Cultivating a Math Rich Learning Space

It's the end of August! This time of year always fills me with hope. Although it's sometimes sad to be leaving the fun and comforts of summer - spending time with my children, sleeping in, enjoying the back yard with my pup - it's exciting to think of the possibilities of another school year. Like a blank canvas waiting to be painted, our classroom evolves and changes over time as the children and I learn and explore together. 

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 thought it would be easiest to create this as a 'math check list' with points to read and consider. 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 weekend of summer and start back in our classroom with open eyes, minds and hearts this week.

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.

These are just a few of the ways in which I cultivate a rich math space with children. I'd love to hear from you! Share your math ideas in the comments below, and consider following my Facebook page  Joyful Learning in the Early Years for regular math ideas from my classroom!

Exploring Magnitude While Playing with Number Lines

 

Number lines are a great tool for helping young children develop an understanding of magnitude—the idea that numbers have a size and that numbers can be compared to one another.

Children may be able to count to 20, but that doesn't necessarily mean they understand how the numbers relate to each other. They may know that 8 comes after 7, but do they understand that 8 is close to 10? Or that 15 is farther from 10 than 12 is?

A number line can help make these relationships visible.

Start Simple

 

We can begin with a simple number line:

0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10

 

Rather than just using it to count, we can ask questions such as:

• “Where would 6 go?”
• “Which number is closer to 5 ... 3 or 8?”
• “What number is between 4 and 6?”
• “Where would you put 9? How do you know?”

These questions encourage children to think about the size and location of numbers, rather than just reciting the number sequence.

Estimate!

 

One of my favourite ways to use a number line is to give children a line with only the endpoints marked.

0 ____________________ 10

Ask:

“Where do you think 5 would go?”

Children have to think about where the middle of the line is.

We can then try:

0 ____________________ 20

“Where would 5 go now?”

This helps children see that the position of a number depends on the numbers at the ends of the line.

 

Use a Floor Number Line

 

A floor number line gives children the opportunity to physically experience number.

“Stand on 4. Move forward 3. Where did you land?”

We can ask children to predict where they will land before they move. This connects counting and movement with the idea that numbers have a position and a distance from one another.

Look for the Thinking

The important part isn't whether children place a number perfectly. We want to hear how they decided where it belongs.

“Why did you put it there?”

“What were you thinking about?”

“How do you know?”

Number lines give children a visual way to see that numbers aren't just a list of words we say when we count. Numbers have size, and numbers have relationships with other numbers.

Helping children develop this sense of magnitude is an important part of building strong number sense in kindergarten.

Exploring Different Fonts of Numbers

Sorting numbers that are presented using different fonts is an effective way to help children understand that numbers can look many different ways. This activity requires children to sort and glue numbers onto a chart. A basket of cut numbers was offered to children along with a template/chart and glue sticks. Children were challenged to find as many of each different number as they could.

Want to try the activity with your students? Click here to get free printable font pages and the template. Happy sorting!

    

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.

A Writer's Dream Come True

“Every morning you have two choices: continue to sleep with your dreams, or wake up and chase them.” 

For as long as I can remember I have always wanted to be an author. I dreamed of writing books that would inspire people. I especially hoped to help educators and children overcome their hesitations and fears regarding math learning, and view math as a beautiful and complex subject that could be discovered everywhere in the world around us.

It was with much excitement that my dream became reality. I was thrilled to publish multiple books regarding both math pedagogy and practice. I was thrilled to find out this summer that many of my books are now available through a favourite Canadian bookstore of mine - Indigo. Thank you to all of you who have helped to support my writing; from those who have proofread and given suggestions for improvement, to those who use the books in their classrooms each day - I am forever grateful!

You can find the books at Indigo here: https://bit.ly/3PSxBJu

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!