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. Continue reading “What is an instructional routine?”

By Jennifer Wilson

1. “Nothing”
2. “Math”
3. “The questions on this worksheet”
4. “Deciding if two figures are congruent”

During class, one of your students asks you, “Is this going to be on the test?”

How do you respond?

1. Pretend like you didn’t hear the question
2. With an eye roll
3. “Everything I say is going to be on the test”
4. “Let’s see how what we’re doing is connected to today’s learning goals”

We know from years of math education research that establishing and sharing learning goals are important for both teachers and students. Even so, we don’t always agree with when and how they should be shared.

By Kristin Gray

As a teacher, curiosity around students’ mathematical thinking was the driving force behind the teaching and learning in my classroom. To better understand what they were thinking, I needed to not only have great, accessible problems but also create opportunities for students to openly share their ideas with others. It only makes sense that when I learned about routines that encouraged students to share the many ways they were thinking about math such as Number Talks, Notice and Wonder, and Which One Doesn’t Belong?, I was quick to go back to the classroom and try them with my students. It didn’t matter which unit we were in or lesson I had planned for that day, I plopped them in whenever and wherever I could because I was so curious to hear what students would say. Continue reading “Warm-up Routines With a Purpose”

By Jody Guarino

As a teacher, I constantly wonder how I can elicit student thinking in order to gain insight into the current thinking of my students and leverage their thoughts and ideas to build mathematical understandings for the class.

First, I need a task that will make student thinking visible. Here’s a task from Illustrative Mathematics, Peyton’s Books.

Peyton had 16 books to take on his trip. He lost some. Now he has 7 books. How many books did Peyton lose?

The entire Illustrative Mathematics team spends a lot of time reading about teaching and learning. Most recently, we have been reading—some of us rereading—and reflecting on the 5 Practices for Orchestrating Productive Mathematics Discussions by Mary Kay Stein and Margaret Schwan Smith. Members of the team were asked to reflect on the following two questions to share with the Illustrative Mathematics community:

• What idea stood out to you when reading the 5 Practices for Orchestrating Productive Mathematics Discussions?
• Why do you feel this idea is important?

By Robin Moore

As a coach, how can I help teachers structure their lesson-planning in order for students to unpack their mathematical understandings?

This question is always at the forefront of my mind as I reflect on my work as an instructional coach. Most times, I walk into classroom after classroom witnessing teachers working harder than the students. To be clear, the students are all on task and working on the mathematical concepts presented to them with little to no behavior problems. The biggest challenge for teachers is attempting to differentiate for the range of learners in the classroom. To address this challenge, teachers have implemented a math workshop format. In this format, teachers communicate the learning objectives for the lesson and present a scaffolded mini-lesson where they gradually lead students through problem-based activities to ensure each student’s success. While the activities are problem-based, something authentic is missing and many would say that the work does not appear rigorous for all students. From a coaching lens, I wonder when and where learning is happening and who is unpacking it.   Continue reading “Using the 5 Practices with Instructional Routines”

By Alicia Farmer

I am the type of teacher you want on your teaching team. I am the person that can remember vast amounts of details, predict potential obstacles, and meet any and all deadlines.

My organized personality is apparent everywhere in my classroom.  From classroom routines to student supplies, everything has its place.  This organization also shows through in how I plan ahead for all of my lessons. Even after 12 years of teaching, I am still not able to “wing it” when teaching a lesson. While I know my organization and meticulous planning are advantages for many aspects of my teaching, I often felt like they kept my instruction from becoming truly student-centered because these characteristics did not leave much room for flexibility. I would have a planned path for a lesson—a very specific, usually teacher-centered, way to get to the end—and never imagined I could rely on my students’ work to guide the pacing, discussion, and overall lesson as effectively as I could.   Continue reading “How the 5 Practices Changed my Instruction”

“Whether we’re asking students to analyze a historical event, reflect on a text, or work toward a scientific discovery, we need to give students a chance to dig into the ideas on their own first.”

By Kristin Gray

I’ve come to think that approaching a lesson plan is like approaching a 500-piece puzzle. It’s hard to know where to start. It takes time. It involves endless trial and error. But when it’s finished – when all the pieces have been put in place – there’s a sense of pride and accomplishment. Continue reading “The 5 Practices Framework: Explicit Planning vs Explicit Teaching”

By William McCallum

Somewhere back in days of Facebook fury about the Common Core there was a post from an outraged parent whose child had been marked wrong for something like this:
$$6 \times 3 = 6 + 6 + 6 = 18.$$
Apparently the child was supposed to do
$$6 \times 3 = 3 + 3 + 3 + 3 + 3 +3 = 18$$
because of this standard: Continue reading “Ways of thinking and ways of doing”