When Thinking is Visible

How do we know that there is really deep thinking, measurable learning, and significant growth happening in our classrooms? If you have followed any of my previous posts, you know that I am pretty passionate about classrooms where there is a high level of rigor, real life engagement, and deep thinking. I love thinking about rigor as "cognitive demand" - in simplest terms, who is really doing the thinking and the work?

This past weekend, I attended the NYSRA Conference in Rochester, New York. One of the most interesting sessions that I attended was by Maureen Boyd, a professor at University of Buffalo, which focused on classroom talk (find her book here). Although the idea of classroom talk seems simple, when you think of classroom talk as visible thinking, it takes on a different shape. Dr. Boyd talked about the power of the "third turn." The initial question is the first turn. The student response is the second turn. The power comes in the third turn - what the teacher does in response to the student response. The teacher can either elevate the thinking in this third turn by asking an additional question or asking for additional student responses, or the teacher can stop the thinking in the third turn by simply saying "okay, good." If the teacher's response ends the thinking, then the student only responds for the purpose of answering the question and getting a correct response - that is definitely not visible thinking. If you really want to learn about what students know or understand, you have to be willing to listen to student responses and all that they show you about what students do, and do not, think.

As School Leaders, it is our responsibility to know the kind of questioning, discourse, and thinking that is being asked of our students in our classrooms. When we see instruction that does not push our students' thinking and learning, it is our responsibility to have the hard conversations with our staff that will help them to think about pushing the thinking of our students. This idea of "the third turn" provides us with a clear strategy that can immediately change the level of questioning and discourse in our classrooms. Our classrooms must be vibrant places, full of cognitive demand and supportive relationships that help our students see their true potential. In this video from PS 359 in the South Bronx, you see exactly that - students who are given opportunities to show their thinking, explain their understanding or misunderstanding, and to take risks that will lead them closer to mastery of the standards. As leaders, we must push for our classrooms to engage our students in this kind of visible thinking in order to ensure that they are thinking deeply and authentically engaged in rigorous thinking.


Making Thinking Visible from NYC Public Schools on Vimeo.

Math Matters

When I was in school, math was about right or wrong: correct or incorrect. If you struggled with figuring it out or had to think about the problem differently, it was discouraged. I have a vastly different understanding and appreciation for mathematics now that I am on the other side of the whiteboard. But, our instructional practices haven't caught up to the purpose of higher standards. The rationale behind higher standards is to move mathematics away from a purely procedural study into a study of questioning, problem-solving, testing hypotheses, and failing forward.

The majority of our metrics in our receivership status focus on mathematics - so math has been on my mind a considerable amount lately.

The purpose of higher standards in mathematics is to bring back the joy and curiosity that should live in problem solving - to inspire the next generation of thinkers, to build confidence in reasoning skills, and to develop young people who can use logic and have a deep understanding of the world around them. Too often, instruction focuses on teaching children to excel at ritual compliance - rather than to excel at thinking, questioning, and problem solving.

So, what would it take to have more of our mathematics classrooms look like what Dan Meyer describes? As we have tried to increase the level of rigor in our classrooms and promote more thinking and problem solving, we may have actually gotten farther away from the actual intent of the standards. Even as we have tried to increase the conceptual understanding of mathematics, we continue to apply procedural approaches and often miss the opportunities for deeper learning. We have to structure our instruction and our questioning to encourage our students to take risks, to think deeply, and to productively struggle. That means that we, as educators, have to do the math to think about how our students might see the challenges that they are facing.

If we are still approaching the teaching of mathematics as a procedural study, we will only produce students who see the procedure of the problems. Even the explanation of thinking can become a procedure if that is the way it is presented. In order for our students to achieve the higher standards, we have to provide them with strong foundational skills and plenty of modeling and practice with thinking about thinking. It is critical for students to understand that it's okay to struggle and to revise their thinking as part of how they make meaning of the problem or task. That struggle is part of what will make our future engineers, computer programmers, or video game designers successful. Building excitement and conceptual understanding about math begins in our elementary classrooms where we can make math fun and show our students that they have the support they need to learn and grow. Giving our children the chance to experience math, rather than just doing practice problems and worksheets, will give them the best chance to gain the skills that they need to not only meet the higher standards, but also to make connections to anything that they wish to pursue in their future.