Discourse in mathematics instruction refers to the verbal interchange of ideas – both written and oral ways of representing, thinking, and communicating – that teachers and students use as they perform mathematical tasks. By orchestrating and promoting discourse, teachers can actively engage students in mathematical thinking. In discourse-rich mathematics classes, students explain and discuss the strategies and processes they use in solving mathematical problems, thereby connecting their own everyday language with the specialized vocabulary of mathematics.
Through discourse, teachers can better understand the mathematical needs of the class—what the students know, misconceptions they may have, and how these might have developed. Focusing on the language of mathematics also helps teachers to reach out to English learners and make mathematics more accessible to them.
Building Options for Discourse
From 2008 to 2011, SCOE and the California Math Project: North Coast (CMP:NC) worked with local teachers to develop effective classroom strategies to increase the academic engagement of all learners. A team of school improvement, language arts, and mathematics specialists developed a framework – Building Options for Discourse: Students and Teachers Responding (BODSTR) – and helped teachers implement it by providing demonstration lessons and onsite support.
This chart (pdf) provides examples of accountable talk, teacher questions, student responses, and teacher strategies that are featured in the BODSTR framework. Discourse options for generalizing, justifying, explaining, recalling, and confirming are highlighted. Using the BODSTR framework, teachers planned lessons that included these key strategies:
- Scaffolding thinking and language
- Providing rehearsal time
- Holding students accountable for listening and responding
Videos of Student Interviews
As the CMP:NC and SCOE team focused on promoting discourse in mathematics instruction, they created a variety of videos that featured student interviews. A sampling of the archived videos is highlighted below.
Student Interviews | Nov 2009
Interviews can challenge our assumptions about what students know and lead teachers to adjust instruction. Learn more and watch students explain their understanding of equivalency.
Student Interview, Division of Fractions | Feb 2008
This is part of a student interview series conducted prior to planning a lesson on the division of fractions.
Lesson, Division of Fractions | Feb 2008
Here is one portion of the five-day lesson developed to meet the needs uncovered during student interviews.
Student Interview, Discussing Math – This interview illustrates how second-language learners learn and talk about mathematics
Student Interview, Fractions 1 – A student discusses whether shapes have to be congruent to have equal areas
Student Interview, Fractions 4 – This interview shows the difference between a teacher’s assumptions and what students actually understand
Student Interview, Paper Folding Lesson – A fifth-grade student shows how mathematics is embedded in paper-folding activities
Student Discussion, Perimeter – Bilingual grade 6-8 students describe patterns they’ve observed in rectangles with the same area but different perimeters
Student Discussion, Perimeter – Two ninth-graders contradict our expectation that the key challenge for bilingual students is to learn mathematics vocabulary
Interview, Promoting Discourse – Edith Prentice Mendez, PhD, examines how promoting discourse can impact student learning