Many teachers have shared with us their successes in implementing the 5 Practices for Orchestrating Productive Mathematics Discussions (Smith and Stein, 2018). Starting with Setting Goals and Selecting Tasks, and moving through Anticipating, Monitoring, Selecting, Sequencing, and Connecting, the 5 Practices provide concrete guidelines about how to prepare for and structure students’ work on rich tasks in ways that address important math content while building on students’ thinking.
Still, implementing the 5 Practices is not without challenges. In a new series of grade-band books, The 5 Practices in Practice (Middle School and Elementary), we take a deep dive into the 5 practices and discuss how to address key challenges that elementary, middle, and high school teachers face in making the 5 Practices as part of their instructional routine. Here’s a look at two of those challenges, along with ideas about how you can address them.
Anticipating students’ responses
The challenge: Moving beyond the way you solved the problem
Central to the 5 Practices is anticipating how students will solve the task you’ve selected. The idea is that by carefully anticipating students’ responses before instruction you will be better prepared to respond to students during instruction. If you are like other teachers we’ve worked with, at times you might feel limited by your own experiences — you have one way to solve a task and find it hard to imagine other ways. What to do? First, grab a colleague or two and ask them to solve the problem or post the task on social media. Even if someone teaches a different subject or grade, their ideas may be similar to what your students would do. Eighth-grade teacher Michelle Musumeci explains that for her: “It helps me a lot just by being able to bounce ideas off other people…If you saw one way, and someone else sees another, then you start thinking ‘Oh okay, maybe a student would approach it this way.’” You might also want to consider different ways to represent the situation. Maybe you used a table to solve the task but perhaps students would create a drawing or model, use manipulatives or make a graph. And don’t forget to take pictures of solutions that your student produce – over time you’ll develop a rich collection of solutions to consider as you prepare to teach the task again.
Selecting and sequencing student solutions
The challenge: Expanding beyond the usual student presenters
When it’s time for the whole-class discussion, you’ll need to select student work to highlight. As you do, you’ll want to pay close attention both to the mathematical potential of a solution and to who will do the presenting. While it might seem easiest to choose students who you know will give clear explanations, over time, all students should have the opportunity to present to their peers. Your choice of which students present in class sends an important message about who and what is valued mathematically in your classroom. You may find it useful to have a dedicated class list where you indicate each day’s presenters. This can provide a quick way for you to see who hasn’t had a chance to share their work recently. As you choose student work to highlight in class, you’ll also be thinking carefully about the mathematics involved in various solutions. Consider who might benefit from sharing a solution that was used by many students in the class, and who might benefit from sharing a solution that is more unique. And don’t feel that you only need students to see correct and complete solutions. Exploring why a solution is not correct can often uncover important ideas and reinforce that making mistakes and revising our thinking is an important part of learning.
When asked about her journey with the 5 Practices, Michelle Musumeci explained, “At first, I was nervous to try doing math tasks with the monitoring tool and facilitating the discussion. However, every time I did it, it got easier and more efficient… And the thinking that comes from the students … is so much deeper than what I was getting from them before teaching this way.” Comment below to let us know about your journey and how you’ve made the 5 Practices work in your classroom!