New Video Resources: Instructional Routines to Improve Students’ Mathematical Thinking
New Visions for Public Schools curriculum teams have adopted instructional routines, which are “designs for interaction that organize classroom instruction” because they are a powerful tool that can help support teachers at all stages of development in their careers. Below is a personal narrative from one of our instructional specialists, David Wees, who has over 25 years’ experience working in education, on why he and the New Visions math team have adopted instructional routines. David also highlights new videos and resources that New Visions has developed to help you get started using these routines in your own classroom.
The Challenge of Initiating Mathematical Discussions in the Classroom
When I first started teaching, I quickly developed procedures and routines for things like handing out materials, but my lesson plans were all over the place. I don’t really remember exactly what I developed except that usually my lessons were based on choosing example problems to go over, producing a worksheet for students to work on, and assigning homework questions.
Any student mathematical discussions that occurred were haphazard and almost always initiated by students. Even though my lesson planning evolved, not once in my classroom teaching experiences did I deliberately plan for student discussion.
At New Visions, we’ve seen that many teachers of mathematics are in this position. As I did, they value mathematics discussions and student thinking, but they are at a loss when it comes to figuring out how to ensure that these are regular features of their classroom, accessible to all students. Magdalene Lampert, our senior project advisor, has long explored this problem and has led efforts to develop instructional routines that guide teachers’ work in this area. The New Visions math curriculum provides this support through the inclusion of instructional routines.
The Evolution of the New Visions Math Curriculum
Three years ago, Magdalene invited the authors of Routines for Reasoning, Amy Lucenta and Grace Kelemanik (pictured to the right) of Fostering Math Practices, to meet the New Visions math curriculum team and teach us two instructional routines. The entire team was amazed by what we experienced.
An instructional routine is essentially a well-defined set of moves a teacher makes to position students to talk to each other about mathematical ideas, surface student thinking, and then orchestrate a classroom discussion in order to focus students on a mathematical goal.
Instructional routines bound the scope of decisions a teacher has to make when planning a lesson. Decisions that are made ahead of the lesson focus on the thinking students will do and how one might respond. During the lesson itself, the routine allows teachers and students the space to think about and respond to each other’s thinking. The routineness of an instructional routine, if the same structure is used many times, allows thinking about roles, what’s coming up next, to fade into the background, so that more thinking can be focused on the mathematical ideas.
Shortly after Amy Lucenta and Grace Kelemanik taught the team about instructional routines, we decided to introduce instructional routines to teachers across our curriculum project through professional development. We developed a small number of tasks to help teachers get started using the routines. When we heard from teachers how classroom discussions flourished, we then decided to focus even more on supporting instructional routines. We added more tasks and supports for instructional routines to all three of our courses and also made instructional routines a consistent feature of our professional development.
Finally, the instructional routines that we incorporated into our curriculum include strategies designed to increase access to mathematics for all learners, including English language learners and students with disabilities. Rather than differentiating the tasks that students are given, teachers can rely on instructional supports that are built into the enactments of the routines to, over time, allow all students opportunities to grow and develop mathematically.
The Need for Real Classroom Documentation
Teachers who participated in our professional development series have shared that using routines increased student learning and access to mathematics across their classrooms. Only a small sample of teachers who participate in our professional development network, however, had the opportunity to see the routines in real classrooms.
We decided that our instructional materials needed to include video documentation to support teachers who cannot attend our professional development workshops. We recorded teachers from different schools and grade levels enacting the same instructional routines, but with different tasks.
How Can Teachers Learn Instructional Routines?
The videos that were produced capture not just the role of the teacher enacting instructional routines, but also the student-talk and whole-class thought process that make these materials so significant. Along with resources, like lesson plans and descriptive steps for enacting routines, the videos support teachers learning the instructional routines.
Below you will find two videos from classrooms in which teachers use instructional routines. Both instructional routines support students in making sense of mathematical ideas through mathematical structure (MP7) and having mathematical discussions with each other (MP3).
This first video to the right shows Contemplate then Calculate, during which students are given a quick flash of a mathematical object and asked to share what they noticed. From these noticings, students work together to create a shortcut to solve the problem. At the end of the routine, students reflect on what they paid attention to that might be useful in future problems.
This second video to the left shows an enactment of Connecting Representations in which students are given two sets of mathematical representations that on the surface may appear different but behave mathematically the same. Through their work together, students make matches between the given sets of representations, eventually creating their own representation. Finally, students are prompted to reflect on what they learned, coming up with a mathematical generalization they can use in the future.
Want to discover how your students could benefit from instructional routines?
Do Now: Try Out a Routine with Your Class
Try out one of these routines in your classroom. Get started now by visiting www.newvisions.org/math-routines where you can watch over a dozen videos of instructional routines from real classrooms and also access free guides and other helpful resources!