Writing in Mathematics
Why Is Mathematical Writing Important?
Writing provides students with opportunities to communicate their mathematical thinking in an organized and coherent way. Students need to consider what mathematical terminology to use in their communication, what expressions or equations might be helpful as they lay out their solutions to problems they are solving, and what models or representations might provide additional insights into those solutions. Essentially, students need to be able to consider how someone else might make sense of their writing; this often involves being explicit about aspects of their thinking that they might otherwise take for granted but which often can contribute to even greater mathematical insight.
While the Standards for Mathematical Practice do not specifically identify and discuss mathematical writing, there are many that focus on the importance of being able to communicate one’s mathematical thinking, and thus have implications for writing. These include being able to construct viable arguments, critique the reasoning of others, model everyday situations with expressions and equations, draw conclusions and interpret results, and communicate precisely to others. All of these practices are consistent with what it means to write within the discipline of mathematics.
Countryman (1992), in her book Writing to Learn Mathematics: Strategies That Work, discusses her own efforts to support mathematical writing in her high school mathematics classroom. She offers the following reasons why she thinks writing is important:
Writing can provide opportunities for students to construct their own knowledge of mathematics. . . . Writing has given them a chance to practice inferring, . . . symbolizing, organizing, interpreting, linking, explaining, planning, reflecting, and activating. Writing helps students make sense of mathematics (pp. vi–vii).
Many others also make the argument that opportunities to write mathematically help students deepen their understanding of the mathematics content itself (e.g., Bosse & Faulconer, 2010; Burns, 2004).
Finally, it should be noted that on some occasions, mathematical writing may serve as a personal log of one’s own mathematical thinking, including questions and confusions as well as new mathematical insights, and may not be intended as a communication to others. This kind of writing may be less precise and analytical, but it plays an important role as students work to construct their mathematical understandings.
The use of this kind of informal writing in mathematics classrooms can help support the full engagement of students (Countryman, 1992). For instance, during whole-class discussions, only one person is speaking at a time. The other students should be actively listening, but some may become disengaged. Even during small-group discussions, where more students have opportunities to speak, others may sit back and just listen passively. When students have opportunities to reflect and write their own thoughts before discussions begin, there is more likely to be full engagement in the discussion.