mitten needed to be. We referred to the book to see if the animals were side by side or on top of each other and then taped together large pieces of butcher paper to create the mitten.
The papers needed to be securely fastened...
...the outline of the mitten cut...
...and the seams stapled closed.
The children noticed that when complete the mitten was almost as big as our carpet!
The children enjoyed decorating it too!
We felt that it would be fun to retell the story while we placed each animal inside the mitten. We were eager to see if we were right and the animals all fit inside.
The children waited until it was their animal's turn and then gently placed their animal inside.
Once the retell was complete the children had one more question they asked to explore. Would a mitten that was large enough for all those animals hold 14 kindergarten children? They were quite eager to find out! One by one they hid inside the mitten, squeezing to the end and making room for their friends to join in!
This was also an incredibly rich math activity. The children had to consider the area of the mitten and if there would be enough room for all the children. They counted as each child entered the mitten and calculated how many more children were waiting on the carpet. They discussed how to preserve the integrity of their design as they entered the mitten so that it held together so all children could have a turn.
They were right! All 14 children did fit into the mitten!
But the best part of all? Getting out of the mitten!
