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Part 2.mp4Part 2 of our Story
Part 2 of our Story
Click here to listen to me tell our story.
If you would prefer to read part 2 of our story, see below.
How Are We Creating a Culture of Inquiry in Math?
At the beginning of the year, as collaborative educators, we make sure to sit down together and set intentions that will help us to foster a collaborative community culture that is rich in inquiry and deep learning.
This year, we decided to connect our learning through our big, beautiful question:
How does better understanding others and the world around us help us to better understand our identity?
Inside of this big question live many smaller questions:
#1: Who are we as unique individuals and learners and what strengths do we bring to our learning community everyday?
Cameron: “A community is made of individuals who do different things with respect for one another.”
Gwyneth: “We all teach each other! The sky’s the limit! There is no end to how much we think or do! It’s a lot of space to think and wonder.”
Brooklyn D: “We’re one big community. We all respect each other. We remember our values. We have fun and it feels good.”
#2: What community agreements do we need to thrive as individuals and together as a learning community?
This year, our community decided that in order to thrive, they needed to create the following agreements:
We will be focused learners. We will give and receive feedback and support one another in learning.
We will be respectful. We will show respect for each other, adults, and the environment.
We will think before we act, be helpful and inclusive.
We will be kind and will perform random acts of kindness.
We will be communicators. We will speak up to share our ideas and feelings.
#3: What becomes possible when we are invited to tell our own stories and to listen intentionally to the stories of others?
Hope: “A community is like a book. All of us are pages. We are all different and together we tell our story.”
#4: How will growing and sharing ideas together invite multiple perspectives and possibilities?
#5: How might understanding stories of the past help us better understand ourselves and stories of today?
We intentionally create opportunities for students to build relationships, get to know each other and feel safe to learn with one another. We honour the time and energy it takes to build and grow these relationships and continue to weave this time into everyday of our year together.
Once we have begun this important work with our students, we feel ready to begin digging in to numeracy.
What becomes possible when every voice is heard and valued? We highlight the power of collective knowledge building and meaning making, and the need for everyone to contribute their voice.
Eli: “A community is like an idea generator. It never stops.”
Shilo: “We ask questions that can spark other people's thinking. We are open to any thoughts that any people have. We are all resources for each other. We feel like we belong.”
Brooklyn beautifully captured our hopes for our learners while reflecting on her journey.
She shared, “I love learning with others and sharing my ideas in the safety and comfort of our community. I love the freedom of following my passions and what I’m curious about. It’s amazing to see the connections between everything we are exposed to. I learn deeply by listening to others. It sparks new ideas and wonders for me as I connect to what others are thinking. It also gives me different perspectives. When we’re together as a group of learners I feel happy and connected.”
Once we feel our students are building trust, we use rich open-ended math tasks and collaboration to explore the questions:
What do mathematicians do?
How can we support each other in community to grow our mathematical thinking?
After a few days of collaborative problem solving, struggle and thinking, we ask our students what they noticed and what they think mathematicians do.
Brooklyn Y: “I really found pictures helped me to think. I always think of Math as numbers but I think it’s pictures too. I think Mathematicians draw pictures or see math in their heads.”
Hope: “Our group tried a lot of ideas…”
Rylea: “A lot of ideas! We kept trying though! We p.. What’s the word?”
Cameron: “You persevered!”
Hope: “That’s it. And we tried different ways to solve the problem.”
Jake: “I noticed how we collaborated to find a way even to start solving the problem. We then did a bit on our own then shared our thinking. We added to each other’s ideas.”
Aiden: “Our group made a lot of mistakes. We knew you wanted us to show our mistakes so we didn’t worry about it. We tried a different way and kept thinking!”
Harrison: “Mathematicians make mistakes!”
From this conversation, and from others we documented and shared with our students, we co-created our criteria for math thinking.
We decided that mathematicians:
Then, we worked to shift our students thinking about what math is, where math exists and how they may grow as mathematicians.
Aiden: “We see how math is everywhere and how it is seen differently by everyone!”
With these ideas in mind, we pause to ask the questions:
How will we show our growth as mathematicians this year?
How will we shift the importance from the product to the process?
In order to celebrate learning and growth throughout the year we co-create learning targets which in turn create a learning map.
Learning maps provide a guide for our students to engage in ongoing, embedded assessment.
One of the purposes of the learning map is to help our students to set intentions. As we build the value of constructing meaning together, we asked the kids to unpack the word intentions with us. This is what they said:
Rheya: “I find it’s a lot harder to spark ideas alone. Intentions help us feel brave together. Like we can achieve anything.”
Breiana: “Yes! They give us courage and strength to reach our goals, they help us become our best selves.”
Brooklynn: “Intentions help us try new things. Like how we set intentions in Math. I intend to try new strategies by listening to others and asking questions.”
Marlee: “I’ve changed my thinking now. I always thought intentions were something you just do. Like I intend to be kind or I intend to always do my best. Now I’m thinking about how intentions can give us courage. For math today, I intend to stretch my thinking and try multiple strategies for multiplication.”
Learning maps guide our personal intention setting.
The learning maps also help our students to: highlight how they are growing as mathematicians throughout the process of learning, select and reflect on evidence of learning, and determine their next steps.
In this way, assessment is student centered and is embedded in the learning process. Through this ongoing process, it is our hope that our students are empowered as they grow their skills as mathematicians.
When our students are ready, they select evidence of their growth and post their evidence with a reflection on their digital portfolios.
We are learners, and Jo Boaler’s work with YouCubed really resonates with us. She has taught us a lot about how people learn math. Using her work as a guide, we have tried to intentionally create classroom norms to help us establish a numeracy learning environment whereby:
Mistakes are powerful
Mistakes are powerful
2.5 years ago, a student coined the phrase CMT (changed my thinking) to show how mistakes help us grow. Now, students have sometimes started to use COT (changed our thinking), as they recognize we think and learn together.
Lux: “Why did you do so many CMT’s (changed my thinking)?”
Marlee: “We didn’t quite get the strategies yet. We were just playing around with the numbers. On day 2, after listening to Jack share his strategies visually, it started to make sense. We came back to the problem here, COT, and were able to solve it together.”
Ziah: “At first we thought 2.47m was further than 2.5m. After feedback we COT. Keenan helped us to think differently. We learned from this mistake that we need to slow down to think about the numbers and not to just look at the numbers. A mistake is an opportunity to learn.”
Depth is More Important Than Speed
Depth is More Important Than Speed
Gwyneth: “We aren’t rushed. We’re given the time we need. Like when we do math council, if you don’t understand a problem you get to think it through with everybody.”
Math is Visual
Math is Visual
Brooklyn: “This is really hard. I don’t even know where to start!”
Marlee: “I’m going to start by drawing a picture. I need to ‘see’ the problem.”
Brooklyn: “That might help me settle my brain a bit! Tell me what you’re doing while you draw.”
Mason: “I know how to do it in my head but it’s really hard to show it.”
Paisley: “What if you tell me what you're thinking about and I try to draw it out. Pictures help me think.”
Mason: “I’ll try. It’s a little crazy in my head you know!”
Math Requires Experimentation
Math Requires Experimentation
Neelyn: “I love how I can step into others thinking when we share. We use so many different strategies. We all see the problems so differently.”
Collaboration Deepens Our Understanding
Collaboration Deepens Our Understanding
London: “It’s really helpful to share what we are thinking with someone else. We can put our thinking together. Your partner can make you stronger.”
Aiden: “It teaches me how to be a better person. I’m helping others. It deepens my understanding.”
We Need Feedback For Learning
We Need Feedback For Learning
Ava: “We use detailed, specific and kind feedback to help. Because, just saying ‘it's not neat enough’ is not going to help anyone.”
McKenna: “We don’t just judge their paper, we ask what their goal is in math, and help them achieve it. We consider this when we give feedback.”
As we describe in the video on the home page of our website, we learn through numeracy inquiry cycles that are rooted in these norms.
We activate thinking, collaborate, engage in feedback and participate in a math council. At all times, we listen closely to our students, and document their conversations, their thinking and questions, and their misconceptions. This helps us to stay aware of where they all are with their understanding.
We also recognize that learning takes patience and time, so we try to go at the pace of their learning, and don’t put any time limits on any part of the cycle.
As you can see, this cycle is not simple. Depending on what our students need, we cycle back, we cycle sideways and we sometimes re-cycle!
When we begin each new cycle, we try to live in questions that will deepen our planning. We wonder:
How do we choose tasks that will nudge our students thinking forward from where they are in their current understandings and strategies?
How will we choose tasks that are connected to what students are inquiring about/exploring together?
We work to understand who each individual learner is. When choosing mathematical tasks, we try to adjust so we can ensure that our learners are at the center and are given opportunities for success. We’re always reflecting and wondering about how to ensure that thinking will occur and that there are entry points for all learners, and that they will also all have the opportunity to extend or stretch their thinking.
Through collaborative learning, our intention is that our students will be collectively making connections, creating meaning and engaging in sense-making through these tasks.
Jaxsen: “When we are on the carpet, it’s not our teacher telling us what to do. She’s part of the circle and asks us questions to guide us. Everyone on the carpet is working together to try to find the answers. As our teacher guides us through the tasks, we kind of teach ourselves. She always asks, what are some strategies we know so far? Just so we have a place to start from.”
McKenna: “I can make new friends and learn more about math at the same time. It helps me grow stronger and deepen my thinking.”
Ava: Building a community means navigating conflict, feeling important and heard, and building empathy for each other.
Bella: When we sit in a circle all of our energy is directed into the center of our circle and then is shared equally amongst us.
With each cycle we reflect and grow alongside our students. We are growing as documenters in order to value and pay attention to each success and struggle.
Max: “When our teachers put our names on the chart paper with our strategies we feel important. I feel like it challenges me to expand my thinking even more. Also, we can connect other’s thinking with our own thinking.”
We observe, assess, ask questions and check for understanding by listening closely. We also make mistakes, but we reflect, adjust and carry on.
Although it was really difficult in the beginning, we are learning to let go of ‘getting things done’ in order to give our students the time and space they need to develop their own understanding and mathematical theories.
One of the places for meaning making to occur is in Math Council.
As Susan Mackay says, “It is our job to draw out the tools of knowing and meaning making and creating that every child is equipped with and create the conditions in which they will reach toward a community of others who are reaching toward them. It is a space of belonging and common humanity and imagination where we experience difference as opportunity to find connection - and to find the joy that exists when we do.”
At the end of a cycle, we celebrate together the depth of thinking, engagement, and understanding we experience by coming together in circle in a math council to make their thinking visible to each other so they can deepen their collective understanding.
During math council, when partners are sharing their thinking, students record strategies they hear, provide further feedback, and ask questions.
Some of the questions our students might ask during Math Council are:
How did you collaborate with your partner?
What worked well?
Where did you struggle?
How did you learn from your mistakes?
How did you know you were on track?
How did you solve the problem in more than one way?
What did you learn?
Our students share their mistakes while highlighting the learning that exists in them. They justify their thinking and strategies to open our minds to new ways of thinking about and solving mathematical problems.
While thinking through how many $6 pennants could
be bought with $25:
Aiden: “I’m pretty sure we did this question backwards.”
Cam: “I would still do circles but with multiplication.”
Aiden: “I realize now what we did was wrong. Technically, we still got the answer. 6 times 4 equals 24, and 24 divided by 6 equals 4. You still have $1 leftover.”
Jake: You’re just flipping around the numbers!”
Mason: I think of it as 6 x what number equals 25. I like using multiplication to solve division.”
During Math Council, Christine and I are observers and documenters. We are teacher researchers. Through listening, we end up learning a lot from our students. We learn how they are making sense of numbers, what their theories about how the numbers work are, and we often learn new strategies we hadn’t thought of before.
We later use this documentation to draw our attention to how students are demonstrating their learning and understanding in each cycle, and it helps us to choose our next steps based on what we notice. Our documentation also helps us to bring our students ‘wise words’ back to the group to amplify the learning of all.
In February, I asked my students how collaboration builds our math thinking. This is what they shared:
Jake: “Talking about math helps me a lot. I hear a good strategy and I put it in the attic of my brain for future use!”
Brooklyn: “I remember Jake once saying, ‘We don’t always get the answer but we get an answer!’ We make mistakes along the way and change our thinking a lot but we stay positive and are learning the entire time!”
Marlee: “I love to see my classmates learn from me! I am learning to share my thinking clearly. I have learned many strategies by listening and sharing.”
Breiana: “I like to share my ideas and put them out there because then I’m given feedback which helps me step up my game. Then we can celebrate together!”
Lux: “When I hear a new strategy I remember it and then I can connect back to it which helps me understand and solve future problems. I am also able to notice strategies within strategies which deepens my understanding.”
Brooklyn Y: “Building onto Lux’s idea, I feel inspired to try out strategies that are shared that I’ve never tried before! Collaboration gives me courage.”
Mayah: “I like to hear how well others are collaborating. It challenges me to improve my own collaboration. I want to share my ideas clearly with others to help them learn.”
When discussing their learning with educators visiting from across the district, our students added:
Casey: "We are exploring who we are as learners. We are still trying to figure that out. Each day we learn something about ourselves or our peers."
Paige: "Our teachers accept us for who we are as a mathematician, and as an inquirer. We learn about far more incredible things than you can actually realize.
We believe that we are learners and that our learning never ends. We are excited about the depth of learning and engagement we are seeing and hearing from our students in the safe learning communities that we are building together.
And we still have so many questions. We are excited to continue to stretch our thinking about how we might further allow inquiry to drive our students learning in Math by honouring their curiosities, strengths, and courage.
Slide Deck
Slide Deck
Look here if you are interested in looking at more of the visuals on the slide deck that we used to tell our story.
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