Author: Sharon Ethier

As a student, I would venture to say that math was felt very different. There were a lot of equations and my teacher would write examples on the board to help us to find the right answer to the problems. I could follow along with the examples and formulas and felt confident in completing my homework and worksheets. 

As an adult in university, I had a really great professor. He was so passionate about mathematics and often talked about the “beauty” of math. Things shifted for me as we spent a lot of time trying different strategies to get the right answers. This was the beauty my professor kept talking about!  Thinking about problems and trying out new ideas for solutions. 

Fast forward a few more years and as a teacher candidate, I was now responsible for helping students to understand math. This was a catalyst for me! I wanted my students to have amazing math experiences that would empower them to become mathematicians. It seemed like some things never changed; I was a math student again, in a different way this time. I had a wonderful professor while studying my Bachelor of Education. His classes were all hands on; there were visuals and there were experiences and he chatted with us about our thinking and learning. He made space for us to explore, to question, to articulate what we saw and thought and wondered about. 

Math continued to be beautiful as I used representations and manipulatives.  Mathematics lived here between what I saw and experienced in magnitude and measurement and what I wrote down on the page.  It wasn’t just magic or following examples, it was a language that helped me to communicate what I was doing and what I saw happening. 

In those early days of my career, I engaged in a lot professional learning opportunities including co-planning and co-teaching with colleagues, watching videos of classrooms, reading research and new resources, and even observed some amazing teacher mentors doing amazing math.  I earned a Math Specialist as an AQ through ETFO and it was such an inspirational experience to engage in thinking about building my knowledge as a math teacher. Teaching math was  was exciting and a space where my teacher colleagues and I found joy. 

At this stage of my math journey, I still find math beautiful, but also enjoy a sense of curiosity and wonder. When I’m planning and reading the curriculum expectations, I always make sure to click on the teacher supports found under the specific expectations. The examples show the kinds of things students might write to demonstrate their thinking and the manipulatives they might use to represent their ideas. I take my time with the key concepts too; they help me deepen my own understanding of the math I want students to explore. The sample tasks are a great tool as well. They paint a picture of what the learning experience could look like in the classroom and spark ideas for how I can frame those moments so students have the chance to experience math in a way that leads them to make sense of the mathematics. All of these supports are there to help math feel vibrant and alive.  

While I’m not a mathematician like Sophie Germain or Maryam Mirzakhani, I find beauty and wonder in math. Of all possibilities, this journey has led me to becoming a math teacher and maybe that’s the kind of mathematician that students need.

There is a moment in the classroom when the students are curious.  You’ve probably noticed this moment because it changes the energy of the entire room.  There’s a certain buzz of anticipation; maybe it’s the moment when they are waiting to see what happens next in a science experiment or listening for the next exciting part in the shared reading.  It’s the moment of pure engagement. 

On the other hand, there are other moments when it seems like the students feel disengaged. The classroom feels sleepy and dull, the students are clearly disinterested. I’m sure you’ve felt that moment, too.  The vibe in the room feels like I’m putting on a performance and getting a one star review. 

It’s at these moments that I recognize we need to take a break; we need something to re-energize our systems and get us back on track.  Over my years in teaching, I’ve learned the importance of breaks.  As a student, I can remember many moments of just listening to information or sitting and working for (what felt like) hours and eventually being unable to absorb any more information. My students feel the same way sometimes!  I’m not always the best ‘edutainer’ and sometimes I’m focussed on getting stuff done, but deep down I know that if the students are hitting a plateau then they are no longer in a place of learning. 

This is a great opportunity to take a break!  Reading the body language and emotions of students also means that we can respond to them.  If you’re feeling the energy start to dip or frustration start to grow, consider taking a break to bring the students back to a learning stance. I know that when I’ve spent a lot of time in heavy thinking, a break is always welcome.  While there are many different kinds of breaks to offer, there are a few of my stand by favourites that can easily be incorporated into the classroom.

Movement Breaks

Have a class that likes to get up a move?  A movement break is a great body break that helps students to move their bodies and have a little fun.  This could look like a dance break. Have your students choose a few of their favourite songs and have a moment of music and fun!  You might choose a movement break that gets them to use their imaginations, such as move around the room like you’re at 1.5 speed or 0.5 speed.  I’ve even had students share their own favourite movement break with me, whether it’s Simon Says or Silent Ball, honouring student voice is a great way to let them be creative and feel heard. 

Talking Activities

I love a good moment to chat with my friends.  You might try some talking breaks that incorporate movement, such as Would You Rather where students move to one side or another when making a decision and share their ideas with their peers.  Another fun talking break we use is Mingling to Music; students move about the room to music and when the music stops they must discuss a question or statement with a friend standing close to them. You might even ask students to create questions or topics that they would like to discuss with their peers.  You will likely find out some cool things about the students’ interests!

Brain Teasers

Not all breaks need to involve movement, sometimes a quick brain teaser or game will do the trick.   A fun strategy game we play are counting games, such as Count To  Ten, where students can strategize how to eliminate their friends from the game. One year my students loved a game we called Top Ten where we would try to guess the Top Ten of something, such as Top Ten Disney Movies, or Top Ten Animals You Would Find on a Farm.  I’d Google the answers beforehand and, in teams, the students would try to guess the answers on the top ten list. I learned a lot about what my students liked that year because they all wanted to submit their top ten subjects which ranged from baseball teams to R&B artists.  

In the rush to get through the lesson plan, these breaks might feel like time away from learning, but they’re actually part of the learning. I consider them an investment that helps students return to engagement, that energy we all feel when the room suddenly comes alive again. In all honesty, they help me return to that place too. We all benefit from a break when tasks feel heavy or our thoughts feel sluggish. Our brains need variety, our bodies need movement, and all of us need moments of connection and play.

When the room feels heavy or the energy dips, this is an opportunity to understand more about my students.  An invitation and a reminder that we are building a learning community together and these fun activities can help us to learn about one another and share some smiles. When we honour these moments, we make space for the magic to return. And that’s when the real learning begins.

Check out these links to some of the games in the post: 

Silent Ball: https://www.playworks.org/game-library/silent-ball/

Simon Says: https://www.playworks.org/game-library/simon-says/

Count To Ten: https://greatcampgames.ca/casual-games/ten/

Mingling to Music: https://www.eleducation.org/curriculum/protocols/musical-mingle/

Would You Rather: https://www.weareteachers.com/would-you-rather-scenarios-elementary/

 

Every year I start in my garden just a little bit later than the year before, not on purpose, but because May and June are so busy as a teacher. “Professional” gardeners on social media share helpful advice – from when to plant to when to close down the garden to what grows best in different light, soil, and other conditions.  Sometimes I’m even able to follow these best practices!

But my favourite ‘professionals’ are the real people in my circle. My friends, with whom I swap stories when they come for a visit.  My neighbours,  when we theorize about why we have the same plant but mine grows a lot bigger and wider while hers is a more manageable size. These conversations, as “amateur” gardeners, are as much about sharing as they are about gardening.  We try new strategies when we are rooting plants, move our leafy friends to different windows or places in the garden and chat about the differences we see in their growth and thriving. We’re trying new things, learning, sharing our results (for better or worse!) and thinking through challenges together.  It’s like ongoing science experiments that we partake in and share the results of in a never ending science fair.  

Our staff at school feels like the same kind of community. Colleagues come together in small but meaningful ways. Maybe it’s the conversation in the hallway, sharing strategies and resources that we felt worked well and ones where I need a little advice. It can be the scheduled prep time where we bring in student work and look at it together.  Sometimes it’s sharing the frustration when things didn’t go as planned and brainstorming together for a solution or a little shift that might make the difference. Every story about someone else’s classroom becomes a little cutting I can root in my own teaching. 

New ideas and resources take time to implement as we adjust, experiment, and observe together. I rarely teach a new lesson perfectly the first time. It can take awhile to work up to best practices, but it’s my colleagues that offer advice, and share their own stumbles that inspire me to keep trying. In teaching, as in gardening, there’s a joy in trying something new and seeing what happens. There’s comfort in knowing that I’m not on this learning journey alone. Just like gardening, teaching is ongoing, collaborative work where the results are never final, but always full of possibility.

Each spring, Annie starts her seeds indoors quite early and always saves some to share with us. Mal builds new structures and garden boxes and shows me her newest creations. Sandy always reminds me to just enjoy playing in the dirt and not to worry about perfection. I’m always late to the garden centres but it gives me the opportunity to get the best deals and share or swap what I find. My busiest time of year, as a teacher, falls during the optimum planting months, hence why I’m usually late to the party. Yet there’s no judgement from my little circle of gardeners, only support for my imperfect-but-always-trying practice. And through their encouragement, their joy, and their acceptance I’m reminded that growth always finds its way in community. 

Those who know me are well aware of my love of live events and especially concerts and musicals.  I love the theatrics, the costumes, the soundtracks. Something beautiful comes together on the stage in that very moment of storytelling that makes the characters come alive through the music and the shared experience. 

I’ve never really found the same love for sports, though.  Don’t get me wrong, put me in a live audience and I’m cheering with the best of them!  But I don’t follow a specific team and I’m not a sports fanatic. I’ve always felt a little removed from sports and the athletes seemed a little impersonal to me.  It’s a storyline I just can’t follow with a lot of excitement or connection. 

Lately, that seems to be changing.  

With the spotlight on women’s sports, I’m finding myself connected with the athletes.  I’m following their stories, their rises through the ranks, their funny commentaries on social media about themselves and their teammates. I’m listening to these women talk during interviews about topics that are important to me: challenges they face, uplifting one another, finding their own stories and who they truly are. Somehow, through all of these interactions, I have gained a renewed interest in sports. 

It wasn’t the shared identity or interest in sports that finally got me to remember the names of professional athletes or put the game on TV. It was that I saw a shared experience, the same struggles that many of us have: being questioned about talent, setting boundaries, trying to balance careers, mental health, and being true to ourselves. Naomi Osaka and Simone Biles stepping away from their careers to take care of themselves and their health.  Alysia Liu drawing boundaries and defining herself in her own way. Ilona Maher championing body positivity. Their journeys helped my lived experience as a woman feel a little more familiar, a little more seen. In their stories I saw humanity and a reminder that representation isn’t just about who we see, but what parts of ourselves we recognize in others. 

The books, the stories we share with students in schools might echo the same way. Flashes where students might see themselves represented through common experiences, emotions, and challenges. Instances where children might recognize their own stories and respond with a quiet, “hey, me too.”  This is exactly why representation matters: when students see reflections of their identities, they feel less alone and a little more understood. These connections can cultivate compassion, confidence and even a feeling of community.  

I still don’t identify as an athlete and it’s pretty unlikely that I will ever willingly join a sports team. But you will find me following some incredible athletes on social media and liking all their posts. I’ll still be cheering loudly and boldly at any live sporting event I’m attending. Perhaps, though, I’ll be a little bit louder for the women with a voice that is cheering for their power, their resistance, their continued pursuit of excellence. This representation feels personal; their presence feels like a win for anyone who’s ever been underestimated or whose struggles felt unseen. When I look at sports through this lens, it would seem we’re no longer in competition with each other.  Instead, we’re all on the same team. 

 

The horseshoe table is a special place in my classroom.  It’s a meeting place where students come when they want academic help or for an alternate workplace.  Sometimes I hold small group instruction at the table and sometimes individual assessments. The table is a safe space to work and talk and learn.  

There is such value in listening to children read. No matter which grade I teach, I always make time to listen to students read out loud. It’s an important interaction that helps  build confidence and creates a space where both assessment and feedback can take place with care. Many of my students have loved coming to the horseshoe table to read aloud and share what they love about stories. This experience is even more valuable when they are not feeling confident about their reading skills. The table gives them a place to practice that is private and safe.  

Each year it takes me a little while to build up to small group and individual reading time.  The first few weeks of school are about learning expectations and finding our way to independent work. I spend time building relationships with students so that they also feel comfortable reading aloud with me. Coming to the table shouldn’t feel like a test, I want to feel like our time together reading is a way for us to learn about ourselves as readers. 

In our first few meetings, I’m transparent about our purpose. I share that reading aloud is important practice and is a way that I can hear what they are doing well. I also explain that listening to them read lets me give them tips about reading. This might be the same as ‘Two Stars and a Wish’ where they hear two great things they are doing and one strategy to practice. 

Listening to students read aloud gives me the opportunity to hear their reading fluency.  In the curriculum, “fluency is the ability to read text accurately, at an appropriate pace, with expression. It is the bridge between word recognition and comprehension.” As students develop their reading fluency, it becomes easier for them to make sense of the text. Fluency is based on more than just word recognition, it also includes pacing and expression. I often marvel at how pacing and expression can indicate a student’s comprehension of a text.  For example, when it’s an exciting part and students are reading fluently I might hear their expression change to match the emotions of a character. These are the parts of reading fluency that I need to hear through reading aloud and the reading table is the best place to listen. 

At the first reading table meeting, I start with a few minutes reading short passages, like poetry or their favourite part of a book they are reading. This quick meet and greet to the reading table helps to set the tone and the time together. As meetings become more regular, selecting engaging and accessible texts is helpful. Check the resources in your classroom or school for books and reading materials that students can access and enjoy. These resources can be invaluable for students practising their reading fluency and building confidence as readers.

There’s so much to learn about the reading strategies students use when encountering a difficult word, how they read with expression, their understanding of characters and emotions and plot.  Whether in a small group or individually, time reading aloud together also offers the chance for us to model to students what fluency could sound like and engage in direct, personalized instruction. It’s assessment in the moment while developing a teaching relationship that is student centred. Whether you have your own horseshoe table or your moment takes place at the carpet or at your desk, listening to student reading will create the opportunity to learn more about your students as readers. 

As a math teacher, I often use my professional judgement* to select word problems for students.  I want to see how students apply math for a specific purpose; whether an open question that allows for multiple entry points or whether I hope to elicit a certain equation. These word problems sometimes integrate one or two strands in math. For example, engaging in both measurement and number as students added side lengths to determine perimeter. There are great problems in the sample tasks of the curriculum that are designed to help students learn through problem solving.

If you’ve looked closely at the math curriculum, you will see one of the overall expectations has no accompanying specific expectations. Located in algebra, this expectation is named Mathematical Modelling.  This expectation offers students the opportunity to: “apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations”.  

What is this and how is it different from the word problems I loved? 

As it turns out, mathematical modelling is quite different. It’s a process based expectation, meaning that while students are solving a real life, messy problem, they are going through the mathematical modelling process. Students apply this process to various contexts, bringing in learning from other strands. This is different from other traditional problem solving in specific math expectations where a word problem leads students to solve a with a specific equation or strategy. In modelling, students look at a problem outside of mathematics and then use math to propose and revise their model. 

To see the modelling cycle, look to the link that leads you to the curriculum and resources tab. You’ll find a graphic that helped me to think a little more about the mathematical modelling cycle. 

You’ll notice this is a repetitive cycle; meaning that the educator guides students to revisit the four components of mathematical modelling. The arrows suggest that each stage of the process allows opportunity for students to return to a previous stage and reflect on their model. Take a look at stage four, the stage where problem solving may be ‘finished’ with the ‘answer’. In mathematical modelling, students can and should revisit  previous parts of the process and revise or reflect on their model. 

This process mirrors real life and all of the messy ‘figuring out’ and decision making. It’s purpose feels different from a word problem where the expectation is the students extend patterns or use addition to solve how much money they spent at the movies. The focus in modelling is on the process of how we think through real life problems and can use mathematics to help us both question whether our model can provide a solution and look for possible alternative models. 

As I explore and learn more about this overall expectation, I find myself growing as a math teacher. There are so many different ways to teach and learn math; so many different purposes for problem solving and questions to pose.  I’m also learning about the ways that I use math in a real life context. Sometimes I’m estimating at the grocery store when trying to stay under my budget. Sometimes I’m solving a problem, such as planning a community event. While the second problem may not feel as ‘math-y’ as the first, I realize that math truly happen everywhere. 

 

*Professional Judgement- Judgement that is informed by professional knowledge of curriculum expectations, context, evidence of learning, methods of instruction and assessment, and the criteria and standards that indicate success in student learning. In professional practice, judgement involves a purposeful and systematic thinking process that evolves in terms of accuracy and insight with ongoing reflection and self-correction. Growing Success policy (p.158, 2010, Ministry of Education)

 

In November at … And Still We Rise, I had the incredible chance to listen to Elisapie speak.  Elisapie is an award winning Inuk musician and she shared with us about her life and her newest release titled, “Inuktitut”.  In this release, she has recorded the songs of her life and childhood that were important to her.  With permission from the original musicians, she sings each song in Inuktitut. Elisapie shared with us that the songs she chose to record each brought back a memory from her childhood; community dances, a moment shared with a friend, and other pieces of her life. The beautiful and familiar songs of my own childhood sung in Inuktitut remind me that life can be experienced so very differently; the same music can bring different memories for people.  

There’s a reflection activity I’ve used at different times of the year is the Soundtrack of My Life.  It’s a chance for myself and my students to share a little about each other in a fun way.  Firstly, we talk about what a soundtrack is and how music can communicate events or emotions. We brainstorm examples together and many students share popular or trending music tied to an event or a memory. So many conversations can stem from this activity and it really helps as a vehicle for us to get to know each other while having fun. 

Thinking back to this past school year, there were so many beautiful moments to take with me.  And just to balance those out, some challenging ones, too. At the beginning of the school year, I always feel so hopeful and excited to meet new students and try new lessons. Mid-year brings different emotions. We’re all in the midst of working hard through the winter as term one comes to an end.  I admit that the shorter days and gray skies weigh on me!  At this time of year, I try to bring more joy to the classroom and school.  We have some fun, hands-on experiments and time for community building activities. By the time spring comes, we have built a community in the classroom. I feel as though we know each other quite well and I hope they feel accepted in our classroom. 

These are all my hopes; my emotions.  They might be represented through some songs, like “True Colours” or “The Dock of the Bay”. These experiences and  songs define my important moments even though they might be different from the students. I try to ensure that the students feel safe enough to share a little something, but I also try to respect their privacy if needed.  Sharing music might mean sharing a story, but it can also mean just sharing a song that we really like and can enjoy together.  I invite you to think of which songs might help to build the soundtrack of your school year and which memories and hopes you will take forward with you to the next. 

Last month, I was chatting with a colleague of mine.  We work down the hall from each other and, as in the nature of education, we rarely get a chance to talk during our busy days.  But this time we learned a little about each other. 

As it turns out, Marc is a pretty cool guy.  He is an expert in audio/visual everything and plays three different instruments. I also learned that he recently started playing with a band.  Though he hasn’t played with others in awhile, Marc and his bandmates were in the beginning stages of getting together.  There’s been jam sessions, practicing, playing at his friend’s parties and the like. He shared that he was quite enjoying this return to music in his free time, but he especially loves it now that he feels he and his bandmates are getting better at playing together. 

Marc shared that the first few months were rough.  The bandmates were still figuring each other out. It was tough to learn to play together and support each other while learning new music and getting used to the new routine of weekly practice. There was a lot of frustration mixed in with the excitement of coming together, but now it feels fun and light and enjoyable.

I think it’s a similar story for every collective.  In the beginning of the year, school staff might have a shift; perhaps new grades or divisions for some, new teaching partners for others.  For some of us, we’re in completely different schools with an established staff and for others a completely new staff is coming together for the first time. Everyone in the school is working hard teaching and supporting the students in different capacities while simultaneously getting used to new routines, new curriculum, welcoming new students and families.   

The early days are filled with excitement and focus on students and curriculum. For me, I’m often so busy that I forget to make time to get to know my colleagues.  The days are long in the school year as I try to keep up with the pace and get to know students.  But it always seems to go better when I take the time to get to know my colleagues, as well.  We are each finding our own places on staff – who tells the funniest stories in the staff room, who is passionate about teaching math or drama or history.  As we find ways to support each other professionally, we also need to remember to support each other personally, too.  Getting to know each other and building community with our colleagues are all ways that help the entire school to feel fun and light and joyful.  

I wish I hadn’t taken so long to connect with Marc and learn a little more about him. While it’s hard to make time to build connections with my colleagues because of the busy, long days it is something that I need to make more effort to do. He reminded me that relationships with colleagues are important. A quick conversation or a shared laugh can shift the tone of an entire day. These connections don’t erase the long hours, but they do remind us that we are all human.

So as I face yet more changes in the coming year with another school move, I’m committing to noticing the people around me and to learn the stories behind the names on the classroom doors. When we build community together, our school becomes a place where laughter rings like music and joy has space to grow.

In our house we’ve recently started watching the show “Abbott Elementary”.  If you’ve never viewed it before, it’s a great modern take on what it’s like to teach in a school.  This satirical comedy is set in Philadelphia and follows the staff members as they approach challenging situations with joy and determination to do their best for the children.  

One of the characters, Geoffrey, is always known for being stoic and reserved.  He takes teaching and learning very seriously; also expecting the children to do the same.  In one episode, a guest musician is hosting a presentation in the school gym.  As the viewer can see, all the other students are laughing and singing and dancing.  However, Geoffrey’s class is following his lead by standing still with arms folded – very serious!  As the teacher looks around and notices the difference between his class and the others, something clicks.  He starts to dance with some fun moves.  And as he starts to dance, so do the kids.  Soon enough, the whole class is looking like it’s having fun at the assembly. 

Educators are often so propelled by competing priorities – paperwork, planning, marking, the newest seating plan, finding resources, etc. These are all important and vital to ensuring that this hard work of educating young minds is centred.  Teaching is the crux of our work, after all.  

At times in my career, I felt a little like Geoffrey.  Focused on making sure the lesson was perfect and that I was well prepared, worksheets photocopied, tests with the right questions. I was focused hard on building my own teaching knowledge, theories about what education should be like, and creating routines that I felt best supported student learning. 

But something felt missing without humanizing myself, staff, families, and students.  My fondest recollections of school are the ones where I felt the most joy.  The moments of learning, yes, but also moments of shared laughter and memories being built together. I remembered what it was like to sing silly songs in music class, to have those shared jokes together, to get to know one another and build a community. Finding joy every day that we spend together is important, too. 

What does that space look like, sound like, and feel like?  It looks like everyone is able to work to their greatest potential at that moment; it looks like smiling faces and silly dance moves.  It sounds like students reading confidently and engaging in discussion; it also sounds like laughter and shared stories about our weekends.  It feels like achievement and success; however, it also feels joyful and fun and accepting – and a little something like home.

I’ve spent almost my whole life in school – as a student and then as an educator. Something I’ve learned about myself is that I learn best when I get the chance to sit in the moment.  As a notoriously slow processor, I need plenty of opportunities to think, slow down, and talk things out before I feel comfortable.  As a student, I loved opportunities to work in small groups, to listen to others, share and gain new ideas.  Classes where collaboration and discussion were encouraged – language, arts, and even science – bring memories of working on projects, debating, discussing, and creating. 

I try very hard to work on creating those same experiences during math classes. Focusing on the process has given me a better understanding of the children’s learning that I would not get from looking only at final solutions, tests, and other products.  I’ve spent a lot of time thinking about meaningful math classes, although my process started off slow it got easier with practice.  

Typically, I try to plan the experience as much as possible.  We are planning all the time as educators, but sometimes those moments come up suddenly and we follow that teachable moment.  When possible, panning is an exercise for myself as a teacher.  It has helped me to understand what I’m hoping to learn about the students’ thinking and it has even helped me to grow as a mathematician. 

Though there are lots of things to consider and every educator has their own planning process, these prompts help to frame my thinking.  They might help you, if you’re looking for a place to start. 

How are the students experiencing this particular expectation? Is it the first time we’re looking at a concept?  Are students applying familiar knowledge to a new situation? Or am I hoping they demonstrate what they have learned about a concept?

Thinking about these questions helps me to think about the student experience and the information I hope to gather about their understanding.  If we’ve worked with this concept for a while, perhaps I’m hoping to see certain strategies developing in their work.  If we’ve not yet learned this particular concept, maybe I’m hoping to see what past knowledge they might be bringing as a starting point to my next lesson.

What do I anticipate students will say or do when presented with this experience? What am I hoping to see or hear? 

Anticipation has been a necessary exercise for me.  When I anticipate what the students might say or do, it helps me to focus on what I am looking for; which tools they are comfortable with, where might they start their solution.  This helps me to map out what my conversations might be with students while they are working and which direction I hope they might go.

How will I present this to the students? Do they need printed ‘rules’?  Do I want to give a personal story to the problem?

I find that presenting math to students helps to frame the experience.  Whether that’s introducing the rules to a math game or sharing context for a problem that needs to be explored – sometimes we don’t get to a firm solution! Scripting what I want to say helps me to frame my own thinking more clearly.  

What are some of the materials we will need?  How will they record their work?  How will I document what I see and hear?  

These logistics are important.  Sometimes I give students a few minutes to think of their own solutions to the question and then they come together in a small group to share and build upon their ideas.  Sometimes they are using manipulatives that I give them to use because I am hoping to observe something specific.  As I am documenting their work, I might write what I see them using or doing or I might have a checklist of expectations I am hoping to observe.  For each opportunity to engage with the students during their math experience, it’s important to have these details planned ahead of time. 

When I first started building my math for teaching knowledge, it took me some time to plan out meaningful experiences and activities for students beyond the initial question.  There are many wonderful research based resources that you can go to for ideas on problems to solve or experiences to offer students, but taking the time to work through the planning is beneficial for all of us.