Bringing It All Together
Suggestions for Teaching and Reflecting on Lessons That Support Disciplinary Literacy Practices
While good teaching requires investing time and energy into structuring and planning lessons, it is also important to attend to how lessons unfold, including what students seem to be learning from the lesson you are offering them.
One important consideration is whether the mathematics problems or tasks you identified to be at the center of your lesson actually engage students in the kind of mathematical thinking and reasoning you had intended and whether students are engaging in disciplinary literacy practices as you had hoped.
For instance, researchers (e.g., Boston and Smith, 2009; Stein et al., 1996) have found that rigorous non-routine mathematics problems and tasks were often enacted in ways that inadvertently reduced the level of challenge. This can happen when problems or tasks are broken down into a series of steps for students to work through, when the focus is on procedures and answers rather than on the thinking and reasoning behind these procedures and answers. It can also happen if the teacher explains how to solve the problems and tasks before letting students engage in trying to figure them out for themselves. There is a much greater likelihood that students will engage in the kind of thinking that is consistent with the authentic work of mathematicians—and the disciplinary literacy practices they engage in—if mathematics problems and tasks are enacted as intended.
An important implication is that mathematics lessons need to allow students to engage in “productive struggle” if they are to learn the mathematics that is the focus of the lesson and if they are to meaningfully engage in disciplinary literacy practices. What are some indicators of whether this is happening during your mathematics lesson? Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014, p. 49) identifies the following classroom-based indicators of success specifically focused on this productive struggle:
- Students are engaged in the tasks and do not give up. The teacher supports students when they are “stuck” but does so in a way that keeps the thinking and reasoning at a high level.
- Students explain how they solved a task and provide mathematical justifications for their reasoning.
- Students question and critique the reasoning of their peers and reflect on their own understanding.
- Students are able to use tools to solve tasks that they cannot solve without them.
- Students explain their thinking about a task to their peers and the teacher. The teacher asks probing questions based on the students’ thinking.
These indicators are consistent with what can be seen in the instructional practice guides on the Achieve the Core website as well as what is captured in many of the videos now available to show what this mathematics teaching practice looks like in action.
A second important implication is that students should be producing work, either during the lesson or at home, that provides evidence of the kind of thinking and reasoning you hope to support and the kind of disciplinary literacy practices you plan to address. What do you see in the work you collect from your students? Do you see evidence of students persisting in the solution of rigorous problems and tasks? Do you see evidence of students explaining their thinking and reasoning? Are you providing students with feedback in ways that support their reengagement with the content so they have opportunities to strengthen that work? To what extent are there opportunities for students to share, discuss, and revise this written work as part of your lesson?