Cultivating a Mathematically Rich Learning Space

It's almost Labour Day! 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 weeks of summer and return soon to our classrooms with open eyes, minds and hearts.

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 ideas 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.

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 Instagram @McLennan1977 for regular ideas from my classroom!

Creating a More Inclusive Math Environment

I grabbed a coffee from a drive through this past weekend. While there I chatted with the employee working at the window. I asked him how his day was going.

"It was great until about five minutes ago," he said. "I just saw my former math teacher. I haven't seen him in years. Nice guy but I dreaded his class. I just never really felt like I belonged. I hated the math. Just couldn't relate. Seeing him brought up all those old feelings for me again."

As someone who loves math I was devastated to hear this story. As a kindergarten educator I try my best to cultivate a safe and supportive space where children feel like they are equal members of a democratic learning environment. I want kids to love math and see themselves as authentic mathematicians. Inclusive learning environments are ones in which children feel fully supported, and that their contributions and perspectives are equally valued and respected regardless of their identities or learning preferences. There is a sense of belonging for everyone.

Every child has the right to learn and reach his or her highest potential. This is especially important in mathematics, where growth mindset and differentiated learning and assessment approaches can make all the difference in how children interact within, and enjoy classroom explorations.

Inclusive math education ensures access to quality learning experiences for all children by meeting their diverse needs in a way that is responsive, accepting, respectful and supportive. Educators should work to diminish and remove barriers that may lead to children's disengagement and exclusion. 

There are many ways we can creative inclusive learning environments. Here are a few suggestions:

Critically Examine your Math Questions and Prompts

Consider the types of questions you ask children. Can they relate to what they are being asked? Are the questions relevant to their age, interests, strengths and needs? Is inclusive language used? I recall feeling troubled reading a question in my daughter's math work about the number of marriages that could be possible in a group of people when X number of men and women paired together. "What about gay couples?" she asked me when we reviewed her homework that evening.

Honour Student Voice in the Learning Process

Consider asking children to create the parameters for math work together in class. As an educator reflect upon the math work you ask children to complete - do they have a voice in the explorations and activities? Does math work ebb and flow around natural learning situations in the classroom or does it exist in isolation from children's lives? In our classroom we often explore new math tools together and play with how they might be used before I suggest a more formal or structured approach. I try to include children's ideas as much as possible.

Encourage Unconventional Ways of Representing Math

Consider the ways in which you ask children to explore math ideas and showcase their understanding. Do you tend to default to paper and pencil activities? Do children work only from worksheets or textbooks? Are you able to encourage children to use their hundreds of languages (e.g., painting, drawing, building) to explore math problems and share their findings with others? In the photo this child is exploring multiplication by creating an array with sticky notes. In our classroom we try to represent math thinking using innovative, non-traditional ways of knowing and being that are self-selected by children whenever possible.

Invite Family Knowledge into Math Experiences

Consider how you can welcome families into your math activities in order to enhance children experiences. Do family members have interesting jobs and hobbies that can be shared to help supplement children's understanding of math concepts or how math is used authentically in the world? How do families feel about math learning? What is it they value as part of the math learning process? Are their feelings about math limiting their children's potential? What role can families play in supporting children's emerging confidence when learning new concepts (e.g., take home math games, reading math books together)? Share information about math learning with families to help them deconstruct tasks and engage more authentically with math explorations.

Use Diverse Learning Materials

Consider the types of materials that are offered to children. Are they diverse and meet the children's interests, strengths and needs? Do they offer multiple ways of engaging with math? Are they inclusive so all children feel a connection in some way to the experience? Offering math materials throughout the classroom and not just in a 'math area' helps children see the connection that math has to the world around them and their own lives. Invite children to co-construct math materials and visuals that are used throughout the learning space.

Examine your Assumptions and Biases

Sometimes educators default to teaching about math the way they were taught. When something is new or uncomfortable it might seem natural to revert back to familiar ways of knowing and being. Many educators do not enjoy math and subconsciously communicate this to children. Consider how you talk about math with others. Do you present a growth mindset when problems occur that you are unsure of how to solve? Do you approach new and interesting mathematical situations with a stance of curiosity and willingness to learn? Math is a beautiful and engaging discipline and talking about it as such will help learners experience positive associations with math learning. 

Hold High Expectations for all Students

Children are natural mathematicians. They are curious about the world around them and want to understand how it works and make connections to others. Offering low floor, high ceiling tasks encourage all children to enter into math explorations and helps differentiate tasks for their individual needs. Activities that relate immediately to a child's world and experiences will be more meaningful for them mathematically. Communicate your belief to children that they are capable of participating fully in rich math learning and hold them to high expectations. Provide as much time, space and support as needed to ensure children experience success.

Use a Community Approach to Learning

Math is a communal experience. Too often children have been asked to complete math tasks in quiet isolation while working at desks. Rethink how you invite children into math exploration and encourage noise, mess, and social exploration. Ask children to work together to solve math problems and share their thinking with others. Resist the urge to default to thinking that math should look and sound like it might have in your childhood. Share with families and the greater community that math learning is rich and layered when we all work together.  

Create Unconventional Learning Spaces 

Math can happen anywhere, anytime. Help children see the authentic and meaningful ways math connects to our world by looking for it beyond the classroom. Be open to math moments that arise in outdoor play and exploration, and be intentional about the whole and small group math experiences you encourage in areas like the gym, library and music room. Embrace the questions children ask that are mathematical in nature, especially those related to risky play (e.g., "How fast/far/high can I run/jump/climb?").

Creating a Space that Cultivates Math Learning

 

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. 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 list isn't all inclusive, I thought it might spark some ideas to support and inspire as we enjoy the first weeks of school and start back in our classroom with open eyes, minds and hearts this month.

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.

A Classroom Tour for September

 

For many years now I have been greatly inspired by the Reggio Emilia approach to early childhood education and have sought any source of information that I could get my hands on! When FDK was first introduced in Ontario I was thrilled to see that many of Reggio's beliefs were interwoven in the document and honouring children's interests through play, inquiry and documentation were highlighted. As educators who follow a standardized curriculum we have great flexibility in our interpretation and implementation of the expectations and this makes our role exciting and dynamic.

I believe in having a fluid, evolved space that continues to change to better reflect the needs of the children and support heightened understandings of explorations and inquiries as well as enhanced abilities in the various domains of learning. We want to support the whole child in developmentally appropriate experiences and integrate learning materials from centres in diverse and unconventional ways.  

Some of the Reggio principles that have guided my work include:

• children are capable of constructing their own learning
• children form an understanding of themselves and their place in the world through their interactions with others
• children are communicators
• the environment is the third teacher
• the adults in the room are mentors and guides
• there is an emphasis and importance on documenting children's thoughts and experiences
• there are hundreds of languages of children and these are used to explore and communicate ideas and experiences

This is the door leading to our classroom. I post information around the door to assure visitors to the space that I believe in an inclusive environment where all children are respected. Building relationships with families and helping them learn about and support growth mindset is a big part of creating a safe and supportive space for learning. Something about which I've had a lot of positive feedback is our 'wish wreath'. Each September we ask families to write their hopes, wishes, dreams, etc. for their children's kindergarten experiences on paper ribbons. We weave each of these onto a grapevine wreath and display it on our door. We want it to be a symbol of our partnership and collaboration with families for the year ahead. We also include a photo of our teaching team and visitors to the room can access our class blog by scanning the QR code on the door.

Above each child's cubby is a recent photo and painted self-portrait. These change a few times each year (usually a new photo and self-portrait per term) to help show their growth. We like including a real photo to celebrate each child and love how the children use the language of art to represent their perception of self. 

Our quiet literacy area has a collection of books and writing materials to explore. It's a comfortable area for children who want a quiet space to read or draw and the sofa and chairs are a great way to calm oneself if a child is tired or needs a break. The whimsical light invites children to stay for a while and read a book or chat with a friend. We ask families to send in photos that are hung by the sofa as a sign of connection and comfort. The light table and weaving wall encourage creativity and fine motor development which will help children with writing readiness. An upcycled photo display holds seasonal vocabulary cards that can be manipulated by children. The wooden shelf holds diverse and inclusive books so all children can see themselves reflected in classroom resources.

 

Our math area has many things available for children. We include mentor texts, learning props, and documentation to showcase and support our program.

Our drama centre changes based on the interests and requests of the children. At the beginning of the year it is set up as a little 'house' to provide comfort and familiarity to children.  We include many real objects for the children to use in their imaginative play; real objects communicate the message to children that they are capable of using these tools and make the context for the imaginary play very real and meaningful. Donations from families and the local community also helps represent the diversity of our population and encourages children to see themselves and their peers reflected in the space. Literacy is interwoven throughout as children can talk on the phone, write on the chalk boards, or follow a recipe when cooking. A variety of scarves encourages children to dress up and create their own costumes and clothing. A large basket of fabric flowers can be turned into different arrangements for the table or inspire other dramatic play (e.g., a flower shop, a farmer's market).

Our building area is the heart of our room and the most popular place to be. Children integrate materials from all around the classroom into their play here. We love the big body play the wooden blocks encourage. Small loose parts (e.g., tile squares, corks, wooden spools) are also included in this area for children to combine with wooden blocks. Pillow are available for incorporation in the creations and photos of local structures are displayed for inspiration.

My favourite center in the classroom is the science area. We are fortunate to have a very large wall of windows on one side of the space. The shelf near the window houses materials that are specific to ongoing inquiries. Loose parts play are a big part of our program as we embrace all things STEAM and love our makerspace. We use many natural and found materials here and always welcome donations from our families. The science area also houses many building materials and the children can freely use these around the room in any area to support their play. Often treasures found outdoors (e.g., pinecones, feathers) and the changing of the seasons inspire inquiries. Invitations for further exploration are sometimes set up on the table in this area. A sensory table integrates imaginative play regarding current interests, here insects and their natural habitat. Children can swap out materials for other small world play (e.g., dinosaurs, fabric flowers).

The art studio is located in a sunny area of the classroom. You can see that colours and colour mixing are ongoing interests and there is much art that supports this. The materials are aesthetically arranged to be accessible for children and also decorate the space. Materials are organized by colour for ease of accessibility and also to embed math and sorting into the centre.

We are often asked by other educators about how we encourage the children to engage in regular reading and writing in a child-driven space. On the back of our bookshelf are writing clipboards, one per child. We ask children to self-select a piece of writing that they are proud of and display it on their clipboard. These are then brought to a sharing circle where children can discuss their work with others. It's a quick and easy way for us to see which children have (and haven't) engaged in regular writing so we know how to better support their needs. This clipboards can also be brought on nature walks in the yard or community as needed.

Thank you for visiting us! We love feedback and to learn about your classroom and program. Please share in the comment section below or connect with us on Twitter @McLennan1977.