By William McCallum and Kate Nowak
People use routines for all kinds of things. Routines give structure to time and interactions. People like structure. When a child comes home from school, there might be a routine. She expects a snack, homework time, play time, dinner, some television, a bath, pajamas, a book, and to get tucked into bed. She might have responsibilities, like setting the table for dinner, and engage in predictable dialog along the way, like sharing something that happened at school. She might expect her father to sing her a song. (Over and over and over again, in the case of my daughters—Bill.) The routine makes her comfortable and makes necessary chores go smoothly.
All classrooms have routines, too. Maybe when students enter the room, they always turn in their homework, sit down, take out their supplies, say hi to other students, and start some bell work. Maybe there is a routine for being excused to use the restroom or for borrowing a pencil.
You may have heard of routines used for instruction. These are also routines: they give structure to time and interactions. But their purpose is for learning academic content. They are a good idea for the same reason all routines are a good idea: they let people know what to expect, and they make people comfortable. Let’s step through an instructional routine that many people are familiar with: think, pair, share.
Instructional Routines give structure to time and interactions. But their purpose is for learning academic content.
A teacher poses a question to the whole class. She asks students to think about it quietly for a few minutes. Then they turn to a partner and explain their thinking, and listen to how the partner is thinking. (Possibly, the teacher is eavesdropping.) Finally, the teacher selects a few students to share their thoughts with the whole class.
This routine reduces the pressure of responding. Everyone can come up with a response, rather than just the first person to raise their hand. Sharing with a partner is less scary than speaking in front of the whole class. Once a few people are asked to share with the whole class, they have already had a chance to rehearse and refine their response.
But why are routines in general good for learning academic content? One reason is that students and the teacher have done these interactions before, in a particular order, and so they don’t have to spend much mental energy on classroom choreography. They know what to do when, who is expected to talk when, and when they are expected to write something down. The structure of the routine frees them up to focus on the academic task at hand.
A well-designed routine opens up conversations and thinking about mathematics that might not happen by themselves.
Furthermore, a well-designed routine opens up conversations and thinking about mathematics that might not happen by themselves. Here are some examples. All of the lessons in our middle school curriculum start with a warm-up to get students’ mathematical juices flowing. One routine we use is a Notice and Wonder routine, like this one from grade 6. Students might notice that the cards are 4 in by 2.5 in, or that the height is missing. They might wonder what the height is, or how many cards will fit in a box. For the rest of the lesson, their minds are activated to seek out dimensions of the polyhedra they work with.
Another routine we use for warm-ups is called Which One Doesn’t Belong? In this example, some students might notice non-mathematical reasons why a figure might not belong. For example, A is the only one with no yellow in it. Others might notice that D does not cover the plane, or that B has no pentagons. As students hear each other’s reasons, they are drawn into thinking more about mathematical properties. Articulating the difference between A and B requires a closer examination of the tiling patterns than you might expect if you simply presented the figures and asked students to examine them.
An instructional routine has the ultimate goal of mathematical learning. If you have a particular learning goal in mind, an instructional routine gives you a framework for moving students toward that goal with a structured sequence of events. A good routine provides all students opportunities to do mathematics. One teacher piloting our middle school curriculum told us that the notice and wonder routines were an eye-opening experience for him. His students who were “too cool for school,” sitting bored at the back of the classroom, started competing for things to notice and wonder. They became mathematically activated for the rest of the lesson.
It’s hard work teaching in a way that gets kids thinking mathematically, sharing their reasoning, and actively looking for strategies and procedures to solve problems. Just as a good bedtime routine eases the burden of caregivers and makes an evening go more smoothly, a good instructional routine eases the burden of teachers and makes more time for doing mathematics.
- If you want to know more about the IM instructional routines, they are described here. (Free registration required to view.)
- To learn more on implementing routines in your classroom, IM has developed a professional learning workshop. Learn More.
- For further reading on applying routines, take a look at featured blog post, Using the 5 Practices with Instructional Routines
Bill McCallum, founder of Illustrative Mathematics, is a University Distinguished Professor of Mathematics at the University of Arizona. He has worked in both mathematics research, in the area of number theory and arithmetical algebraic geometry, and mathematics education, writing textbooks and advising researchers and policy makers. He is a founding member of the Harvard Calculus Consortium and lead author of its college algebra and multivariable calculus texts. In 2009–2010 he was one of the lead writers for the Common Core State Standards in Mathematics. He holds a Ph. D. in Mathematics from Harvard University and a B.Sc. from the University of New South Wales.