Mathematical discourse can be defined as the habits of exchanging mathematical ideas within a classroom. Discourse encompasses the ways in which a classroom community thinks about, talks about, and represents mathematics. A class’s discourse is shaped by the teacher’s facilitation of learning and class discussions, and the nature of the mathematical tasks provided to students.
Curriculum standards require that we help each of our students become increasingly proficiency with mathematical discourse every year they are in school, but how do we accomplish this? How do we teach the skills of mathematical discourse?
The TeachingWorks program at the University of Michigan offers the following strategies for teaching classroom norms and routines, including the norms and routines of mathematical discourse:
|Strategies for Teaching Norms and Routines Introduce the norm or routine.Justify why it matters.Label the norm or routine when it occurs. Provide opportunities to practice.Reinforce the norm or routine over time.|
I saw these strategies enacted in the TeachingWorks Elementary Mathematics Laboratory.* It was the fourth day of the summer math class for 5th grade students. The teacher, Dr. Deborah Ball, began the morning with this problem:
|How many different three-digit numbers can you make using the digits 4, 5, and 6, and using each digit only once? Show all the three-digit numbers you found. How do you know you found them all?|
After the students had worked on the problem independently, Dr. Ball called them together for a class discussion. I scribed Dr. Ball’s questions and facilitation moves during the discussion (students’ names have been changed) and noticed how she taught the skills of discourse while simultaneously teaching mathematics.
|Teacher Prompts and Questions during the Class Discussion Please have your eyes on Claudia when she’s speaking. Who can repeat what Claudia said in your own words? It was really good. Claudia, is that what you said? You were listening carefully, Sierra. Part of what we’re doing right now is learning to listen to each other so we can learn from each other. Claudia, you can pick someone to present another solution for the problem. Erik, would you repeat your solution in a big voice so we can all hear you? Why is that a solution? Does anyone have any questions for Erik? If you didn’t hear Erik, please ask him to repeat his explanation. Does anyone have a comment for Erik? A comment could be “I like the way you….” Do you think this method of recording was useful? What did Claudia and Erik teach us? Do you think we could use this idea with another problem? Who can name one thing that was great about our discussion just now? Why is that important?|
Watching Dr. Ball teach the skills of mathematical discourse helped me to think about how I might teach discourse at the beginning of the year. I could outline the specific skills of discourse I wanted to grow in my classroom or school. Then I would design a month-by-month plan for introducing, practicing, and reinforcing these skills to help each of my students develop the abilities needed to engage in mathematical discourse and to recognize their growth. Time spent teaching the skills of mathematical discourse builds a sense of community in the math classroom and strengthens students’ identities as mathematicians. It is also an investment in our students’ learning capacity for entire school year and well into their futures.
*The TeachingWorks Elementary Mathematics Laboratory (EML) at the University of Michigan is both a summer math program for students and a professional learning experience for educators interested in learning about effective mathematics instruction. More information about the EML can be found at http://www.teachingworks.org/training/LaboratoryClasses.
Ball, D., & Shaughnessy, M. (2017). Lab class #4 lesson plan. TeachingWorks, University of Michigan Ann Arbor.