I’m still beaming from Valentine’s Day – and not just because of the cards and chocolates from my wonderful family and friends. My Valentine’s Day this year was made extra sweet by seeing one of my favorite activities in action, A Piece of My Heart.
On the 13th, I shared this activity on Twitter and passed it along to my teacher friends that are always up for a good discussion prompt. This one in particular may have ticked a few boxes. First, many teachers I know are currently working through ideas about fractions, decimals, and percents with their students, so providing the right prompt at the right time is a plus. Second, this activity may offer a different perspective or way of connecting these ideas. Consolidating basics in a lot of different ways is always a must. And third – it is covered in hearts on Valentine’s Day – come on! Sign me up! Still, knowing it is a good activity – all I can do is share the love and cross my fingers that teachers recognize its value and give it a go. I have to say, when I opened it on the 14th, I was really excited to see a bunch of anonymous animals and the icons of my math buddies at the top of my slide, letting me know that teachers were in the activity and checking it out. Even better was when I popped into a classroom at Brookside Junior High and saw the first slide projected. Yay! I could see this activity in action.
If you haven’t seen this activity yet, have a look at the pictures below. What would your reasoning be for each prompt? What do you think your students would say? How would you use this activity to facilitate a discussion in your classroom?
First, let me acknowledge the fact that the teacher facilitating this activity, Jeanette Brennan, is a seasoned veteran. Every year she spends months building a positive classroom culture based on some critically important and productive beliefs about the teaching of mathematics. The beliefs that made this activity an overwhelming success?
1) Discussion in math class is needed for a deep understanding of topics.
2) Students need to be given the time to play…persist…and prove.
Facilitating a whole class discussion is an art. How long do you wait before you discuss? Who do you call on? In what order? How do you make sure the conversation and discussion is between students as well as between teacher and student? How do you get students to restate what another student has said or build on another student’s idea? What do you do when a student is wrong? How do you create that environment where students share what they figured out so far, share the mistakes they made, how they knew something was not right, and what they did to rethink and adjust? Well, patience is key. So is modeling daily that reasoning is valued. Think about how long you discuss a question after the answer is revealed. Does your math class focus on answer getting or does it focus on the math reasoning that led you to your answer? How does that focus trickle down to student persistence? Do you have to beg students to share and explain their thinking or are they doing this on their own? Could this be a product of what they see valued in your class?
In Jeanette’s class, the students are used to interesting questions and engaging in math discussion. They have whiteboard desks arranged in conversational groups of 4, markers to use, and they get ready for their opening prompt happily with few reminders. That routine took time to establish. Students got to work right away. There was no shouting out of answers trying to be right first. Students that found an answer quickly were carefully crafting their explanation or trying to think about the prompt in a different way. That practice took time, patience, and plenty of gentle reminders to put in place. As I walked around, many students stopped me to ask, “want to hear what I was thinking?” Um…yeah! Not, “Here’s my answer”. That mindset took time to build. Some students took the time to reproduce the picture on their desk while others made their way up to the projected prompt to take a closer look, draw some ideas, or share their thinking with a friend. They didn’t need permission – they knew they were welcome to do this. Movement is good. We have time to draw it out, time to share with a buddy, time to try it another way. These shared values were known.
When we were ready to discuss, Jeanette asked “Who would like to share their thinking?” , not “So what’s the right answer?” I was expecting a few answers and approaches. What I was pleasantly surprised to note was that students were also volunteering how their idea was similar to or different from another student’s idea. That ability and willingness to listen to each other as well as to the teacher takes time to develop.
Here are a few ideas students shared in the class discussion . . .
Pretty cool right?!? And that was just the first prompt!
If Jeanette had stopped after one correct solution was presented, we would have missed out on so many great ideas! Perhaps more importantly, some students may have felt that their solution was not right or not the preferred method based on what was shared. Instead, Jeanette maximized the discussion time. Every student that wanted to, had a chance to speak. Jeanette encouraged students to share with the class ideas she had heard in small groups as she walked around. Some students spoke from their seats, some came up to point out or draw their ideas. It was LOVE-ly.
Jeanette’s values come through in everything she does. You can see that she knows students have cool ideas about math and that these should be shared. She knows that problems can be solved in more than one way and taking the time to compare and contrast methods and reasoning is time well spent. She knows that discussion in mathematics serves many purposes. It helps students without ideas have something to try. It helps students celebrate their persistence and appreciate their math journey. And it helps confident students consolidate their ideas, make connections in methods, and compare strategies with efficiency and flexibility in mind. Her belief that students are already coming with loads of brilliant math ideas is quite evident. They don’t need to be shown a solution. They can get there, lots of ways, all on their own. Yes…it was LOVE-ly indeed.
I also realized during Jeanette’s class that my slide deck needed a revamp. I often share activities I have created but I am not often explicit about how I would facilitate the activity in a class. Are my values coming through in the activities I share? Maybe…? Maybe not. That is a problem.
My tagline is Play…Persist…Prove. And not just because I enjoy alliteration. It is what I value in a math class. It is what I reflect on when I create activities and it is what identifies for me if an activity is worthwhile. Do students get a chance to play around with their math ideas in different ways? How? Are they invited to and supported in persisting with the task when their first idea or strategy doesn’t pan out? And finally is there the chance to prove to others through discussion and modeling that their math ideas are solid? This means students need time to engage with the task, thought partners to strategize with, learn from, and prove to, and a choice of different tools to use especially if they need a fresh start. My task worked well in Jeanette’s class because we share many ideas of what math learning should be. She looked at my slide deck and knew how to facilitate it because this is how she already operates. But these ideas about the ideal facilitation of the activity weren’t so obvious looking at my first draft. My values weren’t obvious…and they should be. I didn’t say anything in my slide deck about giving time, promoting conversation and whole class discussion. These ideals are so ingrained in what good math instruction should be, I sometimes make assumptions about how my activities will be used in classes. If I want more success stories and rich conversations like I witnessed at Brookside Junior High, this activity, and every activity I share, needs more information. Time for some edits.
Originally A Piece of My Heart, was simply a series of four prompts followed by my answer drawn out nicely with a step-by-step solution. When Jeanette made her way through the activity in class, the solutions I offered were really unnecessary. They actually only served to highlight one of the ways to think about an answer, and by highlighting one way it could be interpreted as the best response. Not my intention. I included solutions in an attempt to support busy teachers in using an activity that was ready to go and easy to facilitate. I made assumptions that teachers would know what to ask, what to have on hand, and what the intended learning might be. I have since made some revisions. Hopefully, my values shine through. Now it includes tips for teachers, and some speaker notes on each slide for ideas about facilitating. While I hope that teachers will take the activity and rework it to fit with their own class, notes on the intended facilitation and what materials to have on hand can only help. In addition, the solutions are now updated to showcase the brilliant ideas Jeanette’s classes shared this Valentine’s Day. These possible solutions are found at the end after all the prompts. That way, teachers can see ahead of time where conversations could go. If discussions like these are new to them, they can facilitate with confidence in a way that promotes creativity and connection versus single solution answer getting. Teachers can decide how or if to use the given solutions with their students.
I learned so much from being in Jeanette’s class yesterday. First, give students lots and lots of time. If the activity is worthwhile, like this one, we want to encourage creativity and conversation. We need time for that. Second, students don’t need to see my answer – they’ve got their own answers that are creative, brilliant, and unpredictable. All they need is support as they play, persist, and prove. And third – discuss. Discuss in small groups, share with the whole class, compare and contrast ideas, and see if you can find the math that connects the ideas together. Even with a great task – maximizing the effectiveness takes time. The final message I took away with me was about sharing my values. Jeanette’s values shine through in how she conducts her class daily. If I share an activity, I have to take the time to make sure my values about math learning are not hidden from view. I can’t assume that teachers know how to facilitate an activity I supply. Some classes still operate with the teacher sharing their knowledge and the students repeating given steps or memorizing procedures. If my goal is showcasing a more productive way to operate, the activities I share must always include a why and how. Yes…this will take time. Just as building the productive classroom culture in Mrs Brennan’s class took time. But if it helps students and staff tap into a love for math learning beyond answer getting, then the time spent is certainly worthwhile.
Jeanette sometimes shares that she “knows my warm-ups go on too long sometimes”. Yup – even the best teachers are hard on themselves now and again. Perhaps it is that constant reflection and drive to improve that makes her so great at what she does. When I look around her room at the smiling, confident kids excitedly sharing their ideas about math, I know in my heart she’s got the right focus. Jeanette Brennan is a gem. I am sure the staff and students at Brookside Junior High know how lucky they are to have her.
Are you still working toward building a math class that you and your students will love?
Keep at it. Remember . . . love takes time.
JoAnn Sandford Math 