Bringing It All Together
Structuring and Planning Lessons That Support Disciplinary Literacy Practices
One important question to consider is how mathematics lessons might be structured. How might they begin? How might they end? What happens in the middle? It is clear that structuring lessons around rich non-routine mathematics problems and tasks is important, because solving these kinds of problems and tasks is at the heart of authentic mathematical activity. These kinds of problems and tasks provide opportunities for students to share and discuss ideas, clarify understandings, develop convincing arguments, learn to see things from other perspectives, and develop a language for communicating about their mathematical thinking (Smith et al., 2009). In Thinking Through a Lesson: Successfully Implementing High-Level Tasks (Smith et al., 2008), the following structure is offered for lessons that have rich non-routine mathematics problems and tasks at their core:
Part 1: Select and set up a mathematics problem or task.
Part 2: Support students’ exploration of the problem or task.
Part 3: Share and discuss the task.
This lesson structure has important implications for planning. Below are three aspects of planning a lesson with a rich non-routine mathematics problem or task at its core.
First, identify the kinds of problems or tasks that address the mathematics content that is to be the focus of the lesson. Is the problem one that all students will be able to engage in at some level? Is it rich enough to provide a challenge to students who might need that challenge? Is it likely to elicit rich discussions among your students? Is it aligned with targeted mathematics content and practice standards? This typically involves solving the problem or task in order to think about the range of strategies students might use, what tools and resources they might need, and how you want students to share and record their work.
Secondly, think about the kinds of questions you should be ready to ask during the lesson as students work on the problem. What will help them get started if they are struggling? What will help them focus on the key mathematical ideas? What problem-solving strategies might be helpful? What models or representations might be leveraged? How might you encourage conversation among groups of students so their thinking can be shared? It is useful to identify these kinds of questions before the lesson begins.
Thirdly, identify how you will orchestrate the whole-class discussion of the work that students complete. What strategies and representations will you want students to share, and why? In what order might these best be shared? What important connections do you want to help your students make as they look across the different strategies and representations? How will you help them make the kinds of mathematical generalizations that deepen their mathematical understanding? And how will you build on this lesson in subsequent lessons?
While it can be time-consuming to plan these kinds of lessons, it can be very helpful when it comes to enacting the kinds of lessons that engage students in disciplinary literacy practices that are consistent with the Mathematics Teaching Practices. Over time, you may find that this lesson structure feels increasingly comfortable for you and your students as the classroom culture continues to shift toward the authentic work of mathematicians. You may also find that your students more readily engage in challenging mathematics problems and tasks that reflect the expectations of the CCSSM. Finally, as you become more familiar with the range of materials and resources that are available, and as this lesson structure begins to feel more comfortable, you may find that it takes less effort to plan these kinds of lessons.