CCTM seeks to be a central hub for teachers and leaders across the state of Colorado to come together in learning and teaching mathematics. Feeding our curiosity and desire to continue to grow our practice is enhanced when we learn, attempt and reflect together. Our Teaching for Thinking Book Study provides an opportunity for just that. Each month we dig into a Reasoning Routine, engage in mathematics together, and reflect upon the practices as learners and then as teachers attempting the routines in our classrooms and learning environments. The following quotes are reflections from participants on the experience and impact of our work together this year.
“I liked the real math example that we could analyze in terms of the routine. I will be bringing these ideas up at our next PLC session. I like reading the text and then being able to discuss questions that come up in my mind. My students and coworkers will benefit as I change my teaching practices to make my lessons more engaging for students and enthusiastically share the results with my math team at school.”
~ Richard George
“I like discussing and doing math tasks together. Discussing how the routine went with other participants was so helpful. I feel like I can improve at this! My coworkers will attend next week's session and I'm looking forward to debriefing with them.”
The Teaching for Thinking book study has provided new strategies to math talks. In my classroom students are sharing more of their thinking and enjoying the math discussions and discourse. The ability for students to see different thinking practices and supportive practices really engages student learning and their work is demonstrating a growth in understanding. Having students annotate and seeing each other's annotations has developed individual confidence and thinking.
Unlike other math classes, the Teaching for Thinking book study has allowed me to look at mathematical thinking from a student’s perspective. Throughout the study, I find myself asking “why did I do the problem that way?” I enjoy doing the math with other teachers but I have really learned a lot listening to people articulate how they understand the problems, their thoughts, and approaches.
The Teaching for Thinking book study has allowed me to collaborate with other math teachers from all levels of perspective and experiences. I love the opportunity to work in small break-out rooms and getting to share our individual thinking and problem solving. The facilitators scaffold the learning for all participants to be engaged. Most importantly it has been a joy getting to meet our CCTM teachers!
“The most useful part of the book study for me is the small group working through each of the routines, then the large group with everyone sharing. I learn much by seeing how others see/approach things. I enjoy working in this group of math educators where everyone’s conversation is genuinely affirmed. I feel comfortable and valued and the respect for everyone is modeled throughout the course. I will always keep this in mind in the future.”
We close up this section by bringing some context to the amazing collaboration and learning from the participants of the Teaching for Thinking book study. The following will showcase the routines we have practiced in our monthly book studies with respect to the chapters.
Chapter 4 works through the routine Contemplate then Calculate. In February the group had time to not only learn about annotation but practice in a digital setting. See the images below with how the group thought about finding calculation shortcuts. Can you make sense of the annotations? What would your annotations look like?
Chapter 3 in Teaching for Thinking is digging into the reasoning routine Decide and Defend. Decide and defend is a reasoning routine to support constructing arguments and critiquing the reasoning of others. Check out Jose’s Claim below, what questions would you ask the student about the work?
Essential Strategy Making thinking visible through annotation:
“Annotation is a visual record of student thinking that connects verbal processing to visual processing.” The discourse students engage in help them access the learning and develop mathematical ideas through a variety of modalities (speaking and listening). Including the visual component of pictorial annotations includes another modality and creates accessibility for all students, and a visual record of students’ thinking processes.