Just as conferring is one part of the readers’ and writers’ workshop and could not be implemented in isolation, conferring in mathematics must take place on a broader instructional stage. As teachers, we hope to talk with students about their thinking as they struggle with big ideas and ways of thinking mathematically—in the midst of this kind of grappling there is quite a lot to talk about. But if tasks or expectations in the classroom don’t demand deep thinking, we’re left with thin conversations about answers. So, what does it take to create a mathematical environment ripe for conferring?
Rich math tasks create space for students to struggle with concepts, develop strategies, make mistakes and connections, and engage in math practices. In the messiness of developing understanding through problems, we can have interesting and fruitful conversations with students about their thinking while that thinking is still forming. These are prime moments for nudging students down a productive pathway. The right task creates these opportunities and in this chapter, we’ll look at what makes such a task.
Although students have always been asked to solve problems in math classrooms, in the past these problems have shared some features that make them less productive for learning and discussion. These problems typically have a single prescribed procedure for solving them and a single correct answer, which all students were expected to mirror. Success was defined by the uniformity of students’ work, and any talk was often limited to the reporting and evaluation of answers. This is a desiccated version of mathematics; with just the withered husk of procedures and answers there is not much to discuss.
What Is a Rich Task?
What makes a task rich depends in part on your students' daily experiences, what your students already understand, and what they are ready to learn. However, rick tasks share several features that can guide you when selecting and writing problems for your students:
1. Rich tasks are open-ended, encouraging multiple solutions.
2. They allow students to struggle and make sense of important mathematical ideas.
3. They require justification and the use of other mathematical practices.
In life, mathematics is messy and full of authentic questions and choices. This is what rich math looks like, the ordinary and yet complex problems we face every day as we navigate the real world. Our challenge as teachers is to bring this lively, interconnected, dynamic experience of mathematics to students through rich tasks.
Jen Munson is a postdoctoral fellow in learning sciences at Northwestern University, a former classroom teacher, and a professional developer who works with teachers and school leaders across the U.S. to develop responsive, equitable mathematics instruction. She is coauthor of the Mindset Mathematics curriculum series.