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.
